Final answer:
The R² in multiple regression of y on x1 and x2 represents the percentage of the variation in y explained by the sample regression equation, not merely by one independent variable or the statistical significance of the coefficients. The correct option is D.
Step-by-step explanation:
The R² of a multiple regression measures the percentage of variation in the dependent variable y explained by the regression on multiple independent variables, such as x1 and x2. So the correct answer to the question 'The R² of a multiple regression of y on x1 and x2 measures what?' is d. the percentage of the y variation explained by the sample regression equation.
The coefficient of determination, the squared value of the correlation coefficient (r), reflects the proportion of variance in the dependent variable that can be predicted from the independent variables. For a simple linear regression, this can be visualized as the goodness of fit for the regression line to the data points.
The closer the R² value is to 1, the better the model explains the variation in the outcome. It's important to note that while R² indicates the proportion of variance explained, it doesn't indicate whether the predictions are unbiased or the model is the best among alternatives.