A non-contributing predictor variable (Pr > |t| = 0.658) is removed from an existing multiple linear regression model. What will be the result?

Question

Options

• AAn increase in R-Square
• BA decrease in R-Square
• CA decrease in Mean Square Error
• DNo change in R-Square

• A
  17% (4)
• B
  74% (17)
• C
  4% (1)
• D
  4% (1)

Explanation

Removing a predictor - even a non-significant one - causes R² to decrease (or at minimum stay flat), because R² measures the proportion of variance explained by the model, and any predictor contributes some explained variance, however small. Option A (increase) is impossible; R² can only go up when adding predictors, never when removing them. Option D (no change) would require the variable to have exactly zero correlation with the outcome, which is essentially never true in practice - a p-value of 0.658 means the contribution is weak, not zero. Option C (decrease in MSE) is tempting but wrong: MSE = SSE/df, and removing a variable increases both SSE and degrees of freedom simultaneously, making the net change in MSE ambiguous - for a non-contributing predictor, MSE often decreases slightly (which is why adjusted R² can actually improve), but that's a different metric than R².

Memory tip: Think of R² as a bucket that only gets fuller as you add predictors - pulling a variable out always spills at least a drop, even if the variable was nearly useless.

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