The personnel director for a small manufacturing company has collected the data found in the file Manufacturing.xlsx describing the salary (Y) earned by each machinist in the factory along with the average performance rating (X₁) over the past 3 years, the years of service (X₂), and the number of different machines each employee is certified to operate (X₃).

The personnel director wants to build a regression model to estimate the average salary an employee should expect to receive based on his or her performance, years of service, and certifications.

a. Prepare three scatter plots showing the relationship between the salaries and each of the independent variables. What sort of relationship does each plot suggest?

The input in the box below will not be graded, but may be reviewed and considered by your instructor.

b. If the personnel director wanted to build a regression model using only one independent variable to predict the salaries, what variable should be used?

1. Average performance rating (X₁)
2. Years of service (X₂)
3. Number of certifications (X₃)

Select IIIIIIItem 2

What is its R² value? Round your answer to one decimal place. %

c. If the personnel director wanted to build a regression model using only two independent variables to predict the salaries, what two variables should be used?

1. Average performance rating (X₁)
2. Years of service (X₂)
3. Number of certifications (X₃)

SelectI and IIII and IIII and IIIItem 4

What is its adjusted-R² value? Round your answer to one decimal place. %

d. Compare the adjusted-R² statistics obtained in parts b and c with that of a regression model using all three independent variables. Which model would you recommend the personnel director use?

1. X₂
2. X₂ & X₃
3. X₁, X₂ & X₃

Select IIIIIIItem 6

What is its adjusted-R² value? Round your answer to one decimal place. %

e. Suppose the personnel director chooses to use the regression function with all three independent variables. What is the estimated regression function?

If required, round your answers to two decimal places. For subtractive or negative numbers use a minus sign even if there is a + sign before the blank. (Example: -300)

= + X₁ + X₂ + X₃

f. Suppose the company considers an employee's salary to be fair if it is within 1.5 standard errors of the value estimated by the regression function in part e. What salary range would be appropriate for an employee with 12 years of service, who has received average reviews of 4.5, and is certified to operate 4 pieces of machinery? Round your answers to a whole dollar amount.

$ to $