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# Linear regression questions

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A company has purchased several new, highly sophisticated machines. The production department needed some guidance with respect to qualifications needed by an operator. Is age a factor? Is the length of service as a machine operator important? In order to explore further the factors needed to estimate performance on the new machines, four variables are listed:

X1 = length of time employee was a machinist
X2 = Mechanical aptitude test score
X3 = prior on the job training
X4 = age in years

Performance of the new machine is designated Y.

Thirty machinists were selected at random. Data were collected for each and their performances on the new machines were recorded. The following regression equation was calculated:

Y^ = 11.6 + 0.4x1 + 0.286x2 + 0.112x3 + 0.002x4
(9.6) (0.772) (.75) (0.028) (0.0001)

NOTE: standard errors are in parenthesis.

1. Carl applied for a job on a new machine. He has been a machinist for six years and he scored 280 on the mechanical aptitude test. Carl's prior on-the-job performance rating is 97 and he is 35 years old. Estimate Carl's performance on the new machine.

2. Is mechanical aptitude test score significantly related to performance? Test using level of significance as 0.05. State the hypothesis to be tested, the decision rule, the test statistic and the decision.

3. Interpret the estimated coefficients on mechanical aptitude test score and prior on-the-job rating.

4. As age increases by one year, how much does estimated performance on the new machine increase, holding the other variables constant? Does the estimate seem reasonable?

5. It is argued by the machinists union that for each additional point increase in prior on-the-job rating, performance of the new machine will increase by only 0.05 units, and hence the prior on the job rating would not be an important determinate of future performance on a new machine. What does the data from the Company suggest about this statement? Level of significance is 0.05. State the hypothesis to be tested, the decision rule, the test statistic and the decision.

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#### Solution Preview

I have provided detailed solutions to the 5 questions in the attached Word document.

A company has purchased several new, highly sophisticated machines. The production department needed some guidance with respect to qualifications needed by an operator. Is age a factor? Is the length of service as a machine operator important? In order to explore further the factors needed to estimate performance on the new machines, four variables are listed:

X1 = length of time employee was a machinist
X2 = Mechanical aptitude test score
X3 = prior on the job training
X4 = age in years

Performance of the new machine is designated Y.

Thirty machinists were selected at random. Data were collected for each and their performances on the new machines were recorded. The following regression equation was calculated:

Y^ = 11.6 + 0.4x1 + 0.286x2 + 0.112x3 + 0.002x4
(9.6) (0.772) (.75) (0.028) (0.0001)

NOTE: standard errors are in parenthesis.

1. Carl applied for a job on a new machine. He has been a machinist for six years and he scored 280 on the mechanical aptitude test. Carl's prior on-the-job performance rating is 97 and he is 35 years old. Estimate Carl's performance on the new machine.

Carl's estimated performance is calculated by substituting his 4 values into the regression equation. In Carl's case:

X1 = 6
X2 = 280
X3 = 97
X4 = 35

So,

Y^ = 11.6 + 0.4*(6) + 0.286*(280) + 0.112*(97) + ...

#### Solution Summary

This solution gives detailed explanations along with the answers to five questions regarding a given linear regression model.

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