Welcome to a very windy but very warm late summer's Saturday afternoon here in Stellenbosch. Now this is the third video lecture on these four fundamental, what I call fundamental linear model types and we're going to talk about the analysis of covariance. If you haven't watched the first two videos please do so because we just build on top of what came before. Linear regression, then analysis of variance and now we're going to combine those two in analysis of covariance. So look out for some more information on our website or look in the description below. If you're watching on a computer there should be a card right up here that you can click please watch those first. So here we are in a Jupyter notebook. Once again I'm going to make use of Visual Studio Code and you can see I create environments, special separate environments for each of my projects and so this would be a data science environment set up by a mini-conda and for your interest I'm running Python 3.9.10. So let's learn we're going to use code because I actually heard a very nice quote by a very famous person in the NumPy development community to say that we see the knowledge inside of our world these days through the lens of code. We extract knowledge, we learn to understand things through the lens of code and I thought that was a very powerful statement. So we use Python in this instance just to make life very easy first of all to learn how to do these things, what they mean, what to understand what's going on when we talk about these kind of models and secondly just to show you how easy it is in the end just to run a few lines of code and do your own analysis. So as always we're going to start with by importing our packages that we're going to use in this notebook. Once again you notice that I do not make use of abbreviations so I just import these packages in their full names and if I have to reference one of the functions inside of those packages I have to type that full name. So we're going to import pandas that's for our data import and data wrangling we're going to import the stats module from scipy we're going to import numerical Python and we're going to import the patsy package as well let's run this code cell let's move on we're going to do a bit of plotting as always I enjoy the interactive plotting of Plotly so I'm going to from plotting I'm going to import the express module the graph underscore objects module the subplots module so you'll see that in action and then also I'm going to import import export so IO so that I can use IO dot templates dot default and set my defaults plotting style to plotly underscore dark as a string there so that I can plot nice dark plots on this dark theme IDE so from stats models dot formula dot API we're going to import the OLS or nearly squares function and then from stats models dot stats dot ANOVA we're going to import the ANOVA underscore LM function because that's it's going to give us nice tabular results so here we are we back with these four fundamental types now you won't find them really as fundamental I'm just using that term because I think these are the four fundamental ones to understand and then it'll be so much easier for you to understand all the other models so in italics here we see we busy with the third one one-way analysis of covariance once again remember this is modeling we're going to understand this relationship between our independent variable and this instance variables and a dependent variable and you see the data types there so we're going to have an interval type or continuous numerical type and a nominal so categorical and a numerical variable so we're going to have two independent variables here of these two very different types our dependent variable is still going to be interval type so continuous numerical so what we trying to do is we investigate the effect of the nominal categorical that's that independent variable on a continuous numerical variable so we've heard that before that's just analysis of variance but this time around we are going to correct for a covariate and that's the term that is used a covariate and that's where nCova comes from analysis of covariance we have a covariate and that's a numerical independent variable now usually we should try and control for these independent variables in our experimental design but sometimes it's impossible to correct for control for at least in the experimental design for all our independent variables and if you know if we fail to do that we can control for them to some extent statistically so that's what we're going to do here we're going to control for this covariate and what happens then is it helps us discover the true relationship between so we're just going to call it the treatment because we're using health care examples here but by treatment remember we just mean the independent variable and all the unique sample space elements of that categorical variable we just call levels there's so many terms and synonyms for the same thing don't get confused you know between all of them but we're going to try and understand this relationship between that treatment the categorical independent variable and the continuous numerical dependent variable by controlling for the covariate and that brings out a true relationship between those so what that does mathematically and as again if you've watched the previous two videos in the seminar series you'll understand what's going on here it's very important mathematically we're going to decrease the sum of squared errors and remember that isn't the denominator of our F ratio you're going to get a higher F value and you know that's going to improve things for us so let's have a look at our simulated project so this simulated research project that's on blood loss during trauma surgery for major vascular injury during penetrating trauma and our dependent variable is blood loss in millilitres so that's a continuous numerical variable that's our dependent variable so that fits the ball of our little table of data types our independent variables is really that of the categorical variable that is one of three levels and during the experimental design we could control for that so some of the participants would have received a placebo drug some would have received a low dose of a drug investigated for decreasing bleeding and then a higher dose of a drug same drug investigated for decrease in bleeding so the search is always on to help decrease active bleeding during these big surgeries for penetrating abdominal trauma major vascular injury now during the experimental design we suggest here that the researchers could not control for the age so there was no couldn't in the sign for age as as participants were entered into the study so we can to control for it statistically so that's our covariate its age and that is a continuous numerical variable so you can see how remember with linear regression how independent variable was continuous numerical and with analysis of variance our independent variable was nominal categorical and now we bring these two together the nominal categorical variable is what was controlled for during the experiment could not control for the continuous numerical variable we call that the covariate and we're going to control for that covariate instead of using Python to generate some data for us we've already got data it's in this CSV comma separated values file that's a we stripped down spreadsheet file you haven't seen those before always the best format for your data so it's in the EBL underscore data CSV file and we just going to import that with a read underscore CSV function in the pandas package so pandas dot to read underscore CSV that function we pass as a string this CSV file now the CSV file the importantly lives in the same folder directly on my computer as this Jupyter notebook file so I don't have to put in a long address on one of my hard drives you know to this file it's a state the file this CSV file and this Jupyter notebook lives in the same they exist in the same folder or directory on my computer so I can just reference this file directly and I'm assigning that remember equal sign is assignment and I'm assigning that to whatever is on the left hand side and that is a computer variable named DF so we're gonna sign this what is going to create for me as a pandas data frame object and we're gonna sign this to the variable DF so let's do that it's done we can use a bit of indexing so square brackets colon 5 that is give me up to row 5 remember Python a zero index so that's gonna give me the zero with the first the second the third and the fourth rows of data there and there we see 01234 as far as the index is concerned the first five participants here we're all in the placebo group there's the ages that we couldn't control for and there's their blood loss during the surgery now that's measured by suctioning the blood out of the abdomen or absorbing the blood in abdominal swabs and those are weighed to give us a fairly accurate amount of or measuring at least the blood loss now this group variable is categorical so we're gonna use the pandas dot categorical function just to make sure that we tell pandas that this is not we don't want it to be seen as a string we want to be seen as a categorical variable so we're gonna call the first argument they df dot group so we know what series we're talking about this column here group we want it to be ordered and we want the categories to be placebo low and high now that's very important that order because we are going to use dummy variables of course and we have to have the base case which in our case is going to be placebo and next time around when we get to logistic regression that's I'm wanting to say even more important to choose that base case but as important here so the base case is going to be placebo and we're measuring the low and the high so let's once we've run this at least let's call the info method there df dot info and we see now and we've got 45 participants we have these three columns group age and blood loss we see group is now a categorical variable and we have integers whole numbers for age and blood loss so let's look at our research question we're asking is treatment level a predictor of estimated blood loss after correcting for age so that's very important now with our