Solution:

Regression equation y on x:

The regression equation y on x can be written as:

Y = a + bx

Where,

Y = dependent variable
X = independent variable
a = intercept of the line on the Y-axis
b = slope of the line

Regression equation x on y:

The regression equation x on y can be written as:

X = a + by

Where,

X = dependent variable
Y = independent variable
a = intercept of the line on the X-axis
b = slope of the line

Finding BYX:

BYX is the slope of the regression line of x on y. We can find BYX by using the formula:

BYX = r * (Sy / Sx)

Where,

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

Step-by-Step Solution:

1. Finding the correlation coefficient:

r = ∑((x - mean of x) * (y - mean of y)) / (n - 1) * Sx * Sy

Given, Y = 19 - 5X/2

Comparing with the equation Y = a + bx, we can find:

a = 19
b = -5/2

Therefore, the mean of x and y can be calculated as:

Mean of x = (0 + 1 + 2 + 3 + 4 + 5) / 6 = 2.5
Mean of y = (19 + 16.5 + 14 + 11.5 + 9 + 6.5) / 6 = 12.5

Using the formula, we can calculate the correlation coefficient as:

r = ∑((x - 2.5) * (y - 12.5)) / (6 - 1) * 1.71 * 4.41

r = -0.987

2. Finding the standard deviation of x and y:

Using the formula,

Sy = √∑((y - mean of y)^2) / (n - 1)
Sx = √∑((x - mean of x)^2) / (n - 1)

We can calculate the standard deviation of x and y as:

Sy = √[((19 - 12.5)^2 + (16.5 - 12.5)^2 + (14 - 12.5)^2 + (11.5 - 12.5)^2 + (9 - 12.5)^2 + (6.5 - 12.5)^2) / (6 - 1)] = 4.41

Sx = √[(10/6) * (1^2 + 1^2 + 1^2 + 1^2 + 1^2 + 1^2)] = 1.71

3. Finding BYX:

Using the formula,

BYX = r * (Sy / Sx)

We can calculate the BYX as:

BYX = -0.987 * (4.41 / 1.71) = -2.541

Therefore, the value of BYX is -2.541.

Answer: -2.541

-5/2