Question

You are a personnel director and are interested in predicting the Number of Shares of Company Stock (Y) using the Number of Years Employed with the Company (X). You randomly selected 8 employees and found that the average number of shares is 525 and the average number of years employed is 22.5. If the slope (b1) is 20.0, what is the least squares estimate of the intercept (b0)?

a. 25.0
b. 75.0
c. 40.0
d. 80.5
e. None of these are correct

Answer 1

b. 75.0

Explanation:

Calculation for the least squares estimate of the intercept (b0)

Using this formula

Intercept (b0) least squares estimate=[Shares average number-(Slope (b1)*Average number of years employed)]

Let plug in the formula

Intercept (b0) least squares estimate=[525-(20.0*22.5)]

Intercept (b0) least squares estimate=525-450

Intercept (b0) least squares estimate=75.0

Therefore the least squares estimate of the intercept (b0) will be 75.0