Problem

A partial computer output from a regression analy…

Problem 45 Easy Difficulty

The personnel director for Electronics Associates developed the following estimated
regression equation relating an employee's score on a job satisfaction test to his or her
length of service and wage rate.
$$\hat{y}=14.4-8.69 x_{1}+13.5 x_{2}$$
where
$$\begin{aligned} x_{1} &=\text { length of service (years) } \\ x_{2} &=\text { wage rate (dollars) } \\ y &=j o b \text { satisfaction test score (higher scores } \\ & \text { indicate greater job satisfaction) } \end{aligned}$$
$\begin{array}{l}{\text { a. Interpret the coefficients in this estimated regression equation. }} \\ {\text { b. Predict the job satisfaction test score for an employee who has four years of service and }} \\ {\text { makes } \$ 6.50 \text { per hour. }}\end{array}$

Answer

a. The job satisfaction test score decreases, on average, by 8.69 per year.
The job satisfaction test score increases, on average, by 13.5 per dollar of wage.
b. 67.39

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Chapter 13

Multiple Regression

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Video Transcript

So we're using this job satisfaction equation. So that's our predicted job satisfaction. And the bigger this number is, the more satisfied the person is with the job. And we have 14.4 minus 8.69 x one plus 13.5 ex of two. And on that first question, we have to interpret these coefficients. So if we look at this the output, I think of it in terms of slope, we know the why variable output is a score, and we know that for this particular variable were in putting the length of service, So the number of years of service. So when we input the number of years of service in here, then I plugged that number right here, and the years would cancel in. My unit would call it as a score. So for us, for this particular one, we have negative 8.69 for the score per year. So what does that tell us for every one year increase in service? That means we have a decrease of almost nine points in the score. So the longer someone works there, Apparently the score diminishes versus here. This is in putting a dollar amount the wage per hour. So a number of dollars per hour and we have the score and then the rate here would be per dollar. So we have 13.5 as our coefficient over one. So this coefficient is going to stand for for every $1 per hour. We get the the wage to go up. We have the score going up 13.5. So as dollars go up per hour are scores go up at a quite a large amount. So it doesn't look good for working there as faras years, but it looks good. Give them more money and they're happier, Happier. They're not quite so happy as they stay there longer and longer. Now we need to use this equation to predict when someone has served for 14 year Excuse me four years. So when we plug in the four in here and somebody is making 6 50 an hour and do that calculation and so that score would be about 67 67.39 or about 67.4. And again, the higher numbers would denote that somebody is happier with their their job job satisfaction. So we're done

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