A student regressed Y against both X and X² and obtained the following output tables.

Because X² is not significant at the 0.05 level, the student reran the regression after dropping X² and obtained the following output tables.

Why does dropping a variable that is not significant cause a big decrease in adjusted r squared?
 
 

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Regression Statistics Multiple R 0.682335 R Square 0.465581 Adjusted F 0.406201 Standard 11.70702 Observati ANOVA Regression Residual Total df X X2 21 SS MS F gnificance F 2 2149.211 1074.605 7.840724 0.003556 18 2466.979 137.0544 20 4616.19 P-value Lower 95%Upper 95% Coefficientsandard Err t Stat Intercept 31.88669 3.839323 8.305289 1.43E-07 23.82057 39.9528 -1.49703 0.421892 -3.54838 0.002296 -2.38339 -0.61067 0.13741 0.078164 1.757973 0.095744 -0.02681 0.301626 Regression Statistics Multiple R 0.682335 R Square 0.465581 Adjusted F 0.406201 Standard 11.70702 Observati ANOVA Regression Residual Total df X X2 21 SS MS F gnificance F 2 2149.211 1074.605 7.840724 0.003556 18 2466.979 137.0544 20 4616.19 P-value Lower 95%Upper 95% Coefficientsandard Err t Stat Intercept 31.88669 3.839323 8.305289 1.43E-07 23.82057 39.9528 -1.49703 0.421892 -3.54838 0.002296 -2.38339 -0.61067 0.13741 0.078164 1.757973 0.095744 -0.02681 0.301626

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Based on the updated regression output tables after dropping X2 here is a breakdown of the key metrics 1 Multiple R The multiple correlation coefficient which measures the strength and direction of th... View the full answer