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

1.1 Problem Statement

[20-50] // 30
[3-6,3] // 4.623
[.8-1.3,3] // 1.109
[12-20]
[21-35]
[35-60]
eval(round($a + $b * $x1,3))
eval(round($a + $b * $x2,3))
eval(round($a + $b * $x3,3))
[-20 - -3]

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

y = $a + $bx

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.

1.2 Step 1

questions

Question 1.1

The slope in a regression equation represents the value that DB8eX8yodOo= is 107jI2pFGFf9afifjyK8R1b1wb67i/Fq 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 1.2

The slope of this line means that XrMEveATiHYl0wQl mileage increases by about iSba6t70dtA= when p+QuAfKR2Uk= mileage increases by 0VV1JcqyBrI= mile per gallon.

Correct.
Incorrect.

Question 1.3

The slope in this regression equation (to 3 decimal places) is: Mn7/H2oYk/BAUgn7

2
({1}=$a) 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 $b.
Right, the slope is $b.

1.3 Step 2

questions

Question 1.4

The intercept is the value, according to the regression equation, of OoQWwj+vEeo= when DB8eX8yodOo= = 1Wh3cvJ2xF4=.

2
Correct.
Try again.
Incorrect.

Question 1.5

The intercept in this regression equation (to 2 decimal places) is: DJMxM7tLNDmruLrq

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 $b.
Right, the intercept is $b.

1.4 Step 3

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

Question 1.6

city mileage: $x1 $x2 $x3
predicted highway mileage: iCOO6WQ0p4rRu2K3 plQ7h/t1K2xpXajo lHYXL5+2sZATad7+
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 1.7

UJCwV2obGOtZsl2aMuXMRHaEcU30tS5/2nVNhOVcUkFLc1M/SrXCcorw5z/NlLaZWJ+kJOWCy4Q7r00FPJqOiMjingeL46Y8atwHe55Ddrfo4b/UgXnQGlXxnQkPZWr3bCIUyduAm7yjZnaO8ENZJ0vHRbAqeKWSCfhabcKeRWyACLEKZDFWKGcTPSFoORpOPJte/m6SGxs=
10
Correct.
Incorrect.