Groups of cars to compare:
Minitab Project
MATH-408: Probability and Statistics
David Sickmiller
Dr. B. Dimitrov
Tuesday, December 18, 2001
11:15-12:15 class
Introduction
When purchasing a car, in addition to price, there are several factors to consider. With each make, model, year, and engine option one gets a different car. This car will have its own combination of characteristics such as fuel economy, horsepower, acceleration time, and weight. Buyers may have different priorities in mind when shopping for a car. High fuel economy will save gas money and be healthier for the environment, but a fast acceleration time may provide more excitement while driving.
The objective of this project is to identify cars that have both high performance and good fuel economy. We will analyze the data various ways looking for vehicles that accelerate faster than is normal for their fuel economy. In order to manage the large amount of data, we will frequently group the cars together to make assumptions.
Groupings of cars for comparison:
• Different number of cylinders
• Origin
Characteristics to compare:
• MPG
• Acceleration (0-60 MPH)
Statistics and Distribution of Characteristics
First, we will examine the distribution of the MPG and 0-60MPH characteristics of the cars. To help narrow down the search, we will separate the data by origin (American, European, or Japanese) and by the number of cylinders in the engines. This will help us discover what general type of car we are looking for.
MPG
Miles per gallon (MPG) is analyzed below. The graphs are histograms that have been fitted with a normal curve. Descriptive numeric statistics are below the graphs.
|Origin |N |N* |
| |St. Dev. |95% C.I. |St. Dev |95% C.I. |
|American |6.403 |( 19.288, 20.879) |2.805 |( 14.598, 15.288) |
|European |6.724 |( 26.316, 29.467) |3.011 |( 16.131, 17.513) |
|Japanese |6.090 |( 29.108, 31.794) |1.955 |( 15.741, 16.603) |
Two of our hypotheses from earlier were: Japanese cars have higher MPG than American cars, and American cars have lower acceleration times than Japanese cars. The data seem to support this because the confidence intervals agree and do not overlap.
Regression
Regression gives us the most help in determining which cars stand out as having a good combination of acceleration and MPG. Below is Minitab’s regression analysis:
The regression equation is acceleration = 12.1 + 0.148 mpg
398 cases used 8 cases contain missing values
Predictor Coef StDev T P
Constant 12.0811 0.3986 30.31 0.000
mpg 0.14829 0.01609 9.22 0.000
S = 2.505 R-Sq = 17.7% R-Sq(adj) = 17.5%
Analysis of Variance
Source DF SS MS F P
Regression 1 533.31 533.31 84.96 0.000
Residual Error 396 2485.82 6.28
Total 397 3019.12
Unusual Observations
Obs mpg accelera Fit StDev Fit Residual St Resid
7 32.7 11.400 16.930 0.194 -5.530 -2.21R
33 44.6 13.800 18.695 0.362 -4.895 -1.97 X
41 46.6 17.900 18.991 0.392 -1.091 -0.44 X
99 30.0 21.800 16.530 0.163 5.270 2.11R
108 19.0 21.900 14.899 0.145 7.001 2.80R
109 27.2 24.800 16.115 0.139 8.685 3.47R
135 43.1 21.500 18.472 0.339 3.028 1.22 X
138 26.0 21.000 15.937 0.132 5.063 2.02R
140 23.0 23.500 15.492 0.126 8.008 3.20R
147 43.4 23.700 18.517 0.344 5.183 2.09RX
148 44.0 24.600 18.606 0.353 5.994 2.42RX
150 41.5 14.700 18.235 0.315 -3.535 -1.42 X
151 44.3 21.700 18.650 0.357 3.050 1.23 X
154 15.0 8.500 14.305 0.186 -5.805 -2.32R
159 23.0 20.500 15.492 0.126 5.008 2.00R
182 17.0 21.000 14.602 0.164 6.398 2.56R
217 29.0 22.200 16.382 0.153 5.818 2.33R
221 28.8 11.300 16.352 0.152 -5.052 -2.02R
225 14.0 9.000 14.157 0.198 -5.157 -2.06R
246 24.5 22.100 15.714 0.127 6.386 2.55R
282 32.0 11.600 16.826 0.185 -5.226 -2.09R
307 18.0 21.000 14.750 0.154 6.250 2.50R
316 15.0 19.500 14.305 0.186 5.195 2.08R
337 9.0 18.500 13.416 0.265 5.084 2.04R
345 15.0 21.000 14.305 0.186 6.695 2.68R
352 23.9 22.200 15.625 0.126 6.575 2.63R
362 14.0 8.000 14.157 0.198 -6.157 -2.47R
369 14.0 8.500 14.157 0.198 -5.657 -2.27R
R denotes an observation with a large standardized residual
X denotes an observation whose X value gives it large influence.
Conclusion
Now we know which cars we want! Observations #7, 33, 41, 150, 154, 221, 225, 282, 362, and 369 stand out from the rest of the data. Their residual and standard residual is negative which means they belong in the bottom-right of the scatterplot. Those observation numbers translate to these cars:
• 1980 Datsun 280ZX 32.7 MPG 11.4 sec.
• 1980 Honda Civic 1500 GL 44.6 MPG 13.8 sec.
• 1980 Mazda GLC 46.6 MPG 17.9 sec.
• 1980 VW Rabbit 41.5 MPG 14.7 sec.
• 1970 AMC Ambassador DPL 15.0 MPG 8.5 sec.
• 1979 Chevrolet Citation (V6) 28.8 MPG 11.3 sec.
• 1970 Chevrolet Impala 14.0 MPG 9.0 sec.
• 1982 Dodge Rampage 32.0 MPG 11.6 sec.
• 1970 Plymouth 'Cuda 340 14.0 MPG 8.0 sec.
• 1970 Plymouth Fury III 14.0 MPG 8.5 sec.
The regression equation equations, as stated above, says that for every second above 12 seconds, there should be an additional .148 seconds for each mile per gallon. The Ambassador, Impala, ‘Cuda, and Fury are so fast that it does not matter very much how fuel-efficient they are. And the high fuel efficiency of the Mazda GLC at 46.6MPG means the expected acceleration should be 18.9 seconds. However, the cars in the middle are still quite respectable by 2001 standards. The Datsun 280ZX, Chevy Citation, and Dodge Rampage all have about 30 MPG and mid-11 second times. I would recommend these cars for the consumer interested in both performance and fuel conservation.
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