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Time Series Regression IV: Spurious Regression  This example
considers trending variables, spurious regression, and methods
of accommodation in multiple linear regression models. It is the
fourth in a series of examples on time series regression,
following the presentation in previous examples.   Predictors
that trend over time are sometimes viewed with suspicion in
multiple linear regression (MLR) models. Individually, however,
they need not affect ordinary least squares (OLS) estimation. In
particular, there is no need to linearize and detrend each
predictor. If response values are well-described by a linear
combination of the predictors, an MLR model is still applicable,
and classical linear model (CLM) assumptions are not violated.
If, however, a trending predictor is paired with a trending
response, there is the possibility of spurious regression, where
$t$ -statistics and overall measures of fit become misleadingly
"significant." That is, th