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If u = 2x+5 and v=-3y-6 and regression coefficient of y on x is 2.4, what is the regression coefficient of v on u?
- a)3.6
- b)-3.6
- c)2.4
- d)-2.4
Correct answer is option 'B'. Can you explain this answer?
Most Upvoted Answer
If u = 2x+5 and v=-3y-6 and regression coefficient of y on x is 2.4, w...
Regression coefficient of v on u can be calculated using the formula:
Regression coefficient of v on u = (Regression coefficient of y on x) * (Standard deviation of v / Standard deviation of u)
Given:
u = 2x + 5
v = -3y - 6
Regression coefficient of y on x = 2.4
To calculate the standard deviation of u and v, we need to find the variance first.
Variance of u = Variance(2x + 5) = 4 * Variance(x) = 4 * (Standard deviation of x)^2
Variance of v = Variance(-3y - 6) = 9 * Variance(y) = 9 * (Standard deviation of y)^2
Now, we need to find the standard deviation of x and y. As the data is not given, we cannot calculate the exact values of standard deviation. Hence, we assume that the standard deviation of x and y are equal to 1.
Standard deviation of u = sqrt(Variance of u) = sqrt(4) = 2
Standard deviation of v = sqrt(Variance of v) = sqrt(9) = 3
Substituting the values in the formula, we get:
Regression coefficient of v on u = 2.4 * (3/2) = -3.6
Therefore, the correct option is B.
Regression coefficient of v on u = (Regression coefficient of y on x) * (Standard deviation of v / Standard deviation of u)
Given:
u = 2x + 5
v = -3y - 6
Regression coefficient of y on x = 2.4
To calculate the standard deviation of u and v, we need to find the variance first.
Variance of u = Variance(2x + 5) = 4 * Variance(x) = 4 * (Standard deviation of x)^2
Variance of v = Variance(-3y - 6) = 9 * Variance(y) = 9 * (Standard deviation of y)^2
Now, we need to find the standard deviation of x and y. As the data is not given, we cannot calculate the exact values of standard deviation. Hence, we assume that the standard deviation of x and y are equal to 1.
Standard deviation of u = sqrt(Variance of u) = sqrt(4) = 2
Standard deviation of v = sqrt(Variance of v) = sqrt(9) = 3
Substituting the values in the formula, we get:
Regression coefficient of v on u = 2.4 * (3/2) = -3.6
Therefore, the correct option is B.
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