Question

We know that a linear regression model is limited in its power to project into the future. In other words, one should be very careful in using linear regression to make projections. Follow these steps in addressing this assigned critical thinking question:

1. Provide an explanation of why (or why not) this caution is warranted.

2. Find a real economic or business example to support your position.

Answer 1

1. This cause is warranted because if the X or Y populations from which data to be analyzed by linear regression were sampled violate one or more of the linear regression assumptions, the results of the analysis may be incorrect or misleading. Like if the variance of the Y is not constant, then the error variance will not be constant. The most common form of such heteroscedasticity in Y is that the variance of Y may increase as the mean of Y increases, for data with positive X and Y. Unless the heteroscedasticity of the Y is pronounced, its effect will not be severe: the least squares estimates will still be unbiased, and the estimates of the slope and intercept will either be normally distributed if the errors are normally distributed, or at least normally distributed asymptotically (as the number of data points becomes large) if the errors are not normally distributed. The estimate for the variance of the slope and variance will be inaccurate, but the inaccuracy is not likely to be substantial if the X values are symmetric about their mean. Among other inaccuracies there are problems of outlier, lack of independence in Y, Non normality, overfitting etc. But we will discuss mostly on the problem of variance not being constant.

2. We will use Credit Approval Data to validate our point. The data is available from the UCI Machine Learning Repository.