Homework SourseA researcher at a large company has collected data on the be
A researcher at a large company has collected data on the beginning salary and current salary of 48 randomly selected employees. The least-squares regression equation for pre- dicting their current salary from their beginning salary is yˆ = 2532.7 + 2.12x.
(a) The current salaries had a mean of $32,070 with a standard deviation of $15,300. The beginning salaries had a mean of $16,340 with a standard deviation of $5,970. What is the correlation between current and beginning salary?
(b) Mr. Joseph Keller started working for the company earning $22,000. What do you predict his current salary to be?
(c) Mrs. Kathy Jones started working for the company earning $19,000. She currently earns $40,000. What is the residual for Mrs. Jones?
Solution
The regression equation of y on x is given by
Y = ybar + byx(x-xbar) where byx = correlation(x,y) *sd(y)/sd(x)
(a)
Comparing the given equation with the above form
byx = 2.12
=> r(x,y) *sd(x)/sd(y) =2.12
=> r(x,y)*5970/15300 = 2.12
=> r(x,y) = .8272
(b)
The predicted value of current salary for Mr. Joseph Keller is obtained by putting x=$22000 in the given equation.
Thus Y = -2532.7 + 2.12*22000 = $44107.3
(c)
The predicted current salry of Mrs. Kathy Jones is
Y = -2532.7 + 2.12*19000 = 37747.3
It is given that actual y = 40000
Hence the residual in prediction is res = y - Y= $(40000 - 37747.3) = 2252.7
