Question

An analyst at a consumer organization must develop a regression model to predict fuel economy (also referred to as gasoline mileage) of automobiles measured in miles per gallon (mpg) based on the horsepower of its engine, the weight of the car (in pounds) and the type of transmission (manual or automatic). The data for 50 randomly selected automobiles is presented in the table below. ​Fit a multiple regression model for gasoline mileage as it depends on engine horsepower, vehicle weight, and the type of transmission.

• State (here) the multiple regression equation, including your definitions of the variables.

• Present (here) a copy of the multiple regression output report.

• Explicitly define your coding of the “transmission” variable.

Transmission manual manual MPG 43.1 19.9 19.2 17.7 18.1 20.3 21.5 16.9 manual 15.5 Horsepower 48 110 105 165 139 103 115 155 142 150 71 76 65 100 84 58 88 92 139 18.5 272 automatic automatic automatic automatic automatic automatic automatic automatic automatic automatic automatic automatic automatic manual manual 110 90 63 41.5 46.6 23.7 27.2 39.1 28.0 24.0 20.2 20.5 28.0 34.7 36.1 35.7 20.2 23.9 29.9 30.4 36.0 22.6 364 27.5 33.7 66 Weight 1685 3365 3535 3445 3205 2830 3345 4360 4054 3940 2190 2044 2110 2420 2490 1455 2305 2465 3570 3155 2678 2015 1800 2015 2965 2920 2380 2850 1980 2800 2950 2560 1910 1850 2615 1965 3230 1968 2070 2985 1842 1985 2395 2720 2470 2890 2025 3465 3465 3380 manual manual 80 85 90 65 67 74 110 87 95 75 67 100 67 120 60 70 116 75 68 88 82 80 88 79 85 65 105 32.9 38.0 24.2 38.1 automatic automatic automatic automatic automatic automatic automatic automatic automatic automatic automatic automatic automatic automatic automatic automatic automatic 39.4 25.4 31.3 34.1 34.0 31.0 27.4 22.3 28.0 17.6 34.4 20.6 manual manual manual manual

Answer 1

An analyst at a consumer organization must develop a regression model to predict fuel economy (also referred to as gasoline mileage) of automobiles measured in miles per gallon (mpg) based on the horsepower of its engine, the weight of the car (in pounds) and the type of transmission (manual or automatic). The data for 50 randomly selected automobiles is presented in the table below. ​Fit a multiple regression model for gasoline mileage as it depends on engine horsepower, vehicle weight, and the type of transmission.

1) To do the regression equation we do the following steps in MINITAB:

1. Enter the given values in different columns.

2. Go to “Stat” then “Regression” then “Regression” then “Fit regression model”.

3. Enter MPG in “response” and HorsePower, Weight, Transmission in “continuous predictor”.

4. Click OK.

Thus we get the following output:

MPG = 55.19 - 0.1404 Horsepower - 0.00471 Weight - 3.35 Transmission

The definitions of the variables are fuel economy (also referred to as gasoline mileage) of automobiles measured in miles per gallon (mpg) based on the horsepower of its engine, the weight of the car (in pounds) and the type of transmission (manual or automatic).

2) Here we have to present a copy of the multiple regression output:

Analysis of Variance

Source          DF Adj SS Adj MS F-Value P-Value
Regression       3 2409.1 803.04    42.82    0.000
Horsepower     1   224.9 224.86    11.99    0.001
Weight         1   154.3 154.30     8.23    0.006
Transmission   1   121.9 121.90     6.50    0.014
Error           46   862.7   18.75
Total           49 3271.8

Model Summary

      S    R-sq R-sq(adj) R-sq(pred)
4.33070 73.63%     71.91%      67.46%

Coefficients

Term              Coef SE Coef T-Value P-Value   VIF
Constant         55.19     2.51    22.01    0.000
Horsepower     -0.1404   0.0405    -3.46    0.001 3.17
Weight        -0.00471 0.00164    -2.87    0.006 3.25
Transmission     -3.35     1.31    -2.55    0.014 1.08

Regression Equation

MPG = 55.19 - 0.1404 Horsepower - 0.00471 Weight - 3.35 Transmission

Fits and Diagnostics for Unusual Observations

                            Std
Obs    MPG    Fit Resid Resid
4 17.70 12.47   5.23   1.45     X
13 46.60 36.14 10.46   2.48 R
49 34.40 26.41   7.99   2.18 R X

R Large residual
X Unusual X

3) Here we consider the transmission variable as a dummy variable so to compute the coefficient for regression we take manual=1 and automatic=0 and make the column transmission.