Question

The weight of a car can influence the mileage that the car can obtain. A random sample of 20 cars’ weights and mileage is collected. The table for the weight and mileage of the cars is given below. Use Excel to find the best fit linear regression equation, where weight is the explanatory variable. Round the slope and intercept to three decimal places.

Weight   Mileage
30.0   32.2
20.0   56.0
20.0   46.2
45.0   19.5
40.0   23.6
45.0   16.7
25.0   42.2
55.0   13.2
17.5   65.4
35.0   28.0
27.5   49.9
27.5   35.1
30.0   31.2
25.0   29.5
40.0   25.6
22.5   43.4
35.0   28.9
27.5   35.0
22.5   38.8
45.0   17.2

Y= ___x + ____

Answer 1

Let's assume Weight as X and mileage as Y, then

Sum of X = 635
Sum of Y = 677.6
Mean X = 31.75
Mean Y = 33.88

Sum of squares (SS_X) = 2026.25
Sum of products (SP) = -2392.8

Regression Equation = ŷ = bX + a

b = SP/SS_X = -2392.8/2026.25 = -1.1809

a = M_Y - bM_X = 33.88 - (-1.18*31.75) = 71.3736

ŷ = -1.181X + 71.374