Asked by Sydnee Smith on Apr 28, 2024
Verified
In a regression and correlation analysis, if r2 = 1, then
A) SSE = SST.
B) SSE = 1.
C) SSR = SSE.
D) SSR = SST.
Coefficient Of Correlation
A statistical measure that calculates the strength and direction of a linear relationship between two variables.
SSR
In statistics, SSR stands for Sum of Squares due to Regression, which measures the variation explained by the regression line.
SSE
A metric indicating the variance between an estimated model's predictions and the actual data, calculated as the sum of squares of errors.
- Extract and comprehend the significance of the coefficient of determination in regression analytic procedures.
Verified Answer
AA
Abdal Aziez AlogaidiMay 01, 2024
Final Answer :
D
Explanation :
When r=1r = 1r=1 , it indicates a perfect positive linear relationship between the variables. This means all the points lie exactly on the regression line, and there is no variation of the actual values from the predicted values. Therefore, the Sum of Squares for Regression (SSR), which measures how well the regression line fits the data, is equal to the Total Sum of Squares (SST), which measures the total variation in the data. This implies that there is no error (SSE, Sum of Squares for Error) because all variation is perfectly explained by the regression line.
Learning Objectives
- Extract and comprehend the significance of the coefficient of determination in regression analytic procedures.