Question

A low regression means that:

A)the regression is bad.

B) there are other important factors that influence the left hand variable.

C) the SSR is low relative to the total variation in Y.

D) tells you what the other factors influencing the left hand variable are.

Answer 1

A low regression would imply a poor model fit to the data, i.e low R2

By definition of R2,

It measures the explained variation in the response variable Y. Let SSB and SSR denote the Between Sum of Squares and Sum of Squares due to Residuals respectively. Then the total Sum of Squares (SST)

SST = SSB (Explained variation) + SSR (Unexplained variation)

Hence,

If R2 is large, it would imply that a large amount of variation is explained by predictor 'x', and hence, few other influence y other than x.

However, if R2 is low, it would imply that only a small amount of variation is explained by predictor 'x', and thus, there is a large amount of variation left unexplained which suggests that there might be other significant variables that influence y other than x.

Hence, the correct option would be:

B) There are other important factors that influence the left-hand variable.