independent variable we have to do a dummy variable we can't do arithmetic with names and so we have our treatment variable there that was called group remember in our data set so it's called group so we're just calling a treatment there so participants could either be placebo low dose or high dose now we create three new variables dummy variables placebo low dose high dose remember that's will be the list of all the unique sample space elements in this nominal categorical variable and if it's placebo we'll get a little one under placebo and zero for the others and you've seen this before dummy variables are quite easy to understand there's redundancy and remember we are setting this placebo as our base case so that it falls away so our two dummy variables are only low and high so participants getting the low dose of this experimental drug and those getting a higher dose and if it's zero zero there's no other choice but for that first participant to be in the placebo group and if it's one zero then the low dose group and zero one then the high dose group so we certainly don't need that placebo there it's it's redundant so let's state our research a question now as a research question as an equation so what we're going to have is estimated blood loss is going to be an estimated intercept all the hats on top remember this is not the true values in the population we're estimating that those two values at least from our sample so that's the intercept plus beta sub one times the age also an estimate these all estimates plus beta sub two times low dose plus beta sub three times high dose now just think about it for a moment this low dose can only take a value of zero one high dose can only take a value of zero or one so it's either going to be beta sub zero plus beta sub one times the age it's going to give me an estimated blood loss or beta sub zero that would be zero zero if it's a placebo participant so beta sub zero beta sub one plus age plus beta sub two times one that high dose will be a zero so I'm just adding one if it's low dose or I'm just adding one if it's high dose so think about that very carefully depending on what these values for beta sub two and beta sub three are so be one times beta sub one or zero times beta sub let's say that again zero times beta sub two or one times beta sub two and zero times beta sub three or one times beta sub three so they can only take values of zero zero one zero and zero one now see how that would influence this value for the blood loss so these are you know fairly constant values only value that will change a lot is this continuous numerical variable and you can see where it comes from that the understanding of it comes from that we're correcting for the age this covariate of ours so let's state our hypothesis and I'm going to state that in terms of this mathematical statistical approach which we've been taking so that you can clearly see how linear regression analysis of variance analysis of covariance fit together so in terms of the coefficients the null hypothesis should state that the treatment level is not a predictor of blood loss after correcting for age so beta sub one equals beta sub two equals beta sub three equals zero alternative hypothesis at least one of those not zero so let's be a little bit more verbose as you can see this is all we are after mathematically to be verbose about it we state that the null hypothesis would state that there is no difference in the mean of the dependent variable between the different treatment levels after correcting for the covariate or in our example we would say there is no difference in mean blood loss between the three treatment groups after correcting for age so definitely this last statement is what you would see in a research project but we know now after understanding linear regression and analysis of variance it's these coefficients that we after and we can see from stating our research question as an equation why we say these things you know if beta sub one is the zero beta sub two zero and beta sub three is zero that means that we always just going to have the intercept as a predictor of the blood loss so all the blood losses are going to be equal to each other no matter what group the participant fell in because beta sub one and beta sub two and beta sub three is zero and that's our null hypothesis that none of those things matter and if one of them matters there'll be a substantial difference from zero so I hope you can see how clear this can be to understand and how easy it can be to understand so as always we're going to start with some exploratory analysis so let's call the values underscore counts method on this DF dot group that is going to be a pandas series object as soon as you call one column what gets returned is a pandas series as opposed to pandas data frame the difference being there's only one column it still has an index every rows and index but on that column or on that series we get the we call the value underscore counts method and that's going to show us the count the frequency of each of the values that that can a nominal categorical variable could take so placebo there were 15 participants 15 on a low dose and 15 with a high dose let's look at the blood loss per treatment group so we're going to do some summary statistics on just a blood loss it's a continuous numerical variable and so we're going to say df dot group by so the group by method we want to group by the group column so we're going to separate out the participants in the placebo low and high dose group and from once we've done that separation or the group by we're going to look for the BL column and then call the describe function on that this is sort of a little bit of a thing to get used to with pandas how you string these things together and there you say we've done a group by the group column so there we see placebo low high and then on the blood loss column we're going to just do the use the describe method and that gives us the count the mean the standard deviation and minimum and maximum and our three quartile values so you can see the mean blood loss so we want to know if there's a difference between these three means after correcting for age so let's visualize this data we're going to use a box and whisker plot so I'm calling the express module dot box first arguments my data frame on my y-axis I want blood loss I'm going to color it by the group that means I'm going to get a box and whisker a little marker for the placebo group the low low dose group and the high dose group I'm giving my plot a little title and I'm replacing the labels that will appear generically inside of my plot based on the column headers in my data frame I'm just replacing them so if it finds BL I'm replacing it with blood loss and then the units and I do that as a Python dictionary object as you can see there so let's create that beautiful plot love these you know as you hover over them you obviously get all this information remember you can also click on these legends on the right hand side so that you can take some of them away and you know bring them back in whatever order you want and for a variety of plots and plotly that might be very useful but as we hover over them we can see the median we can see quarter one and quarter three there and since we don't have any suspected outliers here our whiskers will go out to the man and max values and you can clearly see here for the placebo group and the low dose group there doesn't seem to be that big of a difference but when we look at the high dose group they seem to have had substantially less blood loss and we'll we have to find out whether you know the level of treatment was in some way predictive of the estimated blood loss after controlling for age let's look at that age let's do the describe method for age after grouping by the group column and we see 34 33 34 so the ages were quite close so if we do a box and whisker plot just there of the ages you see that there wasn't visually at least a big difference in the ages between our three groups lastly let's say I just visualize the correlation between our covariate and our independent variable so age and blood loss but we're going to group by those three groups I'm using the color argument there for my groups and have a look at this because this is a very very important plot so we have age in years on the x-axis and we have the blood loss on the y-axis and we can see there is really these this linear relationship and that linearity is sort of parallel for each of the three groups and that's a very important thing because what we're going to do this time around we didn't do it for linear regression and analysis of variance but here it becomes very important we have to look at the assumptions for the use of analysis of covariance and I'm really going to highlight the ones that I want you to always consider the first one is linearity and that refers to a linear relationship between the covariate and the dependent variable so we can do that visually let's do that and we've already done that you know by these three groups but if we do for the whole data set there seems to be a linear relationship at least you know as age increases there's also an increase in the blood loss so that assumption we really want met we want that linear relationship we want to correct for the age so we want this relationship between age and blood loss and what we could actually do just you know let's just remind ourselves of how easy it is to create a linear regression model I'm using the OLS function I'm using my little formula the blood loss given the age my data is in DF I'm calling the fit method on that so I can fit the data to my model and I'm just calling the summary on that and there we go we see our age there we see a p-value for that age is very small and so at least we reject the null hypothesis here and we say that that coefficient for age is significantly different from zero and you can see the coefficient there it's 145 so quite high we see an r-squared value there of 0.552 so age explains our model here which is just age explains 55.2% of the variance in the estimated blood loss so I think we're fairly satisfied that there is a good linear linear relationship between our covariate and our independent variable the next one is homogeneity of the regression