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(3.059 + 1.110 * 13,3))
eval(round(3.059 + 1.110 * 21,3))
eval(round(3.059 + 1.110 * 54,3))
[-20 - -3]

We expect a car’s highway gas mileage to be related to its city gas mileage. Suppose that we collect data on 26 vehicles manufactured by one particular automaker and calculate the following regression line:

y = 3.059 + 1.110x

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.

Question 2

The slope of this line means that mileage increases by about when mileage increases by mile per gallon.

Correct.
Incorrect.

Question 3

Explain in your own words what the slope represents
Model answer goes here...

Question 4

The slope in this regression equation (to 3 decimal places) is:

2
({1}=3.059) No, that's the intercept.
That's not it. Remember that the slope is the value that x is multiplied by in the regression equation.
No, the slope is 1.110.
Right, the slope is 1.110.

 
Step 2

questions

Question 5

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

2
Correct.
Try again.
Incorrect.

Question 6

The intercept in this regression equation (to 2 decimal places) is:

2
That's not it. Remember that the intercept is the value, according to the regression equation, of y when x = 0.
No, the intercept is 1.110.
Right, the intercept is 1.110.

 
Step 3

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

Question 7

city mileage: 13 21 54
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 8

Would it make any sense to calculate a predicted y value for x = -6 using this regression equation? Explain why or why not.
10
Correct.
Incorrect.