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. click here to view the weight and gas mileage data. (a) find the least - squares y^=□x+□ (round the x coefficient to)

Explanation:

Step1: List data pairs

x: 3703,3830,2650,3599,3242,3005,3781,2509,3527,3774
y:16,16,26,19,22,24,16,23,20,16

Step2: Calculate Σx, Σy, x̄, ȳ

Σx=33620, Σy=198
x̄=33620/10=3362, ȳ=198/10=19.8

Step3: Compute Σxy, Σx²

Σxy=650380, Σx²=115170846

Step4: Find slope b

b=(10650380 - 33620198)/(10*115170846 - 33620²)=-152960/21404060≈-0.0071

Step5: Find intercept a

a=19.8 - (-0.0071)*3362≈43.8

Answer:

ŷ = -0.0071x + 43.8