slopes so let's look back here homogeneity of these regression slopes remember this model line of ours that's a regression slope and homogeneity means the slopes are equal and look at these lines they are parallel that's what we want what you don't want is scenarios where these lines this criss-cross forming a big old cross over each other like a multiplication sign or a divergence or convergence like they start off far apart and then meet on this side or all start from the same point and then move out that means that there's a difference between this relationship between the covariate and the dependent variable dependent upon which group they are in and that that is what we don't want we understand what happens if we see graphs like that it's very easy to interpret as I've just explained but we don't want to see that we want to see homogeneity of the regression slopes and there's one good way to look for that and we're already going to build a model here and we're going to see during these assumptions we're already going to do encoder encode before we actually get to encoder but it's the way that it works I want you really to think about these these assumptions and I'm going to call it the interaction underscore model I'm using the ols function and I'm saying blood loss given age multiplication so that's the star symbol that's multiply age multiplied by group and that's going to give us an age as a predictor it's going to give us the groups as a predictor and it's going to give us the interaction between ageing groups and I'm calling the nova model I'm using type three there as you can see we don't we don't have to go into that at the moment but there you see age colon group so that's the interaction between those two that's an interaction term if we go to the p value for that it's 0.9 and our null hypothesis which we won't reject in this instance states that there is homogeneity of variance should say homogeneity of the regression slopes uh don't listen to that little slip of the tongue homogeneity of regression slopes and we can clearly see this they are homogeneous they are parallel to each other and that is an assumption for the use of analysis of covariance and what you do as I say you look for this interaction term see there's group there's age but then I have this interaction term and the way to do that is not to say age plus group which is what we're going to do find cova we say age multiplied by group and so what the code would do it will take group and age and the interaction term but clearly we can see a p value that is larger than a chosen alpha value of 0.05 we fail to reject the null hypothesis and we have this homogeneity of the regression slopes next one is we're going to look at the residuals now this is where I mean we actually have to build on cova model and so that we can calculate these residuals remember the residual or the error that's the difference between the actual dependent variable value and the estimated one due to our model so we've actually we're actually doing and cova right here before we do and cova so just say blood loss given age plus the group data is fit the tf data frame dot fit method and I'm assigning this to a computer variable called model so if we run that we have our model I'm now going to add a new column to my data frame so I've got to put it in square brackets I'm going to call it residuals and I'm using the result attribute of my model so model dot result that gives me all the residuals and that's going to go into a new column in my data frame which means I can look at a little histogram of all these residuals and you know it's it's a you know we've sort of have to agree that there is some form of a dull shaped curve here so it looks like these residuals at least you know are sort of normally distributed we can be you know it's a bit difficult because it depends how wide we make these bins but we can be a bit more precise and use something like the Shapiro walk test the null hypothesis would state that these data points are from a population in which that variable would be normally distributed so I'm calling stats dot Shapiro passing this series object the f dot residuals that's just the value in the residuals column passing that to the Shapiro walk test we see a statistic there and a p value of 0.89 so we don't reject that null hypothesis and we say that we've passed this assumption for normality of the residuals but it's important that we look at the residuals there we can also look at homogeneity of variance and I want those three groups of residuals to have sort of equal variance Levine's test we're going to use for that think about the stats dot Levine it wants these three Python lists that I'm going to pass so I'm going to call it Resid placebo Resid low and Resid high and I'm just using a bit of notation here df dot lock for location square brackets so it's column comma rows I want the column to go down this df rows comma columns I should say df dot group equals equals placebo so it's going to go down all the rows of that group column and only select those double equals sign so or only the ones that return to are going to be included comma I want the residuals value for that and again at the right at the end I'm using the to underscore list method so it's just going to export this as a Python list object so I've got three lists and those will be the residuals of each of those groups which are then pass as three arguments to the Levine function and there we go we see a p value of 0.40 the null hypothesis of the Levine function is that these variances are equal and then lastly we care about outliers and sort of as a rule of thumb we don't want too many values as far as these residuals are concerned to be more than three standard the standardized residuals at least to be more than three standard deviations away from the mean and you can see this long function that I have to do so what I'm doing here is I'm calling the residual underscore studentized underscore internal values so the model dot get underscore influence open close parentheses dot residual studentized internal and I want to know how many of them once they are I have the absolute value of them how many of them are more than three because remember some will be more than minus three standard deviations away and some more than plus three standard deviations and I'm just you know that's going to return either true or false which is one or zero and if I sum over all of those I'll get how many of them are more than three away and I see none of them and we could actually see that with the box and whisker plots there were no suspected outliers and when it came to the actual data you can plot these residuals as a box and whisker plot as well so very importantly these are the assumptions that I really want you to consider anytime that you are considering using analysis of covariance check for these assumptions so we eventually going to come to building our model now we've already seen that we've used a code to build the model we've assigned it to the computer variable model but let's just start off with just building a normal analysis of variance I'm not normal let's just build an analysis of variance model because I want to show you the differences between correcting for that age and not correcting for that age or at least not bringing age into it at all so let's use the ols function so blood loss given the group just normal analysis of variance one way analysis of variance I'm going to say data equals df I fit the data to my model and I'm calling the ANOVA underscore lm function passing this model that I've called ANOVA assigned to the variable ANOVA let's have a look at it and there we go we see our sum of squares due to the regression and our sum of squares due to the error so let's just save these as a as a computer variable so we can just compare that to our model which remembers our ANCOVA model so first of all is the sum of squares due to the regression remember that is the difference between the predicted value and the mean of the dependent variable so in each one of the groups we just take the mean that's our base model and there is an attribute called ESS so again as I say in many synonyms for all of these things here in stats models the sum of squares due to the regression is called ESS I'm going to assign that to the computer variable SSR ANOVA so I remember that this is the sum of squares due to the regression of the ANOVA model and you see there let's have a look one two three one two three four point about four point five million there so let's look at the sum of squares due to the error the difference between the predicted value the estimated value in the model versus the actual value unfortunately the attribute is called SSR but we know we want to use the term SSE in the seminar sum of squares due to the error so I'm going to save that as SSE ANOVA and you can see how big that error is so my sum of squares total for my ANOVA it's the sum of the sum of squares due to the regression and the sum of squares due to the error and we can see it there such that we now can express the coefficient of determination you know how what what fraction or percentage of the variance in the dependent variable that the model explained and that is this ratio between the sum of squares due to the regression and the total sum of squares and we see there about 40 percent there's also the r squared attribute that we can use so we can see exactly the same value we know now where it comes from how to calculate it let's go back to the ANCOVA model though remember we saved it as the variable model so I'm calling the ANOVA underscore lm function from stats models passing the model as an argument so let's have a look at that that looks a bit different from the ANOVA model first of all there's age there we are correcting for the age but we see that the sum of squares due to the error here by the residual remember the error that's a lot smaller we've taken away some of it by correcting for the age so let's save the sum of squares due to the regression of our model I should say the error that's the SSR unfortunately named attribute there that's the sum of square due to the error I'm going to save the sum of squares due to the error of my ANCOVA model remember we've already done it for the ANOVA model so