A farmer wants to conduct a regression analysis to study the relationship betwee

Question

A farmer wants to conduct a regression analysis to study the relationship between the bushels of com per acre, Y, and the amount (in pounds) of fertilizer used per acre, X. Consider the corn produced as the dependent variable and the amount of fertilizer as the independent variable. Suppose that the sample mean and standard deviation of Y are 60 and 5 and that the sample mean and standard deviation of X are 18 and 2. Furthermore, their covariance is 12. Find the predicted amount of corn produced per acre when 20 pounds of fertilizer is used per acre. (Use the OLS estimators.) a. 60 b. 69 c. 66 d. 63 e. 57

Explanation / Answer

Solution:

option c) 66

Explanation:

Given = 60, x = 2
x = 18
cov(XY) = 12
now b = cov(XY)/x2 = 12/4
= 3
Now regression line

a = - bx
= 60 - 3(18)
= 6
y = 6 + 3x
when x = 20
y = 6+ 60 = 66

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