Question

When the coefficient of determination R-square is 0.88, it indicates that

A. 88 percent variation of Y is explained by the independent variables.
B. 88 percent variation of the independent variables is explained by Y.
C. the model does not fit the data.
D. it is unknown that whether the model fits the data.

Answer 1

An R-square value of 0.88 signifies that 88% of the variance in the dependent variable is explained by the independent variables in the regression model.

Step-by-step explanation:

When the coefficient of determination R-square is 0.88, it indicates that 88 percent of the variation in the dependent variable (Y) can be explained by the variation in the independent variables. The R-square value, also known as r², is the square of the correlation coefficient (r) and represents the proportion of variance for the dependent variable that's predictable from the independent variables.

In the context of a regression analysis, if we have an R-square of 0.88, this means that the regression model explains 88 percent of the variance in the dependent variable. The remaining 12 percent of the variance is due to factors that the model does not capture.