Question

True or False:

1. The fit of the regression equations yˆ = b0 + b1x + b2x2 and yˆ = b0 + b1x + b2x2 + b3x3 can be compared using the coefficient of determination R2.

2. The fit of the models y = β₀ + β₁x + ε and y = β₀ + β₁ln(x) + ε can be compared using the coefficient of determination R².

3. A quadratic regression model is a special type of a polynomial regression model.

Answer 1

1. False. The coefficient of determination of the two models cannot be compared because the number of independent variables in the model are different. In the first equation, the number of independent variables are two while in the second equation, the number of independent variables are three. Thus, R squared value of the two equations cannot be compared.

2. True. The fit of the model can be compared in this case because the number of independent variables in the equation in the above case are same. The fit will tell whether logarithmic transformation of the independent variable is a better fit as compared to the no transformation of the independent variable. Thus, the two can be compared in this case.

3. True. The statement is true because a quadratic regression model is a special type of a polynomial regression model. Polynomial model includes quadratic regression model in it.