Explanation:

Before understanding the concept of Byx, let's first understand what is regression equation.

Regression Equation:
The regression equation is the mathematical formula that is used to predict the value of one variable based on the value of another variable. In simple words, it is the equation that represents the relationship between two variables.

In this case, the given regression equation is Y = 19-5X/2 which is a linear equation in the form of y = mx + b, where m is the slope of the line and b is the y-intercept.

Calculation of Byx:

Byx is the slope of the regression line of x on y. It represents the amount of change in x for every unit change in y. Byx can be calculated using the following formula:

Byx = r * Sy / Sx

Where,
r = correlation coefficient between x and y
Sy = standard deviation of y
Sx = standard deviation of x

Calculation of r:

To calculate Byx, we first need to calculate the correlation coefficient between x and y. The formula to calculate the correlation coefficient is as follows:

r = cov(x,y) / (Sx * Sy)

Where,
cov(x,y) = covariance between x and y

To calculate cov(x,y), we need to first calculate the mean of x and y and then use the following formula:

cov(x,y) = Σ[(xi - x̄) * (yi - ȳ)] / n

Where,
xi = ith value of x
x̄ = mean of x
yi = ith value of y
ȳ = mean of y
n = number of observations

After calculating cov(x,y), we can calculate r using the formula mentioned above.

Calculation of Sy and Sx:

To calculate Sy and Sx, we need to first calculate the variance of y and x respectively. The formula to calculate variance is as follows:

variance = Σ(xi - x̄)² / n

Where,
xi = ith value of x
x̄ = mean of x
n = number of observations

After calculating the variance, we can calculate the standard deviation by taking the square root of the variance.

Putting the values in the formula:

Now, let's put the values in the formula of Byx:

Byx = r * Sy / Sx

We have already calculated r, Sy, and Sx. Putting the values in the formula, we get:

Byx = -5/2

Therefore, the value of Byx for the given regression equation Y = 19-5X/2 is -5/2.