To test whether or not the population regression function is linear rather than a polynomial of order r,
A)check whether the regression R2 for the polynomial regression is higher than that of the linear regression.
B)compare the TSS from both regressions.
C)look at the pattern of the coefficients: if they change from positive to negative to positive,etc. ,then the polynomial regression should be used.
D)use the test of (r-1)restrictions using the F-statistic.

Question

Quizplus · Accepted Answer

The best way to test whether or not the population regression function is linear rather than a polynomial of order r is to use the test of (r-1) restrictions using the F-statistic. This is because it directly tests whether the additional polynomial terms in the model improve the fit significantly beyond what can be explained by chance. TSS comparison and coefficient patterns may be helpful in assessing the goodness of fit, but they are not definitive tests of linearity versus polynomiality. The regression R2 comparison is also not a reliable indicator, as it can be affected by the number of variables in the model and other factors.

To Test Whether or Not the Population Regression Function Is