Question

A company performs linear regression to compare data sets for two similar products. If the residuals for brand A are randomly scattered above and below the x-axis, and the residuals for brand B form from a U-shaped pattern, what can be concluded?

Answer 1

It can be concluded that the linear regression for brand A is a good match for the data. Since, the residuals are scattered randomly, the equation is fairly representing the data.

However, in brand B, a U-shaped pattern appears. This means that a different model (other than linear) would be better suited for this data.

Answer 2

Prediction for brand A will be better as compared to brand B.

Explanation:

We are given the following:

A company performs linear regression to compare data sets for two similar products.

The residuals for brand A are randomly scattered above and below the x-axis, and the residuals for brand B form from a U-shaped pattern.

Homoscadacity in Residuals:

In a linear regression we want our residuals to have constant variance that is is we want to minimize the noise. This can be verified if the scatter plot of the residuals shows randomness and does no show any pattern.

Since the residuals of brand A are randomly distributed, it is a good thing, the regression will give better results as compare to brand B where the residuals form a pattern(U shaped).

The prediction for brand B will not be so good and we need some other approach to predict brand B.