Question

y is regressed on x1, x2, and x3 giving R²_adj= 0.87. Y is then regressed on x1, x2, x3, and x4, giving R²_adj = 0.86. What does this indicate?

Answer 1

The adjusted R-square gives percentage of variation explained by only those independent variables that, in reality, affect the dependent variable. Importantly, it's value increases only when the new term improves the model fit what would be obtained by probability.

The adjusted R-square value actually decreases when term doesn't improves the model fit by a sufficient amount.

So , Y regressed on x1,x2,x3 and x4 gives R-square adjusted=0.86(decreases) implies that x4 does not improves the model.