It's easy to get caught up in all the calculations of regression. Always remember that understanding and interpreting your results is just as important as calculating them!

A building contractor examines the cost of having carpentry work done in some of his buildings in the current year. He finds that the cost for a given job can be predicted by this equation:

y= $50x+ $65

Here, *y* is the cost of a job (in dollars), and *x* is the number of hours a job takes to complete. So the cost of a given job can be predicted by a base fee of $65 per job plus a cost of $50 per hour. Assume that the scatter plot and correlation both indicate strong linear relationships.

## Sample questions

What is the predicted cost for a job that takes 4.75 hours to complete?

**Answer:**$302.50To figure out the predicted cost of a job, use the equation

*y*= $50*x*+ $65, replacing*x*with the given number of hours to complete the job. In this case,*x*= 4.75, so*y*= $50(4.75) + $65 = $302.50.How much more money do you predict a job taking 3.75 hours to complete will cost, as compared to a job taking 3.5 hours to complete?

**Answer:**$12.50You can solve this problem in two ways.

First, the slope measures the change in cost (

*Y*) for a given change in the number of hours (*X*). So you can simply calculate the change in hours (3.75 – 3.50 = 0.25), and then multiply by slope (50) to get the difference in cost, (0.25)(50) = $12.50.Second, you can calculate the costs based on both number of hours, and then take the difference. So substitute

*x*= 3.75 (hours) into the equation, and substitute*x*= 3.50 (hours) into the equation, calculate their*y*values (costs), and subtract. So you have*y*= $50(3.75) + $65 = $252.50*y*= $50(3.50) + $65 = $240.00Subtract these two values to get $252.50 – $240.00 = $12.50.

This means the job is predicted to cost $12.50 more if the hours increase from 3.50 to 3.75.

Suppose that in a different city, a similar equation predicts carpentry costs, but the intercept is $75 (the slope remains the same). What is the predicted cost for a job taking 2 hours in this city?

**Answer:**$175If the intercept is $75 while the slope remains the same, the new equation for predicting costs will be

*y*= 50*x*+ $75.In this case,

*x*= 2, so*y*= $50(2) + $75 = $175.

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