Calculation of bvu

To calculate bvu, we need to find the coefficient of regression of V on U, which is bvu. Here, U = 2X + 3 and V = 3Y + 6.

Step 1: Calculate the coefficient of regression of Y on X (byx)
Given that byx = 1.2, it means that for every unit increase in X, Y is expected to increase by 1.2 units.

Step 2: Find the relationship between U and X
U = 2X + 3
This equation shows that U is a linear function of X, where the coefficient of X is 2 and the constant term is 3.

Step 3: Find the relationship between V and Y
V = 3Y + 6
This equation shows that V is a linear function of Y, where the coefficient of Y is 3 and the constant term is 6.

Step 4: Calculate the coefficient of regression of V on U (bvu)
To find bvu, we need to determine how V changes with respect to U. We can rewrite the equation for V as:
V = 3(2X + 3) + 6
Simplifying this equation, we get:
V = 6X + 9 + 6
V = 6X + 15

Comparing this equation with the general form of a linear equation (Y = bX + a), we can see that the coefficient of X is 6. Therefore, the coefficient of regression of V on U, bvu, is 6.

Step 5: Interpretation of bvu
The coefficient of regression of V on U (bvu) tells us that for every unit increase in U, V is expected to increase by 6 units. In other words, U is a significant predictor of V, and the relationship between U and V is positive and linear.

Summary:
The coefficient of regression of Y on X (byx) is 1.2, indicating that for every unit increase in X, Y is expected to increase by 1.2 units. By substituting U = 2X + 3 and V = 3Y + 6 into their respective equations, we find that the coefficient of regression of V on U (bvu) is 6. This indicates that for every unit increase in U, V is expected to increase by 6 units. Therefore, U is a significant predictor of V, and the relationship between U and V is positive and linear.