The standard error of estimate in linear regression will be zero when.
A)r = zero
B)r = -1.00 or +1.00
C)the slope of the regression line is 0.00
D)the slope of the regression line is 1.00

Question

Quizplus · Accepted Answer

The standard error of estimate, also known as the standard deviation of the residuals, measures the amount of variation around the regression line. Therefore, it can only be zero if there is no variation, which occurs when the correlation coefficient (r) equals -1 or +1. In these cases, all the data points fall perfectly on a straight line, and there are no residuals left to estimate the error. The slope of the regression line and the correlation coefficient are related but distinct, so choice C and D are not necessarily equivalent to choice B. Choice A is incorrect because r = 0 means there is no linear association, but it doesn't imply a lack of residual variation.

The Standard Error of Estimate in Linear Regression Will Be