Question

When we standardize the values of a variable, the distribution of standardized values has a mean of 0 and a standard deviation of 1. Suppose we measure two variables X and Y on each of several subjects. We standardize both variables and then compute the least squares regression line. Suppose the slope of the least-squares regression line is 20.44. We may conclude that

a. the intercept will also be −0.44.

b. the intercept will be 1.0.

c. the correlation will be 1/−0.44.

d. the correlation will be 1.0.

e. the correlation will also be −0.44.

Short answer

The correct option is (e) the correlation will also be $-0.44$

Step-by-step solution

Given information

$$\begin{gathered} \overline{x}=\overline{y}=0 \\ {s}_x=s_y=1 \\ b=-0.44 \end{gathered}$$

Concept

$b=r\frac{s_y}{s_x}$

Explanation

$$\begin{gathered} b=r\frac{s_y}{s_x} \\ r=b\frac{s_x}{s_y} \\ =-0.44\frac{1}{1} \\ =-0.44 \end{gathered}$$

Hence, the correct option is (e).