EXECUTIVE SUMMARY

This analysis uses the 1974 Motor Trend data to answer the following: Is an automatic or manual transmission better for miles per gallon (MPG)? What is the difference between automatic and manual transmissions? Information about the data can be found in Appendix 1.1. The analysis indicates that when adjusting for differences in other variables, the automatic and manual transmissions had similar miles per gallon. Comparing the automatic to manual transmission they appear to have several notable differences. For example, the manual transmission has higher miles per gallon (17.1 vs 24.3), higher displacement (290 vs 143 cu.in.), and horsepower (160 vs 126). This analysis has limitations. The data set included only a small sample size (32 observations). This limits the ability to generalize beyond this analysis.

Research Question 1: Is an automatic or manual transmission better for miles per gallon (MPG)?

The dependent variable, miles per gallon, is a continuous variable, so we will use a linear regression model. The independent variable transmission is binary. It appears that some variables might be confounders and should be adjusted for in the linear rgression model. There are two models considered in this analysis:
Model 1: indicates that the manual transmission has a significantly higher mile per gallon compared to the automatic tranmission (7.245 mpg higher; p=0.0002).
Model 2: indicates that after adjusting for number of cylinders, weight, and horsepower, there is no significant difference between the manual and automatic transmission in miles per gallon.
  mpg mpg
Predictors Estimates CI p Estimates CI p
(Intercept) 17.15 14.94 – 19.35 <0.001 33.71 28.60 – 38.81 <0.001
Manual 7.24 3.79 – 10.70 <0.001 1.81 -0.93 – 4.55 0.206
6cyl -3.03 -5.79 – -0.27 0.041
8cyl -2.16 -6.64 – 2.31 0.352
wt -2.50 -4.23 – -0.76 0.009
hp -0.03 -0.06 – -0.01 0.027
Observations 32 32
R2 / adjusted R2 0.360 / 0.338 0.866 / 0.840
To compare Model 1 and Model 2, an Analysis of Variance (ANOVA) was used. The ANOVA can be found in Appendix 1.2. The p-value for the ANOVA tests whether the adjustment variables are necessary. The ANOVA indicates that Model 2 with the adjustment variables is necessary over Model 1. From these results, the adjustment variables are necessary, and adjusting for these variables indicate that there is not a significant difference in miles per gallon when comparing the automatic and manual transmissions. The residual plots of Models 1 and 2 can be found in Appendix 1.2.

Research Question 2: What is the difference between automatic and manual transmissions?

To quantify the differences between the automatic and manual transmission, descriptives methods and graphgs are used. The table provides the mean for each variable by transmission type. Graph A shows the difference in the number of cylinders by transmission type. Graph B shows the above and below average miles per gallon for each type of transmission. Graph C is a regression plot of miles per gallon on weight, by transmission type. Graph C shows the distribution of weight by transmission type. A full descriptive analysis can be found in Appendix 1.3.
1974 Motor Trend, averages by Transmission, 0=automatic, 1=manual
am mpg cyl disp hp drat wt qsec vs gear carb
0 17.14737 6.947368 290.3789 160.2632 3.286316 3.768895 18.18316 0.3684211 3.210526 2.736842
1 24.39231 5.076923 143.5308 126.8462 4.050000 2.411000 17.36000 0.5384615 4.384615 2.923077

APPENDIX

Appendix 1.1

The data comes from Henderson and Velleman (1981), which extracted data from the 1974 Motor Trend US magazine, and comprises fuel consumption and 10 aspects of automobile design and performance for 32 automobiles (1973–74 models). The variables in this data set include: Miles per gallon (mpg), Number of cylinders (cyl), Displacement cubic inch (disp), Gross horsepower (hp), Rear axle ratio (drat), Weight in 1000 lbs (wt), 1/4 mile time (qsec), Engine (vs; 0 = V-shaped, 1 = straight), Transmission (am; 0 = automatic, 1 = manual), Number of forward gears (gear), and Number of carburetors (carb). Data source: Henderson and Velleman (1981), Building multiple regression models interactively. Biometrics, 37, 391–411.

