R: Calculate and interpret odds ratio in logistic regression
<p>I am having trouble interpreting the results of a logistic regression. My outcome variable is <code>Decision</code> and is binary (0 or 1, not take or take a product, respectively).<br>
My predictor variable is <code>Thoughts</code> and is continuous, can be positive or negative, and is rounded up to the 2nd decimal point.<br>
I want to know how the probability of taking the product changes as <code>Thoughts</code> changes. </p>

<p>The logistic regression equation is:</p>

<pre><code>glm(Decision ~ Thoughts, family = binomial, data = data)
</code></pre>

<p>According to this model, <code>Thought</code>s has a significant impact on probability of <code>Decision</code> (b = .72, p = .02). To determine the odds ratio of <code>Decision</code> as a function of <code>Thoughts</code>:</p>

<pre><code>exp(coef(results))
</code></pre>

<p>Odds ratio = 2.07.  </p>

<p>Questions:</p>

<ol>
<li><p>How do I interpret the odds ratio?  </p>

<ol>
<li>Does an odds ratio of 2.07 imply that a .01 increase (or decrease) in <code>Thoughts</code> affect the odds of taking (or not taking) the product by 0.07 <strong>OR</strong>  </li>
<li>Does it imply that as <code>Thoughts</code> increases (decreases) by .01, the odds of taking (not taking) the product increase (decrease) by approximately 2 units?</li>
</ol></li>
<li><p>How do I convert odds ratio of <code>Thoughts</code> to an estimated probability of <code>Decision</code>?<br>
Or can I only estimate the probability of <code>Decision</code> at a certain <code>Thoughts</code> score (i.e. calculate the estimated probability of taking the product when <code>Thoughts == 1</code>)?</p></li>
</ol>