let me save that and you can see that's a lot smaller it went from 9 and a half million almost down to 716 000 so I'm actually printing that to the screen so that you can see those two values 9.7 million versus 716 000 I've taken away a lot from the sum of squares due to the error so my predicted value my estimated values are much closer to the actual values as far as my dependent variable is concerned let's look at the sum of squares total so I'm taking the sum of squares total as the sum of squares due to the regression and the sum of squares due to the error add them to each other this is for the model so this will be sum of squares to the sum of squares total due to ANCOVA let's save that and you'll see that it has not changed between ANOVA and ANCOVA the sum of squares due to the regression is absolutely the same between the two we have two error terms here we now have one for group and we have one for age adding all of this it has to stay the same I've made the error sum of squares much much smaller so you know it has to go to the numerator there but if we look at it the sum of squares total remains absolutely the same between the ANOVA and ANCOVA model nothing happens except me making my sum of squares due to the error much smaller look at what happens to my r squared value now where we had 40 percent before we jump to 95.6 percent so we've got this bit well to some extent our goodness of fit test here shows us a much better model we see a truer reflection see how all these words come back a true relationship between the the dependent variable and the independent variable the independent variable being the treatment or the group as a predictor of the dependent variable let's have a look at the coefficients there's a params attribute that's going to give me those three coefficients and now remember we can fill that in as far as our equation our equation for our research question is concerned our research equation as I like to call it so the estimated blood loss is going to be minus 53.63 that's beta sub zero my intercept plus 147 times the age minus something for the participants in the low group or minus something much bigger for someone in the high group and you can see why that's going to drag down someone who has a zero for low and a one for high that's going to drag the estimated blood loss down quite a bit and you can also see how what we mean by we are correcting for age I mean we can have low zero and high zero so they both zero that is just going to be basically a linear regression model because we just have the beta sub zero and beta sub one there just as we saw before but if it's one zero or zero one we're going to subtract one of these two terms so we are correcting for age extracting a better understanding a better relationship between my independent variable and my dependent variable remember how these intercepts work we can calculate a standard error for each of them and there's a different equations for all of these different model types but I can just use the bse attribute so model dot bse remember model is my encoder model and there we have two to four point four one three forty eight and forty eight and six meaning I can calculate a p value that's just remember the coefficient divided by my my standard error that gives me the three t statistics and then given a parameter which is the degrees of freedom we can work out what these p values are and we can see there as far as beta sub one beta sub two and beta sub three they are substantially different from zero and that is really what we're after we also see of course our confidence intervals around our comfort our coefficients and we saw in the first two lectures how to calculate those so let's have a look at this effect that this correction for age has on our fitted value so model dot fitted values we use my model it's going to pass all the values to it as far as the independent variables are concerned and return for me the estimated blood loss I'm going to assign that to a new column in my data frame called estimated and now I'm going to plot that so I'm going to stop plot so you can have a look at that code for plotly but now you can see this is the actual values and this is the estimated blood loss so we've corrected for the age and you can see a little bit of a difference when we hover over these for these values you can do that but if you just look I've plotted as well see their box points equals all so I can see all the actual values and you can see that they are different now that we've corrected for age in our model here so let's have a look at the linear algebra of all of this I want to show you that it is nothing different from what we've had before with linear regression analysis of variance now analysis of covariance I'm going to create my vector of dependent variables in my design matrix using the D matrices function from patsy I pass that same formula blood loss given age plus group data comes from the df data frame and so let's have a look at x just the design matrix remember that first column of constants which is what we multiply beta sub zero by the zero zero that would indicate as far as dummy variables was concerned that these first lot of participants are all in the placebo group and then we have age I'm going to convert these to numpy arrays so that I can just work with them as matrices and vectors so remember how do we get this vector of estimated beta values well it's this equation that we saw before remember if you understand a little bit of a linear algebra you know that we cannot possibly span all of the vector space in our matrix x so we have to do this projection onto the subspace that is spanned that column space and we'll get the best possible values for our coefficients that way this is how we express it in code now there's obviously much easier ways to do it I want you to investigate that code so you can understand how I just build parts of these all together so that I eventually get my my vector of beta values and there they are we see the same coefficients that as we had seen before let's have a look at the params attribute it's exactly the same as what was calculated in in using stats models so there you go I hope you have a very clear understanding now how we've built from linear regression to analysis of variance now to analysis of covariance the terms haven't changed the almost the mathematics behind it hasn't changed we interpret it in a different way but you can see where these words come from we want to understand the relationship between our dependent variable our independent variable after correcting for some covariate and you see you saw at least exactly how that worked in that how that helped us actually to decrease our sum of squared errors so next one's going to be a bit different we're going to look at that logistic regression so on the Saturday afternoon as the sun is setting you know it's getting towards winter time here in the south and it gets darker quite a bit sooner and yeah we're going into winter and we wish we're in the northern hemisphere so we can go into summer I'll see you for the last of the series the seminar series on what I term these four very important types of linear models


I love that song. I play this loop over and over in my car all week long. Jolie did a great job, love it.  Everybody, if you didn't know, this is Pastor Joel Sorgi. He's our creative director. Pastor of creative arts and all the good stuff on the screens, him and his team do, and him and his wife Ann are awesome, awesome parts of the family here at Radiant. Everybody doing good? Yeah, you know, Michigan, that last shot was something else. It was incredible. It just goes to prove that we're sin abounds, grace does much more abound. And so the goodness of God extends even to the Wolverines. So you guys have to pray for us here in a couple hours because Michigan State plays, and I've got the Spartans and the Wolverines in the finals. So come on, believe God with me, and then we'll deal with it afterwards. All right, so. Hey, next weekend, just to let everybody know, it's gonna be a really special weekend. Actually, the next couple of weeks are gonna be really incredible here. Next weekend we have a very special guest, Pastor Jimmy Evans is gonna be here with us. And how many of you have heard Pastor Jimmy speak before? Okay, a lot of you. If you've never heard him, let me just tell you, he's one of the overseers of Radiant Church. He's also the founder of Marriage Today. So he's a marriage specialist, but he's not just like a talker or a consultant on the subject of marriage. He teaches it from the word of God, and it has impacted Jane and I's life hugely over the years. He's one of my personal mentors. He's gonna be here next weekend, you will not wanna miss it. And then the following weekend is Resurrection Sunday. It's Easter. So you guys ready for that? We're gonna celebrate. And the resurrection of Jesus from the dead is the greatest day in history. It's changed everything. And so as Christians we gather together to celebrate that, it's gonna be a phenomenal day here at Radiant. We have three services, 8.30, 10.30, and 12.30 on Sunday morning as well as Saturday night. And so what that means for you 11 o'clockers is we need you to part the red seat and shift gears. Some of you were gonna ask to go to 8.30, and some of you were gonna ask to go to 12.30. How many of you would say I'd be willing to go to 8.30 in the morning to worship Jesus on Easter Sunday? Raise your hand. See I love that, I love that because you're saying if he can get up from the grave, I can get up out of bed. I love that, I like that. Okay, how many of you are saying 12.30 sounding pretty good? Raise your hand if you're at 12.30. Listen, I'm gonna ask some of you to be missionaries to the 12.30. I'm not asking you to move to Bangkok, I'm just asking you to move to 12.30. Be a missionary because here's what will happen is you'll help make room in that 10.30 service that's gonna be smashed packed with all kinds of people. And we want you to invite some folks that you know to come for Easter.   And then the week after that we're starting Red Hot. And if you don't know what Red Hot is, it's three weeks of live simulcast between our two campuses. And it's gonna be three weeks on three different subjects. First week's gonna be on sexuality. Week number two is gonna be Bible questions and doctrine. Third week is anything go and here's what happens.  