Question

A company performs linear regressions to compare data sets of two similar products. If the residuals for brand A form an increasing curve, and the residuals for brand B form a U-shaped pattern, what can be concluded?
A. Brand A's data are probably linear, while brand B's data are probably not. B.Neither data is likely to be linear.
C.Both data sets are probably linear.
D.Brand B's data are probably linear, while brand A's data are probably not.

Answer 1

I think the correct answer would be B. If the residuals for brand A form an increasing curve, and the residuals for brand B form a U-shaped pattern, then neither of the data is likely to be linear. In order to be linear, the residuals of both data set should be, more or less, linear or approaching linearity in nature. Therefore, the linear regression that was done would not give good results since it is only applicable to linear data sets. Also, you can say that the relation of the data sets of the products are not linear. It would be best to do a curve fitting for both sets by using different functions like parabolic functions.