If all the points of a scatter diagram lie on the least squares regression line, then the coefficient of determination for these variables based on this data is
A)0
B)1
C)either 1 or -1, depending upon whether the relationship is positive or negative
D)could be any value between -1 and 1

Question

Quizplus · Accepted Answer

When all the points of a scatter diagram lie on the least squares regression line, it means there is a perfect linear relationship between the two variables. In other words, there is no variability left in the data that is not explained by the regression line. Therefore, the coefficient of determination (r-squared) is equal to 1, which means that all the variability in the dependent variable can be explained by the independent variable. Hence, the correct answer is B.

If All the Points of a Scatter Diagram Lie on the Least