Question

Regional Rent-A-Car is interested in studying how weight of a vehicle is related to the fuel efficiency for

several of its rental vehicles.
A random sample of 13 vehicles from Regional Rent-A-Car yielded the data in the table.
Weight (in pounds)
2000
3123
3775
2287
4000
2485
2114
2433
2525
2889
3186
3258
3622
Fuel Efficiency (in miles per gallon)
32.7
22.8
18.6
26.1
18.4
26.2
33.1
28.3
26.2
22.5
20.9
21.3
18.1

Answer 1

Explanation:

SolutionFinal answers are given below.

Back-up Theory and Details of calculations follow at the end.

Part (a)

Estimate of the slope for the least-squares regression line = - 0.0073 Answer 1

InterpretationFor every increase of 1 pound in car’s weight, the fuel efficiency would reduce by 0.0073 mpg. Answer 2

Part (b)

Correlation coefficient, r = - 0.9438 Answer 3

Interpretation An r-value of - 0.9438 indicates that there is a strong inverse linear relation between car’s weight and fuel efficiency.

Negative sign implies that as car’s weight increases, the fuel efficiency would come down.Answer 4

Part (c) The estimated regression equation is: Fuel efficiency = 45.4705 – 0.0073 x car’s weight. Substituting car’s weight = 2684 in the above equation, the estimated fuel efficiency = 25.83.So, residual = 24.5 – 25.84 = - 1.23.

Thus, Residual for a car weighing 2684 pounds and having an average fuel efficiency of 24.5 mpg= - 1.23 Answer 5

Part (d)

Substituting fuel efficiency = 20.2 in the above regression equation, the estimated car’s weight = 3461Estimate of the weight of a car whose fuel efficiency is 20.2 mpg = 3461 pounds Answer 6