Question

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 predicting their current salary from their beginning salary is ˆy = −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?

Answer 1

a) The least Square regession eqiation for predicting the current salary from their beginning salary is

Where the slope is called as regression coefficient for the linear equation Y on X

b₁ = 2.12

The relatioship between Regeression Coefficient and Correlation Coefficient is

b) When X = 22000

The predicted current salary of Mr. Joseph is

Answer: Predicted Current Salary is $44,107.3

c) When X = 19000

The predicted current earnings of Mrs. Kathy Jones is

Her Observed Current earning is Y =$40,000

The Residual for Mrs. Jones is