# 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 R-squared, adjusted R-squared, and F-statistic values. What’s the difference among them and is one of these preferable to the others?  Thanks.

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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 R-squared, adjusted R-squared, 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

Two multiple regression models are given. The superior model has to find.

Step 2

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,

Step 3

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 es...

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