Question

In regressing Y on a single, quantitative independent variable X, if the sole criterion for choosing a model was the R^2 value, explain why a second-order model would almost always be favored over a simple linear model. Assume n>3.

Answer 1

As R^2 always increases, when we increase the number of independent variables

for simple linear model - k = 1

for second-order model - k = 2

hence a second-order model would almost always be favored over a simple linear model.