Chapter 1. Tutorial 5.1: Estimating y from x given a regression line equation

Problem Statement

[20-50] // 30
[3-6,3] // 4.623
[.8-1.3,3] // 1.109
[12-20]
[21-35]
[35-60]
eval(round(4.543 + 0.986 * 20,3))
eval(round(4.543 + 0.986 * 27,3))
eval(round(4.543 + 0.986 * 36,3))
[-20 - -3]

We expect a car’s highway gas mileage to be related to its city gas mileage. Suppose that we collect data on 34 vehicles manufactured by one particular automaker and calculate the following regression line:

y = 4.543 + 0.986x

where y is highway mileage and x is city mileage.

Use this regression line equation to calculate the predicted highway mileage for three new car models produced by this automaker.

Step 1

questions

Question 1

The slope in a regression equation represents the value that is by in the regression equation.

1
No. The slope is the value that x is multiplied by in the regression equation.
You've got it.

Step 2

questions

Question 4

The intercept is the value, according to the regression equation, of when = .

2
Correct.
Try again.
Incorrect.

Step 3

Calculate predicted highway mileages for car models with the following three city mileages (round each prediction to 3 decimal places):

Question 6

city mileage: 20 27 36
predicted highway mileage:
2
Great job!
Remember: to calculate a predicted value for y, multiply x by the slope of the regression equation, then add the intercept.
Incorrect. See the table for correct answers.

Question 7

Would it make any sense to calculate a predicted y value for x = -16 using this regression equation? Explain why or why not.
10
Correct.
Incorrect.