Question

An engineer wants to determine how the weight of a​ gas-powered car,​ x, affects gas​ mileage, y. The accompanying data represent the weights of various domestic cars and their miles per gallon in the city for the most recent model year. Complete parts​ (a) through​ (d) below. Weight (pounds), x Miles per Gallon, y 3773 17 3793 16 2706 25 3645 20 3308 22 2908 24 3675 17 2687 24 3522 18 3827 16 a) Find the​ least-squares regression line treating weight as the explanatory variable and miles per gallon as the response variable y= x+( ) A certain​ gas-powered car weighs 3511 pounds and gets 18 miles per gallon. Is the miles per gallon of this car above average or below average for cars of this​ weight? ​The estimated average miles per gallon for cars of this weight is ( ) miles per gallon. The miles per gallon of this car is average for cars of this weight.

Answer 1

y= 0.007x- 4.945

The estimated average miles per gallon for cars of this weight is (20.829 or 21 ) miles per gallon.

The miles per gallon of this car below (18 < 20.829) the average for cars of this weight.

Explanation:

Weight Miles

(pounds), x per Gallon, y xy

3773 17 64,141

3793 16 60,688

2706 25 67,650

3645 20 72,900

3308 22 72,776

2908 24 69,792

3675 17 62,745

2687 24 64,488

3522 18 63,396

3827 16 61,232

∑y²=4075; ∑y=199; ∑x²= 116,406,174 ; ∑x=33,844 ; ∑xy=659,808

b= n∑XY - (∑X)(∑Y)/ n∑X² - (∑X)²

b=(10) (659,808) - (33,844)(199)/ 10 (116,406,174) - 1,145,416,336

b=6,598,080- 6,734,956/ 1,164,061,740 -1,145,416,336

b=136,876/18,645,404

b= 0.007341

a= Y`- bX`

a= 19.9- (0.007341) (3384.4)

a= 19.9 -24.845

a=-4.945

Y^= -4.945+ ( 0.007341) X

y= 0.007x- 4.945

Putting the values

y= 0.007x- 4.945

18 = 0.007(3511) - 4.945

18< 20.829

​The estimated average miles per gallon for cars of this weight is (20.829 or 21 ) miles per gallon.

The miles per gallon of this car below (18 < 20.829) the average for cars of this weight.