Chapter 3, Problem 8PT

To determine

To find: the conclusion of the given data

Answer to Problem 8PT

Option (e) is the correct one

Explanation of Solution

Given:

The least-squares regression line is $-0.44$ .

Mean 0 and standard deviation 1

(a) The correlation will be $1/-0.44$ .

(b) The intercept will also be $-0.44$ .

(c) The intercept will be 1.0.

(d) The correlation will be 1.0.

(e) The correlation will also be $-0.44$ .

Calculation:

The slope of the least - square regression is defined as follows:

  $b=r\frac{s_X}{s_Y}$

Substituting the standard deviations of standardized X and Y variables, we get $b=r$ since $s_X=s_Y=1$

In other words, the slope is equal to the correlation.

Here, slope of the least-squares regression line is given as $-0.44$ . Then, we may conclude that the correlation will also be $-0.44$ .

Conclusion:

Therefore, the conclusion will be the correlation which is $-0.44$ .