When an explanatory variable is dropped from a multiple regression model, the adjusted r² can increase.

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The adjusted r² value takes into account both the number of variables and the amount of variation in the dependent variable that is explained by the independent variables. When a variable is dropped from a multiple regression model, the adjusted r² value can increase if the variable had a low correlation with the dependent variable and was not contributing much to the overall explanation of the variation in the dependent variable.

When an Explanatory Variable Is Dropped from a Multiple Regression