 Making Predictions About Linear Regression - dummies

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

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

To figure out the predicted cost of a job, use the equation y = \$50x + \$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.

2. 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?

You 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 = \$240.00

Subtract 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.

3. 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?