Solution:

Given:

Regression line of y on x: y = -2x + 3
Regression line of x on y: 8x = -y + 3

We need to find the coefficient of correlation between x and y.

Step 1: Find the slope of the regression lines

Slope of the regression line of y on x: -2
Slope of the regression line of x on y: -1/8

Step 2: Find the correlation coefficient using the formula:

r = slope of regression line of y on x / slope of regression line of x on y

Substituting the values, we get:

r = (-2) / (-1/8)
r = 16

Therefore, the coefficient of correlation between x and y is 16.

Explanation:

Correlation coefficient is a measure of the strength and direction of the linear relationship between two variables. It ranges from -1 to 1, where -1 indicates a perfect negative correlation, 0 indicates no correlation, and 1 indicates a perfect positive correlation.

To calculate the coefficient of correlation between x and y, we need to find the slope of the regression lines of y on x and x on y. The slope of the regression line of y on x gives us the change in y for every unit change in x, and the slope of the regression line of x on y gives us the change in x for every unit change in y.

The correlation coefficient is calculated by dividing the slope of the regression line of y on x by the slope of the regression line of x on y. A positive coefficient indicates a positive correlation, a negative coefficient indicates a negative correlation, and a coefficient of 0 indicates no correlation.

In this case, the slope of the regression line of y on x is -2, which means that for every unit increase in x, y decreases by 2 units. The slope of the regression line of x on y is -1/8, which means that for every unit increase in y, x decreases by 1/8 units.

Dividing the slope of the regression line of y on x by the slope of the regression line of x on y gives us a coefficient of 16, which indicates a strong positive correlation between x and y.