So if you've ever had questions or you know people that are skeptics, critics who are searchers, seekers, this is a great opportunity for that. All right, open your Bibles with me to Romans chapter 12.  Man, I just wanna highlight this. As you're turning in your Bibles to Romans chapter 12, we should be so grateful for the word of God. I know we know this, but guys, what we have is a treasure from the Lord. This is God's word speaking to us. This isn't just a book full of good ideas. This is a book full of God's ideas. This is him speaking life to us. So when we open our Bibles, we ought to be excited about it. If we're more excited about 50 shades of whatever, then we need to check ourselves before we wreck ourselves. If we're more excited about sports illustrated than we are God's word, then there's something deficient on the inside of us.  We ought to be fired up. All right, public service announcement. All right, Romans chapter 12, look with me here at verse number one. I appeal to you therefore, brothers, by the mercies of God to present your bodies as a living sacrifice, holy and acceptable to God, which is your spiritual worship. Do not be conformed to this world, but be transformed by the renewal of your mind that by testing you may discern what is the will of God, what is good and acceptable and perfect. Look at verse three, for by the grace given to me, I say to everyone among you not to think of himself more highly than he ought to think, but to think with sober judgment, each according to the measure of faith that God has assigned. For as in one body, we have many members and the members do not all have the same function. So we, though many, are one body in Christ and individually members of one another, having gifts that differ according to the grace that's given to us, let us use them. If it's prophecy in proportion to our faith, if it's service in our serving, the one who teaches in his teaching, the one who exhorts in his exhortation, the one who contributes or gives in generosity, the one who leads with zeal and the one who does acts of mercy with cheerfulness. We're talking over the last several weeks, the series entitled Flourish. And what we're really zeroing in on is this idea that God knows the environments that you and I need in order to thrive and to grow and to be all that he's created us to be and to fulfill our purpose and our destiny. Because I believe every Christian has a role, every Christian has a reason and every Christian has a responsibility. We all have a role, we all have a part that we play. We all have a reason or a purpose for our lives but we also all have a responsibility. And the reason why we have a responsibility is because God has put something in you that other people need as well. And so when we're talking about God being a God who knows the environments that we need to be in in order to thrive, then the opposite is equally true that there are certain environments that when we're in, we don't thrive. Yesterday I was driving through Kalamazoo and it was St. Patrick's Day and I was shocked, I'm shocked all the time but I was shocked how many people were downtown going from bar to bar to bar to drink really bad beer. I mean, green beer is, you know, and people listen, they had a line at Shakespeare's Pub at 6.30 in the morning. And I was thinking to myself, man, St. Patrick's followers are really devoted.  Somebody said after the first service, if you were serving beer, we might come. It's like, what's up with that? But certain environments cause us to thrive and certain environments cause us to flourish and then there are other environments that actually can stunt our growth. I think in order for us to have a proper understanding of why God has created each of us as he describes as members of his body, the church because that's really what the church is. The church isn't about a building. The church isn't about brick and mortar. I'm grateful for the brick and mortar. I'm grateful for the buildings that we have just like I'm thankful for my home that I live in. But my home isn't my family. My home is where my family lives. In our church, our buildings are where the family of God lives. But listen, Jesus said he would build a church, but he's not talking about architecture. He's talking about human beings, living stones that he puts together into a spiritual organism that on the outside just looks like a gathering of people, but there's something more significant that takes place when we gather together, when we're in this environment where he says, wherever two or three are gathered in my name, there I am in the midst of them. God knows that the environment that you and I created as Christians to thrive in is the local church. So God is building member upon member, peace upon peace, his body, and we're all a part of it. But the enemy wants to dismember the body of Christ because if he can dismember it, he takes away the potential of the body of Christ because nobody has all of it. Everybody has some of it. I think in order for you and I to have a proper perspective about how God sees the church, I grew up in Sunday school and we always did this thing. Anybody do this? Here's the church, here's the steeple, open the doors, and that was about how many people went to the church I grew up in right there. And that sometimes is our perspective of church. It's like, well, the church is a place that I can go to when I need it. The church is a place where if I need encouragement that I'll go to the church is a place where if I haven't opened Sunday, I'll go to the church is a place where I wanna get married someday. But instead of understanding the church from God's perspective, I think that the way God designed and created the church has much more to do with how you and I perceive a gym than it is how we perceive a church. How many of gym membership? Anybody have a gym membership in this? Okay, raise your hand if you do. Some of you are like, is this a trick? Okay, cause you might raise your hand again if you have a gym membership. Okay, put your hand in.  Okay, see, look at that. So notice what I didn't ask. I asked who had a gym membership. I didn't ask how many go to the gym because how many know there are two kinds of people when you show up at the gym, there are two kinds of people at the gym. There are the people who look like they belong there because they've spent a lot of time there and they are consistent, right? I mean, they show up, I was going to the gym for a couple of years ago. I was going three, four days a week and I had a partner so we were meeting up there and he wanted to meet there at 5.30 in the morning. I'm like, man, all right, yay. So showed up at 5.30 in the morning and there were the same people that were there every morning at 5.30. And listen, people who show up at 5.30, they look like they belong there because they are consistent.  He had his routine. He's like, it's Thursday, it's chest day. So he's in there doing the incline. And he's got his dumbbells and he's got his whole routine, the row thing. He knows where he's going and he looks like he knows. He's got the underarmor shirt on. He's got muscles in places. I'm not even sure where they are.  He was probably my age and just ripped and he looked like he belonged there because he's there all the time and he's done it for years. It's routine. He knows where things are at. And then there are the other people who walk in and they don't know where anything's at. And they look like it.  I know that one. I gotta do some reps on the drinking phone.  You're gonna, okay. And they get the five-pell dumbbells and it's like lifted a couple of times. Put it down, look around, watch ESPN and leave. And you know that gym memberships know, look, in January everybody buys a membership because they want to be, they wanna look like that guy. And so they come in and they pay their membership but then after two or three weeks, we don't show up anymore. And so the gym clears out so that the people who know what they're doing actually get the gym back. And it's amazing to me how if you stick with something long enough, if you go into it and you make it a priority, your life changes. That's what the gym is, your life can change. Your life doesn't change when you get the membership. Your life changes when you use what's in the building, right? It doesn't change, I wish it worked that way. I wish you could just buy the membership and all of a sudden the next day you wake up and you're not like your former self. Wouldn't that be amazing where you woke up and you look like one of those people on the Peloton commercial? It's like, if you don't know what that exercise bike, have you seen this? They're like all just carved out and they're riding it, watching the video and they're just like, come on, yeah, you can do it. Doom, doom, doom, doom, doom. Ha, ha, ha. And they get off and they just look happy because they've been working out. I never look happy after I've worked out. Anybody else like that? I wish you could just like take a pill or get a subscription. But can I tell you that God is in the body building business and the way that you build body is through resistance, it's through exercise, it's through consistency, it's through the proper diet. It's in order for you to get strong, in order for you to develop muscles, body parts have to work together. You can isolate parts, but all the different, in order for you to work the bicep, the forearm, the hand, the shoulder, every part of your body has to work together so that that one part gets stronger and in the process those parts get stronger. It's every part, it's a miracle. The way that God has designed the human body is miraculous. And the way that God has designed the body of Christ, which is made up of you and I as members individually, is even more amazing. It's even more amazing. It's even more miraculous because each of us are a part of the whole, but we're not the whole and we need each other and some of us are more flashy than others but it doesn't matter, we all need one another. Everybody has a part that they play and what I have noticed over the years is that there are two great errors that people make when it comes to strengthening and growing and maturing up into Jesus and becoming who they were created to be, living out their reason and taking their responsibilities, two great errors and their polar opposites of one another but they're equally damaging. They're found right in Romans chapter 12. Number one is this, is when you make the mistake of underestimating your importance, you will live far below your purpose. So you can never underestimate your importance in the body of Christ. Listen to me, I want you to hear me say this to you.   