Final answer:
When the coefficient of determination r^2 is equal to 1 in a regression analysis, it indicates perfect prediction of the dependent variable by the independent variable, meaning there are no errors. Therefore, the SSC (Sum of Squared Errors) would be zero and the SSR (Sum of Squares due to Regression) would be equal to SST (Total Sum of Squares), thus the correct answer is SSR = SST.
Step-by-step explanation:
In regression analysis, the coefficient of determination r2 indicates the proportion of the variance in the dependent variable that is predictable from the independent variable. When r2 = 1, it means that the regression predictions perfectly fit the data. In this context, the terms we are concerned with include:
- SST (Total Sum of Squares): The total variance in the dependent variable.
- SSE (Sum of Squared Errors): Variance that is not explained by the regression line.
- SSR (Sum of Squares due to Regression): Variance explained by the regression line.
In the case where r2 = 1, the SSE would be zero because there are no errors between the observed values and the regression line's predicted values. Consequently, the SSR would be equal to SST because all variability in the dependent variable is accounted for by the regression model.
Therefore, the correct answer is d. SSR = SST.