Suppose that the value of R² for an estimated regression model is exactly one. Which of the following are true?
(I) All of the data points must lie exactly on the line
(ii) All of the residuals must be zero
(iii) All of the variability of y about is mean have has been explained by the model
(I) The fitted line will be horizontal with respect to all of the explanatory variables

Question

Quizplus · Accepted Answer

When the R-squared value (R² seems to be a mistyped representation of R^2) of a regression model is exactly one, it means that the model explains 100% of the variability in the dependent variable. This implies that all data points lie exactly on the regression line (i), all residuals are zero because the predicted values exactly match the observed values (ii), and all of the variability of y about its mean has been explained by the model (iii). The statement about the fitted line being horizontal is incorrect; the slope of the line depends on the relationship between the independent and dependent variables, not the R-squared value.

Suppose That the Value of R2 for an Estimated Regression

Suppose That the Value of R² for an Estimated Regression