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.

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The most appropriate method to test whether the population regression function is linear or a polynomial of order r is to use the test of (r-1) restrictions using the F-statistic. This test compares the fit of the linear and polynomial models by comparing the residual sum of squares (RSS) for each model, taking into account the number of restrictions placed on the polynomial model. If the F-statistic is significant, it implies that the polynomial model is a better fit than the linear model and that the population regression function is non-linear.

To Test Whether or Not the Population Regression Function Is