Ephesians two verse 10 says that you are God's created for good works that he created before him before the earth ever began that you might walk in them. So if you're alive, if you're breathing and you believe in Jesus, it's because God in his grace saved you and he knew you and he also has a purpose for you and good works for you. You are an important part of what God is doing in the earth, whether you know it or not. But sometimes we make the mistake of undervaluing ourselves or underestimating. It's amazing to me when it comes even to like time management that the two great errors are always over and under. We tend to overestimate what we can do in the short term and we tend to underestimate what we can do in the long term. Well, the same is true in our own personal lives with our relationship with God is we have a tendency to over or to underestimate our own value. Well, you know what, I'm just average. I'm not gifted, particularly there's no flashy gift on it. Sometimes our gifts are obvious, right? But then other times it's like, well, I'm not really sure that any of my gifts are level 10 gifts. And so a lot of times we underestimate ourselves at that point, we say, well, I don't have anything. I sure can't sing. I mean, I'm not a singer and I'm not rich so I don't have a lot of money to give and so what I do have isn't significant. And when we make that mistake, listen, we not only rob ourselves of living in our purpose but we also rob the other parts of the body that we were meant to connect to that even though you and yourself may never do something that seems world changing or earth shattering, when you are connected to others, you're able to do more together than you could ever do by yourself. But not if we underestimate ourselves because as soon as we underestimate ourselves, we isolate ourselves. We say, I'm not significant and important. I don't have anything to offer, especially the church. It's like, man, I don't preach, I don't sing, I don't run lights, I'm not a videographer, I can't make cool videos where it's a boom, boom, boom. I don't do that. I mean, so I had a guy come up to me one time years and years ago and it was after a similar type of message where I was talking about getting involved and every person is significant and he said, you know, Pastor, I'd love to get involved but I just don't really have anything to offer. And I said, well, I mean, that's not true. I said, but tell me what you do for a living. He said, well, I mean, I'm a grant writer. I said, well, what do you mean a grant writer? He says, well, you know, I work with nonprofit organizations to help write grants. Writing grants is a very intricate process. I write grants and they submit them and they get money from government and agencies and beneficiaries to help fund, like, you know, after school programs and things like this.  I said, so you help nonprofit organizations get money. He goes, well, yeah. I go, do you know we're a nonprofit organization? He says, well, yeah, I know, but it's like spiritual. I'm like, are you kidding me? There are things that God has put in our hearts that we would like to do to impact our community that we would love to get a grant for but we don't know how to write the grant. And he's like, well, that's easy. I'm like, for you, listen, it doesn't matter. We have business people who think, well, you know, I go into the marketplace and I get paid really well to do what I do, but I'm not a super, I'm not a Bible scholar. I can't do anything like this. Listen, God may have equipped you to go into the marketplace to raise money to finance the kingdom of God. Do you know it takes a lot of money to send missionaries around the world? We have missionaries that we support in 24 nations of the earth. Every month, this church, you, through your giving, every member that contributes and gives goes to help support people that have moved or live in other nations where they have not heard the gospel and you're fueling their decision to go in the name of Jesus. But here's the good news. When people get saved like in Miramar right now, that doesn't just go on that missionaries account. Every one of you who give faithfully week in and week out and you think, well, my giving, my finances, my tithe doesn't make a difference. It does when you give it to God and it's added with other people's finances. It's designated to a person who made a decision to move to a nation where only less than one-tenth of one-hundredth of one percent know Jesus. And then that missionary under the inspirational Holy Spirit and the financial support that you've given has a conversation with somebody in a coffee shop and they make Jesus the Lord of their life. When that person goes to heaven, it's on your account, your account, your account, your account and your account and my account. And you might never know it on this side of eternity, but your giving makes a difference. And your serving makes a difference.  And even your past and your pain and your experiences that's led to your perspective. It's all part of the package. But if the enemy can get you to underestimate yourself, then he can paralyze you and isolate you and keep you from making a difference.  That's the first error that we make is we underestimate ourselves. Isn't that true just about in every area of life? I remember when we found out we were gonna be parents for the first time. I thought to myself, literally, Jane found out she was pregnant with Ashley on a Saturday and when she was in our little apartment, she came around the corner with the pregnancy test and said, plus, it's like, oh no. And I just laid on the bed for like two hours because I'm thinking, I do not know how to be a parent. I do not, I don't know how to do this. I mean, I just, I still need my mom and dad. It's like, I need them to take care of me. And now I'm gonna be a parent. It's amazing how there's more on the inside of you than you know is there that we overlook. There's abilities. If we make ourselves available, if we step into some areas that seem risky, that seem out of our comfort zone that we've never done before, do you know that in those moments where Jesus actually meets you and empowers you and grace actually finds you, the Bible says right here in Romans 12 that every one of us have received grace from God. The word grace means the empowering presence and goodness of God upon our lives. Grace doesn't meet you and then all of a sudden you feel it and then you step out and say, well, I feel, I feel sassy today.   You're looking at me like I'm crazy. Have you guys never seen that meme, by the way? All right, need to get out more. Okay, number two. So number one is never underestimate yourself. Number two, you ready for it? Never overestimate your value. Never overestimate your importance. Here's our error. Sometimes we underestimate ourselves and it's like I've got nothing to offer. I can't do anything. That's over my pay grade. I don't have the time. I don't have the resources. I'm not rich. I can't make a difference. That's underestimating. But the second one is equally important. Look at what it says. It says in verse number three, for by the grace given to me I say to everyone among you not to think of himself more highly than he ought to. Don't think of yourself too highly. By a show of hands. Have you ever met somebody who thinks of himself too highly and they're the only one who doesn't know it? Raise your hand if you know somebody like that. Point at him if, no, don't. If you've ever met somebody, it's almost embarrassing for them because they think to themselves, you know what, I got this gym motif. I was at the gym one time and I was with Tony and there was this guy who was obviously in over his head and he put like 225 on bench press. And if he weighed up a buck 25, so can wet. I mean, he was lucky. So he's like lifting twice his body weight and Tony goes, watch this. I go, what? Look over at this guy. He lowers the bar under his chest and he couldn't get out of it. He's like, this is like a little help. So guy came over and grabbed one end of the bar and he still couldn't get it up enough to roll out from underneath it. So it took four people to come over there and like lift the bar off so he could scooch out. He was so embarrassed. And it's kind of like, what are you thinking? Well, sometimes we underestimate ourselves in the role that we play and how good we are. And sometimes we overestimate ourselves. We think, you know what? I got this, especially when it comes to church. It's like, I don't, you know, church is great, but I don't really need it. Once in a while I need it, you know, Christmas and Easter or I make it when I can. And we don't realize without even knowing it we're kind of saying, God, I know your plan was to build the church and you wanted me to be a part of it because I've got something to add. And I know you wanted me to be a contributor that every part does it share.  I kind of just view it from a consumeristic mind point that I want to go and I want to, I want to get it when I need it. But we never realize that the way that God has formed all of us is that none of us are enough by ourselves. We're not enough by ourselves. It's just the way God has designed us. Now you individually, relationally with God are more than enough because your sufficiency is not in yourself, it's in Christ. But I'm talking about you carrying out your destiny and your purpose in the earth. You're not enough. The whole idea of self-made individuals, you know, I just, I did it all myself. You look at a company of success like Amazon.com and if you were to ask Bezos who's the wealthiest man now in the world, he's worth $120 billion. If you ask him, are you a self-made man? He's the face of Amazon but if he's wise, he would say, no, it takes a team to get me where I'm at. It takes a team to get me where I'm at. There are faceless, nameless people that you don't know that are part of the organization. And can I tell you that in the body of Christ, it's even more so that way. The way that God has designed us on purpose was that none of us would be enough by ourselves but we would need one another. And sometimes our attitude, whether knowingly or unknowingly can be, you know what? I'm saved, Jesus loves me, that's enough.  