I stumbled on this while doing MLR, and was curious as to why this happens. The adjusted R-squared is (if I understand correctly) supposed to be a way of comparing the predictive quality of models with different numbers of explanatory variables. In the second model, I've added a statistically insignificant variable (weight), which has apparently improved the model.
My only thought that this is because the point estimate of this value is not 0 - so there may be a 'significant' effect at a lower level. Is that right?
Model 1:
Model 1
Sum of Mean
Source DF Squares Square F Value Pr > F
Model 2 6017.30007 3008.65004 12.36 <.0001
Error 424 103221 243.44647
Corrected Total 426 109239
Root MSE 15.60277 R-Square 0.0551
Dependent Mean 120.03044 Adj R-Sq 0.0506
Coeff Var 12.99901
Parameter Estimates
Parameter Standard Variance
Variable DF Estimate Error t Value Pr > |t| Inflation 95% Confidence Limits
Intercept 1 75.85363 8.91793 8.51 <.0001 0 58.32478 93.38249
age 1 0.66112 0.15314 4.32 <.0001 1.00204 0.36011 0.96212
chol 1 1.86495 0.82213 2.27 0.0238 1.00204 0.24900 3.4809
Model 2 (with addition of insignificant variable):
Root MSE 15.58705 R-Square 0.0592
Dependent Mean 120.03044 Adj R-Sq 0.0525
Coeff Var 12.98591
Parameter Estimates
Parameter Standard Variance
Variable DF Estimate Error t Value Pr > |t| Inflation 95% Confidence Limits
Intercept 1 57.69446 16.03325 3.60 0.0004 0 26.17970 89.20922
age 1 0.66180 0.15299 4.33 <.0001 1.00205 0.36110 0.96251
chol 1 2.02756 0.82993 2.44 0.0150 1.02320 0.39626 3.65885
weight 1 0.09687 0.07111 1.36 0.1738 1.02122 -0.04290 0.2366