Key to "Consider the following two regression models (at the..."

Carolyn Moore

Answered question

2021-12-03

Consider the following two regression models (at the population level):

M_{1} : y = β_{0} + β_{1} x_{1} + β_{2} x_{2} + ξ

M_{2} : y = β_{0} + β_{1} x_{1} + β_{2} x_{2} + β_{3} x_{1}^{2} + β_{4} x_{2}^{2} + β_{4} x_{2}^{2} + β_{5} x_{1} x_{2} + ξ

.
Assume that we fit the two models to the same data.
Can we compare the

R^{2}

of the two models without looking at the results of the fittings? Justify your answer.

Answer & Explanation

George Spencer

Beginner2021-12-04Added 12 answers

Step 1
The given two regression models are shown below

M_{1} : y = β_{0} + β_{1} x_{1} + β_{2} x_{2} + ξ

M_{1} : y = β_{0} + β_{1} x_{1} + β_{2} x_{2} + β_{3} x_{3} + β_{4} x_{4} + β_{5} x_{5} + ξ

R^{2}

or squared gives an idea of a fitted model appropriateness to the given data.
Step 3 a) Generally, the more number of predictors increases R squared by a certain amount. That is, as the number of predictors (independent variables) increases, the R squared also increases (even by a very small amount).
Here, model 1 has 2 predictors while model 2 has 5 predictors. So,

R^{2}

will be greater for Model 2 when compared with Model 1.
Therefore,

R^{2}

for model

1 < R^{2}

for model 2.

Do you have a similar question?

Recalculate according to your conditions!

New Questions in High school statistics

Didn't find what you were looking for?