In simple linear regression, which of the following statements indicates no linear relationship between the variables x and y?
A)The coefficient of determination is 1.0.
B)The coefficient of correlation is 0.0.
C)The sum of squares for error is 0.0.
D)The sum of squares for regression is relatively large.

Question

Quizplus · Accepted Answer

The coefficient of correlation measures the strength and direction of the linear relationship between the variables. A coefficient of 0.0 indicates no linear relationship between x and y, as there is no correlation between the two variables. Therefore, option B is the correct answer. The coefficient of determination (option A) being 1.0 indicates that all data points fall exactly on the regression line, which indicates a perfect fit but not necessarily a linear relationship. The sum of squares for error (option C) being 0.0 indicates that all data points fall exactly on the regression line, which again indicates a perfect fit but not necessarily a linear relationship. The sum of squares for regression (option D) being relatively large could indicate a strong linear relationship between the variables if the total sum of squares is also large.

In Simple Linear Regression, Which of the Following Statements Indicates