Question

A researcher at a large company collected data on the beginning salary and current salary of 48 randomly selected employees. The beginning salaries had a mean of $16,340 with a standard deviation of $5,970. The current salaries had a mean of $32,070 with a standard deviation of $15,300. The least-squares regression equation for predicting current salary (y) from beginning salary (x) is: predicted salary (y) = LaTeX: -2532.7+2.12x− 2532.7 + 2.12 x

A. Joseph Keller started working for the company earning $22,000. What do you predict his current salary to be? Round answer to the nearest dollar.

B. Use the summary statistics for current and beginning salaries and the least squares regression coefficients to find the correlation between current and beginning salary. for B: Round answer to four (4) decimal places.

Answer 1

The least-square regression equation for predicting current salary(y) using beginning salary (x) is:

y = -2532.7 + 2.12*x

Hence, = -2532.7 and = 2.12

Part A) - Joseph keller started working for the company earning $22,000.

x = 22000

We can use the given least-square regression equation to predict the current salary.

current salary = y = -2532.7 + 2.12*22,000 = -2532.7 + 46640 = 44,107.3 = $44,107

Hence, the predicted current salary of Joseph is $44,107.

Part B) -  We know the formula for least-square estimates of regression coefficients as:

Correlation Coefficient between current and beginning salary = r = =

Given, = 2.12 SD(x) = 5,970 SD(y) = 15,300

Hence, the value of correlation between current and beginning salary is 0.8272

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