Consider a regression and correlation analysis where r² = 1. We know that ________. A)SSE must be greater than one B)SSE must be greater than SS Total C)SSE can take on any negative or positive value D)SSE must equal to zero

Question

Quizplus · Accepted Answer

The correlation coefficient (r) can only take on values between -1 and 1. When it equals 1, it indicates a perfect positive relationship between the two variables. In this case, r² = 1 tells us that there is a perfect linear relationship between the predictor variable (^{2) and the response variable (}). This means that all of the variation in the response variable can be explained by the predictor variable. In other words, the regression model fits the data perfectly, and there is no unexplained variation left. This is only possible if SSE (the sum of squared error, which measures the amount of variation that is not explained by the model) is equal to zero. Therefore, the correct answer is D.

Consider a Regression and Correlation Analysis Where R2 = 1

Consider a Regression and Correlation Analysis Where R² = 1