Question

The standard error of estimate in linear regression will be zero when...

a. r=0
b. r= -1/+1
c. the slope of the regression line is 0
d. the slope of the regression line is 10

Answer 1

The standard error of estimate in linear regression will be zero when r=0, r=-1/+1, or the slope of the regression line is 0.

Step-by-step explanation:

The standard error of estimate in linear regression will be zero when...

1. r=0 - When the correlation coefficient, r, is 0, it indicates no linear relationship between the variables x and y. In this case, the standard error of estimate will be zero.
2. r= -1/+1 - When the correlation coefficient is -1 or +1, it indicates a perfect positive or negative linear relationship between x and y. In both cases, the standard error of estimate will be zero.
3. the slope of the regression line is 0 - When the slope of the regression line is 0, it means that there is no change in the dependent variable (y) for every unit change in the independent variable (x). In this case, the standard error of estimate will be zero.