Question

Which of the following is not a characteristic of the least-squares regression line?

a. The slope of the least-squares regression line is always between –1 and 1.

b. The least-squares regression line always goes through the point (x¯,y¯) .

c. The least-squares regression line minimizes the sum of squared residuals.

d. The slope of the least-squares regression line will always have the same sign as the correlation.

e. The least-squares regression line is not resistant to outliers.

Short answer

The correct option is (a) The slope of the least-squares regression line is always between$-1$ and $1$

Step-by-step solution

Given information

The properties of the least square regression line can be seen in five different ways.

Explanation

The equation of the regression line is:

$$\begin{gathered} \stackrel{⏜}{y}=a+bx \\ a=y-intercept \\ b=Slopecoefficient \end{gathered}$$

line's values are not limited in any way. It might be positive or negative and have any value. As a result, the slope of the regression line cannot be considered to be between $-1$and $1$

Thus, option (a) is not the characteristic of the regression line.

Hence, the correct option is (a).