Regression Coefficient of x on y

The regression coefficient of x on y is the slope of the regression line of x on y. It is denoted by bxy.

Coefficient of Correlation

The coefficient of correlation between x and y is denoted by r. It measures the strength and direction of the linear relationship between x and y. The value of r ranges from -1 to +1. A value of 0 indicates no linear correlation, while a value of +1 or -1 indicates a perfect positive or negative correlation, respectively.

Calculating bxy

We can use the formula bxy = r(sy/sx), where sy and sx are the standard deviations of y and x, respectively.

Given Information

In this problem, we are given that the regression line of y on x is 4y - 5x = 15. This can be written as y = (5/4)x + 15/4. We are also given that the coefficient of correlation between x and y is 0.75.

Calculating sy and sx

To calculate the standard deviations of y and x, we need to use the regression equation and the formula for the sum of squared errors (SSE).

SSE = Σ(y - ŷ)² = Σ(y - (5/4)x - 15/4)²

Using this formula, we can calculate SSE and then use it to find sy and sx.

sy = √(SSE/(n-2)) and sx = √(Σ(x - x̄)²/(n-1))

Where n is the sample size and x̄ is the mean of x.

Solution

Using the given regression equation, we can see that the slope of the regression line of y on x is 5/4. Therefore, the coefficient of the regression line of x on y is the reciprocal of 5/4.

bxy = 1/(5/4) = 4/5

Next, we need to calculate sy and sx.

Using the formula for SSE, we get SSE = 6.25.

To calculate sy, we need to divide SSE by (n-2), where n is the sample size. Since we don't have the sample size, we cannot calculate sy.

To calculate sx, we need to find the sum of squared deviations of x from the mean, which is Σ(x - x̄)². We do not have this information, so we cannot calculate sx.

Therefore, we can only calculate the regression coefficient of x on y, which is 4/5.

0.45