Question

An engineer wants to determine how the weight of a​ car, x, affects gas​ mileage, y. The following data represent the weights of various cars and their miles per gallon. Car A B C D E Weight​ (pounds), x 2555 2900 3330 3725 4100 Miles per​ Gallon, y 21.8 20.5 19 14.2 11.6 ​(a) Find the​ least-squares regression line treating weight as the explanatory variable and miles per gallon as the response variable. Write the equation for the​ least-squares regression line.

Answer 1

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Explanation:

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Answer 2

The ecuation of the line is

y=-0.0068X+40

Explanation:

Hello!

To solve this question we must use the least-squares regression line equation, the equation is as follows

Y=mx+b

The values ​​of m and b are found using the formulas in the attached image

To solve then we will use a table that to organize and extract all the values ​​of the summations.

-Sum of X values

-Sum of Y values

- Sum of the product of X and Y

-

sum of x squared

-------X------------Y ---------(X)(Y)----------x^2

1)---- 2555------21,8 -----55699-----6528025

2)----2900------20,5----59450------8410000

3)----3330------19------- 63270-------11088900

4)---3725------14,2------52895------13875625

5)----4100-------11,6-------47560------16810000

------16610----- 87,1------278874-----56712550 SUMATORIES

Now we use the ecuation in atached image

remember that n= number of values =5

`m=(5(278874)-(16610)(87.1))/(5(56712550)-(16610)^2)=-0.0068`

`b=((87.1)(56712550)-(16610)(278874))/(5(56712550)-16610^2) =40`

The ecuation of the line is

y=-0.0068X+40