In comparing two multiple regression models, one with variables that are a subset of the other, bigger model's variables, to infer which model is superior, I get confused in looking at R2, adjusted R2, and F-statistic values.  What's the difference among them and is one of these preferable to the others?  Thanks.

Question
Asked Nov 4, 2019

In comparing two multiple regression models, one with variables that are a subset of the other, bigger model's variables, to infer which model is superior, I get confused in looking at R2, adjusted R2, and F-statistic values.  What's the difference among them and is one of these preferable to the others?  Thanks.

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Step 1

R-squared:

The coefficient of determination (R2) is defined as the proportion of variation in the observed values of the response variable that is explained by the regression. The squared correlation gives fraction of variability of response variable (y) accounted for by the linear regression model.

The coefficient of determination, R-squared value is defined as,

SSR
R2
SST
SSE
=1-
SST
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SSR R2 SST SSE =1- SST

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Step 2

Where SSR is the sum of squares of regression, SST is the total sum of squares, SSE is the error sum of squares.

Adjusted R-squared:

The adjusted coefficient of determination (R2Adj) is defined as the proportion of variation in the observed values of the response variable that is explained by the estimated regression model. If in the model the new terms arise the adjusted square will increase.

The Adjusted R-squared value is defined as,

п-1
R11R
Adf)
п- (k+1)
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п-1 R11R Adf) п- (k+1)

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Step 3

F-statistics:

The general formula for the F...

MSR
F =
MSE
SSR
п-1
SSE
п -k
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MSR F = MSE SSR п-1 SSE п -k

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