Consider a k-variables linear regression model, i.e., Y=X 131 +X2 32 + E, Where, X is...

 

 

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Consider a k-variables linear regression model, i.e., Y=X 131 +X2 32 + E, Where, X₁ is (N.k1 ), X₂ is (N. K₂), and k = k₁ + kz. As you may recall, adding columns to the X matrix (including additional regressors in the model) gives a positive definite increase in R². The adjusted R² attempts to avoid this phenomenon of ever-increasing R². Show that the additional k₂ number of variables (regressors) in this model increases R² if the calculated F-statistic in testing the joint statistical significance of coefficients of these additional regressors (B₂) is larger than one. Consider a k-variables linear regression model, i.e., Y=X 131 +X2 32 + E, Where, X₁ is (N.k1 ), X₂ is (N. K₂), and k = k₁ + kz. As you may recall, adding columns to the X matrix (including additional regressors in the model) gives a positive definite increase in R². The adjusted R² attempts to avoid this phenomenon of ever-increasing R². Show that the additional k₂ number of variables (regressors) in this model increases R² if the calculated F-statistic in testing the joint statistical significance of coefficients of these additional regressors (B₂) is larger than one.

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ANSWER The coefficient of determination R2 measures the proportion of variation in the dependent variable Y that is explained by the independent varia... View the full answer