Appendix 1.2: ANOVA and Residual Plots for Question 1

anova(model1, model2)
## Analysis of Variance Table
## 
## Model 1: mpg ~ am
## Model 2: mpg ~ am + cyl + wt + hp
##   Res.Df    RSS Df Sum of Sq      F    Pr(>F)    
## 1     30 720.90                                  
## 2     26 151.03  4    569.87 24.527 1.688e-08 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
plot(model1)

plot(model2)

Appendix 1.3: Descriptive data for the data set

kable(mtcars, caption="1974 Motor Trend Car Data") %>%
  kable_styling(bootstrap_options = "striped", full_width = F, position = "left")
1974 Motor Trend Car Data
mpg cyl disp hp drat wt qsec vs am gear carb mpg_z mpg_type
Cadillac Fleetwood 10.4 8cyl 472.0 205 2.93 5.250 17.98 0 Automatic 3 4 -1.61 below
Lincoln Continental 10.4 8cyl 460.0 215 3.00 5.424 17.82 0 Automatic 3 4 -1.61 below
Camaro Z28 13.3 8cyl 350.0 245 3.73 3.840 15.41 0 Automatic 3 4 -1.13 below
Duster 360 14.3 8cyl 360.0 245 3.21 3.570 15.84 0 Automatic 3 4 -0.96 below
Chrysler Imperial 14.7 8cyl 440.0 230 3.23 5.345 17.42 0 Automatic 3 4 -0.89 below
Maserati Bora 15.0 8cyl 301.0 335 3.54 3.570 14.60 0 Manual 5 8 -0.84 below
Merc 450SLC 15.2 8cyl 275.8 180 3.07 3.780 18.00 0 Automatic 3 3 -0.81 below
AMC Javelin 15.2 8cyl 304.0 150 3.15 3.435 17.30 0 Automatic 3 2 -0.81 below
Dodge Challenger 15.5 8cyl 318.0 150 2.76 3.520 16.87 0 Automatic 3 2 -0.76 below
Ford Pantera L 15.8 8cyl 351.0 264 4.22 3.170 14.50 0 Manual 5 4 -0.71 below
Merc 450SE 16.4 8cyl 275.8 180 3.07 4.070 17.40 0 Automatic 3 3 -0.61 below
Merc 450SL 17.3 8cyl 275.8 180 3.07 3.730 17.60 0 Automatic 3 3 -0.46 below
Merc 280C 17.8 6cyl 167.6 123 3.92 3.440 18.90 1 Automatic 4 4 -0.38 below
Valiant 18.1 6cyl 225.0 105 2.76 3.460 20.22 1 Automatic 3 1 -0.33 below
Hornet Sportabout 18.7 8cyl 360.0 175 3.15 3.440 17.02 0 Automatic 3 2 -0.23 below
Merc 280 19.2 6cyl 167.6 123 3.92 3.440 18.30 1 Automatic 4 4 -0.15 below
Pontiac Firebird 19.2 8cyl 400.0 175 3.08 3.845 17.05 0 Automatic 3 2 -0.15 below
Ferrari Dino 19.7 6cyl 145.0 175 3.62 2.770 15.50 0 Manual 5 6 -0.06 below
Mazda RX4 21.0 6cyl 160.0 110 3.90 2.620 16.46 0 Manual 4 4 0.15 above
Mazda RX4 Wag 21.0 6cyl 160.0 110 3.90 2.875 17.02 0 Manual 4 4 0.15 above
Hornet 4 Drive 21.4 6cyl 258.0 110 3.08 3.215 19.44 1 Automatic 3 1 0.22 above
Volvo 142E 21.4 4cyl 121.0 109 4.11 2.780 18.60 1 Manual 4 2 0.22 above
Toyota Corona 21.5 4cyl 120.1 97 3.70 2.465 20.01 1 Automatic 3 1 0.23 above
Datsun 710 22.8 4cyl 108.0 93 3.85 2.320 18.61 1 Manual 4 1 0.45 above
Merc 230 22.8 4cyl 140.8 95 3.92 3.150 22.90 1 Automatic 4 2 0.45 above
Merc 240D 24.4 4cyl 146.7 62 3.69 3.190 20.00 1 Automatic 4 2 0.72 above
Porsche 914-2 26.0 4cyl 120.3 91 4.43 2.140 16.70 0 Manual 5 2 0.98 above
Fiat X1-9 27.3 4cyl 79.0 66 4.08 1.935 18.90 1 Manual 4 1 1.20 above
Honda Civic 30.4 4cyl 75.7 52 4.93 1.615 18.52 1 Manual 4 2 1.71 above
Lotus Europa 30.4 4cyl 95.1 113 3.77 1.513 16.90 1 Manual 5 2 1.71 above
Fiat 128 32.4 4cyl 78.7 66 4.08 2.200 19.47 1 Manual 4 1 2.04 above
Toyota Corolla 33.9 4cyl 71.1 65 4.22 1.835 19.90 1 Manual 4 1 2.29 above