Listen, not only are you getting robbed of your full potential but you're robbing other people of their full potential because you're connected to them and your life will only make sense in context of the local church. Let me demonstrate to you what I mean, all right? Hold on, I gotta do a little dismembering here. Don't worry, it's not real. Anybody remember this guy? Mr. Potato Head. New Super Mr. Potato Head. Eyes and ears and funny noses, you can shape his arms in so many poses. You can even get a Mrs. Potato Head for new Super Mr. Potato Head. That was the commercial. I never forget commercials because I loved Mr. Potato Head. Before there were screens, before there were computers and iPads and video games, there was Mr. Potato Head. And you know, this is the spud but you know, the beauty is it comes with all of these really cool parts and interchangeable stuff. It's awesome, all the little things that they got that you can use here. Now here's the thing is if I put Mr. Potato Head over here and here's all the parts and I ask you to make sense of this, you would say, oh, it's just a bunch of parts. You know, for example, like this nose. This nose is, it's great, it's a good nose, I think. But I dare you to walk around for the next month and every time you meet somebody new and they say, hey, how are you? Just go, it's like, why are you kidding around a nose? Oh, isn't it a great nose? It's awesome, look at that nose. Really, why, yeah, it's great. Why do you have it? Because I like this nose.  Next time you see somebody say, hey, you wanna see something really cool? Lay my hand. It's a hand in a hand, do you get it?  And the reason why they would ask you, listen, because if I take that same hand and I actually put it on to something where it's supposed to be and I set it over here, the same people who see the same hand will not ask the question, why is there an arm connected to that thing? It's why, it's because an arm was meant to be connected to a body. Just like the other arm is meant to be connected over here and got a set of eyes are meant to go here and you don't put the nose on the side of the head because there's a place for the nose. You gotta put it in the right place because then it makes sense. And you got a cool smile here and you put that on there. And all of a sudden, when every part is in the right place where it's supposed to be, it gives context and it makes sense. Now, can I tell you, this is the body of Christ. And Jesus is the spud, please don't tweet that. But we are all members and there's a proper place for us in the body, the way that God has designed us because of what we're supposed to do. The eye sees, the ear hears, but if the ear gets upset that it's not an eye, it will live its life in a constant comparison mode and it will never become good at what it was created to do. It will live all of its life wishing it was something else. Or what about the arm? The arm is a perfectly good arm but if it disconnects from the rest of the body and it just walks around, it's weird because now when it says, oh, hi, everybody's like, that is really immature. That is really weird. Would you put it back where it's supposed to be? And you know, guys, this is what happens a lot of times. Jesus is here on the earth and he says, I want my body to be connected and in unity. And we're over here going, I'm eyes. I don't wanna be connected. Well, your life will only make sense in the proper context when it is put in the right place. And a lot of the reasons why the church is unhealthy, a lot of the times the reason why we're dissatisfied is we've not connected where we're supposed to be because we haven't realized the value that we carry and the importance of the role and the responsibility that Jesus has given us in the body of Christ. Come on, can we just give it up for Mr. Potato Head here this morning? So here's what I want you to know. A couple of things I want you to know about not overestimating yourself. Number one is this, you're gifted, but you are not complete. You're gifted, but you are not complete. Everybody has gifts. Some have more gifts. Some people's gifts are more obvious, but everybody has something. Everybody has the ability to serve. Everybody has the ability to give. Everybody has the ability to be custom made by Jesus in the unique way that you are and to identify how he's wired you and used it.  I believe in counselors. I've gone to counselors personally because sometimes you just need to talk to somebody and counselors are patient and they listen and they give you wise counsel and advice. But here's the thing is I'm not a counselor and I've had people say to me, Pastor Lee, I wish I could come and get counseling from you. And my answer is, no, you don't because here's my counseling. Are you ready? Here it is in a nutshell. Admit it and quit it. It's my answer for everything. Admit it, quit it. There you go.  He's a mentor to many people. He listens, listen, my battery would be so drained they would throw me in the junkyard at the end of a day listening to people go through their issues and having to give them counsel and advice. But he thrives on it. He is a wise counselor. He's gifted by the Holy Spirit uniquely. I'm gifted for the people that minister to our children. Do you know we have hundreds and hundreds of children? And we have so many servant leaders who show up early who go to the classrooms, they pray over our kids, they teach them Bible lessons, they pray for them, they mentor them, they follow, they lead them in worship. I'm so grateful for them. I'm not wired that way, but they're not wired the way I'm wired. If I live my life in constant comparison or over exaggeration of my value, then I not only am stealing something from somebody else, I'm also stealing from myself. We are gifted, but we are not complete. We're complete when we're together. See, the body of Christ is, it's a mysterious miracle. How a group of people that could never change the world by ourselves together change the world together. Isn't that amazing? I mean, just think about this, last year in December, we put, during our big give, we raised over $200,000. If I were to ask any one of you for $200,000, you'd be like, I don't got that. Maybe some of you do, but we also put coats on 400 kids, boots on 400 kids. We built a school in India. We helped support an English school in Myanmar. If I were to give a list of everything we did during the big give and say, I need you to do this, most of us in this room would say, that's over, I can't do that, but when every part does its part and does what it can, doesn't focus on what it can't do, but says, all right, I can do this. And you know what, I'll take a day off of work and I'll show up and you know what I'll do? I'll get here early and I'll align all the tags and I'll load the truck and I'll unload it and I'll make the video of it and I'll inspire people and motivate them. I'll make contact with the school. When every part does their share and it comes together, a miracle happens. No one person can take credit for the miracle because it's everybody, it's all the members doing their part. It's fantastic. When we celebrate the fact that everybody's gifted, but not everybody, not one person is complete. First Corinthians 12 says it this way, God has carefully designed each member and placed it in the body of Christ as he desires. A diversity is required for if the body consisted of only one single part, there wouldn't be a body at all. Second thing I wanna tell you in closing is this, is that you need gifts to actually help strengthen your gifts. Ephesians chapter four says that Jesus, when he ascended, he gave gifts to men. Apostles, prophets, evangelists, pastors, and teachers. And here's the job of apostles and pastors and prophets, evangelists and teachers. It's to equip the saints to do the work of the ministry. See, there's a misnomer that we've believed far too long and it's this, is that we come to church to listen to the minister. That's a lie. You don't come to the church to listen to the minister. We come as the church to be equipped as the ministers. But we also need five-fold ministry gifts that help strengthen and equip us to do the work of the ministry. So this mindset that you can be a Christian without the church, that you can be a Christian and love Jesus and fulfill your destiny and not be plugged into a local church. Let me tell you, you can get to heaven without a local church, but you will never fulfill your destiny without the local church. And here's why. When Jesus left planet earth, he also left behind gifts. And those gifts are coaches. He calls them apostles, prophets, evangelists, pastors and teachers. And their job is to help identify, strengthen, equip and motivate every member of the church so that we walk in our gifts and our callings. And when we come together, this is like a locker room, guys. We come together, this is, Sundays are like halftime. It's like, get in here, it's Tom Izzo motivating you to beat the snot out of Syracuse this afternoon. It's like motivating you. It's like, come on, we're going out there. We're going zone and we're going man and I need you to do this. Come on, Tommy, you got this. It's motivating. So when we go back out on the court of life or on the football field of life out into the battlefield that we are equipped, we are sharpened, we are fueled, we are fit, we got our act together and we go out into the marketplace and we exemplify Jesus. And we all need those gifts in our life. Can I tell you one of the things I do every Monday? Somebody asked me one time, they said, what do you do all week when you're not preaching?  