Question

A consumer Organization want to develop a regression model to predict gasoline mileage (as measured by miles per gallon) based on horsepower of the car's engine and the weight of the car, in pounds. A sample of 50 percent recent car models was selected, with the results recorded.

1. State the multiple regression equation.

2. Interpret the meaning of the slopes, b and b2 in this problem.

3. Explain why the regression coefficient b0, has no practical meaning in the context of this problem

4. Predict the mean miles per gallon for cars that have 60 horsepower and weigh 2000 pounds.

MPG	Horsepower	Weight
43.1	48	1985
19.9	110	3365
19.2	105	3535
17.7	165	3445
18.1	139	3205
20.3	103	2830
21.5	115	3245
16.9	155	4360
15.5	142	4054
18.5	150	3940
27.2	71	3190
41.5	76	2144
46.6	65	2110
23.7	100	2420
27.2	84	2490
39.1	58	1755
28.0	88	2605
24.0	92	2865
20.2	139	3570
20.5	95	3155
28.0	90	2678
34.7	63	2215
36.1	66	1800
35.7	80	1915
20.2	85	2965
23.9	90	3420
29.9	65	2380
30.4	67	3250
36.0	74	1980
22.6	110	2800
36.4	67	2950
27.5	95	2560
33.7	75	2210
44.6	67	1850
32.9	100	2615
38.0	67	1965
24.2	120	2930
38.1	60	1968
39.4	70	2070
25.4	116	2900
31.3	75	2542
34.1	68	1985
34.0	88	2395
31.0	82	2720
27.4	80	2670
22.3	88	2890
28.0	79	2625
17.6	85	3465
34.4	65	3465
20.6	105	3380

Answer 1

1)

Regression Equation

MPG = 58.16 - 0.1175 Horsepower - 0.00687 Weight

2) Interpreting Coefficient of Horsepower: For unit increase in Horsepower,  MPG for cars is expected to decrease by  0.1175 units, when Weight is kept fixed.

Interpreting Coefficient of Weight: For unit increase in Weight,  MPG for cars is expected to decrease by  0.00687 units, when Horsepower is kept fixed.

3) If Horsepower=0 and Weight=0, we get predicted MPG=58.16, which is absurd because, we can not get a car with zero weight having zero Horsepower. Hence b0 has no practical meaning in this context.

4)  Predicted mean miles per gallon for cars that have 60 horsepower and weigh 2000 pounds is  58.16 - 0.1175 *60 - 0.00687 *2000=37.37 MPG