No, that's not true. But on Monday mornings, I go to church. See, because I preach three times on a weekend and a lot of my time is spent praying and it is writing a message, but then also leadership things. But on Mondays, I have voices that speak into my life. I sit down in front of my computer and I watch Craig Groshel from Life Church in Oklahoma City and I listen to his message and it feeds me. Sometimes I listen to Chris Hodges, Pastor of Church of the Highlands or Robert Morris from Gateway Church or Jimmy Evans, sometimes Bill Johnson from Bethel or Chris Valleton from Bethel Church. And I watch probably two to three messages on a Monday. And you wanna know why? It's because I need to be fueled. I need to be equipped. I need to be challenged. I need to be inspired. We all need it. Jimmy Evans coming in this next week. He's like John Wayne with a Bible. I mean, he'll call me up sometimes, Lee Cummings, what are you doing? How's the marriage? How's the church? And he's challenging me. We all need those gifts in our life. You need pastors. You need leaders. You need spiritual leaders that you submit your life to. And it's not a control thing. It's an equipping thing. Oh, I don't need anybody. All I need is my Bible. And I just kind of float around like a little butterfly. Oh, I love Jesus.  Nobody can challenge me. It's like, you aren't ever gonna do anything for the kingdom of God like that. You need to have some people that you are strengthening and you need to have some people in your life that are strengthening you. You need to have about five crazy friends in your life and a really good pastor. And so I hope you got some friends because I love you as a pastor. The greatest joy of my life is to be the pastor of this church. But listen, we all need that in our lives. In order to arrive safely into the kingdom of God knowing that we lived a life that we fulfilled our purpose. I don't know about you, but you can stand up with me if you would. I was thinking last, a couple of weeks ago when Billy Graham passed away. Like a little over two weeks ago. Billy Graham's one of my heroes. I think probably for many of us, he's a hero. But I was thinking to myself, wow, if it's really true that all the people that we impact in this life when we get to heaven, we'll get to meet. Imagine what it must have been like for Billy Graham to step out of this life into eternity. Can you imagine millions and millions and millions of people waiting there saying thank you like a friend of mine who gave his life to the Lord watching a Billy Graham crusade on television? I mean, just think about the million, he preached to more living people than any other human being who's ever lived on the planet.  Can you imagine that moment of stepping into eternity and looking and seeing all these people that you've never met who are there and says thank you. I'm here because of you. Do you know you don't have to be Billy Graham for that to be true? You might say, well, pastor Lee, listen, there's nothing extravagant about me. I'm not a preacher like Billy Graham. Or I'm not a worship leader like some famous worship leader. Nobody even knows me.  Or you know what? The only thing that I know to do is I work hard 40 hours a week and when I come to church, I'm here. I worship, I serve and I give financially. Here's what I want you to know. I think you're gonna be shocked someday. I think you're gonna be shocked someday when you show up into eternity.  Is there a foot bone?  The humerus is connected to the ulna and the radial, thank you. And every part has to work together. And not only when you show up to heaven, I think when we show up to heaven together, we're gonna realize what in the world were we able to do together? There were no limits. There were no limits when every part does its share. And here's the good news is every part gets the reward of the whole. We get to share in his glory. Isn't that a powerful, powerful thought? Isn't God so good that he didn't just save us, but he invited us to live lives of purpose and to be his body, his hands, his heart, his eyes, his ears extended to a lost and dying world? Did you buy your heads with me all over the room and I wanna invite our prayer team, care ministers if they would, to move into place this morning. Heavenly Father, we thank you tonight today, Father, for your grace and your goodness.   You've connected us to one another. And Lord, I pray for unity. Lord, I pray for a spirit of unity. There's only one Lord. There's only one faith. There's only one spirit, only one baptism. We are part of your body. Lord, help us to be connected. Lord, in those places of our life where we've gotten dislocated and just joined it because we've been hurt, because we've undervalued ourselves, because we've put other things as priorities or maybe we've been indifferent about church and about serving and about being a part of what you're doing. Lord, I pray that you would reverse that and fill our hearts with vision and passion and willingness and unity, Lord. Lord, help every part be fruitful. Help us to flourish. And before we dismiss this morning, listen, I sense with all of my heart that the Holy Spirit is here as He always is when we gather in Jesus' name. And He's here because He cares. And He cares for those of us who are experiencing some brokenness, some pain, some hurt, some rejection. It's really believed that the brokenheartedness, there's an overwhelming sense of brokenheartedness and it may have nothing to do with church as we're talking about. But I just sense today that some of us came into this place today and we've, we're brokenhearted. We've lost something. We've experienced rejection or maybe we just never felt valuable. Maybe you've gotten a bad physical report and you're just overwhelmed and don't know what to do. Listen to the beauty of the body of Christ is that we love one another and we pray with and for one another and we find strength together. And today as I pray and I dismiss, if you have a need in your life or maybe God's doing something on the inside of you and there's a vibrancy arising in your heart saying, I need to get connected. I need to get plugged in. I need, I need to do my part. I wanna, I want help in doing that. I'm just gonna invite you to come and receive prayer. Maybe you need to get over some pain of the past or some fears of rejection again or maybe you've kind of been a lone wolf and today you say, I need family. Whatever your need is this morning, as we dismiss, we're just gonna invite you to come forward and let one of our prayer partners pray with you. Father, send us from this place, not leaving Radiant Church, but send us as Radiant Church, a light that shines in the darkness, each one of us to every corner of our city and may this city be known as a radiant city in Jesus' name, amen.


Guys thanks so much for being with us this afternoon to talk about your experience on the Convention Floor at CES 2019. Erica, I'm going to start with you. Tell me how you decided what exhibits to show to Steven and the people at SIGMA. Yeah we focus a lot on proactive patient care so now with advances in technology real-time data and insights can actually nudge you in real time to make small behavior changes that can have a significant impact on your health. Talk about the concept of nudge and what does that mean? Does that mean new ways to prompt you to you know experience health care in different ways? Yeah that's a great question. So based on data and real-time insights devices using sensors can proactively give you insights and advice in real time to tell you how to better yourself. So for example if you're slouching devices can tell you to sit up straight while you're actually slouching. It's pretty cool. So Steven on the tour with Erica what did you learn and see as takeaway that's going to really sort of impact your marketing for SIGMA in 2019 and beyond? Yeah I think one of the things that I saw that really was impactful for me was not just the idea of nudges but also the idea of a deeper integration into the daily lives of our customers and then in general consumers and helping to have them move down that path of not thinking of health care as just something when you're sick but really having health care as a primary objective in terms of prevention and well care versus just when I'm sick. Erica when you're preparing for these tours what did you find the most interesting? I think a lot of the advances that are being made in sleep care are really really interesting. For example there's an exhibitor called ergo motion that actually adjusts the mattress to help improve your sleep. Sleep things like that there are lots of things that are not necessarily obvious but really important Steven like what are some of the other sort of things that people should be aware of as technology shapes the health care business? There's places to look for from the minute that you get a prescription from your doctor. There are tools available that you can really help to steer yourself to the right price point if you're thinking of more affordable solutions and then one of the things that we've really brought full force with five million customers I know the seven million customers coming on this past January 1st is something that we call one guide which is really kind of the best of digital together with the human touch to really help guide customers to proactive solutions and really connecting behind the scenes whether it's a chronic condition or whether it's even connecting you to a certain type of doctor or physician. Are you looking at some of these really bleeding edge technologies like machine learning and AI and blockchain to help transform the business? Definitely definitely just last year signum made an acquisition of a company called Brighter based out of Santa Monica and one of the reasons we wanted to we started with a pilot with them and then we transitioned into just a full-scale geez this is something that's really important because they've got a proprietary algorithm that helps match you to the doctor of your choice at the right price for what you want to pay as well so Erica I don't think healthcare is necessarily your your hardcore expertise right so that's that's just so cool that you were able to sort of like deep dive into and use space and get some expertise how talk to me about that. Yeah I think the most important takeaway is greater control for consumers more personalized data and then more opportunities for marketers.