Share
Explore BrainMass

Analyze mileage and vehicle weight vs miles per gallon data

See attached file.

Using Data set 'G', choose the dependent variable (the response variable to be 'explained') and the independent variable (the predictor or explanatory variable) as you judge appropriate. Use a spreadsheet or a statistical package (e.g., MegaStat or MINITAB) to obtain the bivariate regression and required graphs. Write your answers to exercises 12.28 through 12.43 (or those assigned by your instructor) in a concise report, labeling your answers to each question. Insert tables and graphs in your report as appropriate.

12.28 Are the variables cross-sectional data or time-series data?

12.31 State your a priori hypothesis about the sign of the slope. Is it reasonable to suppose a cause and effect relationship?

12.35 Use Excel, MegaStat, or MINITAB to fit the regression model, including residuals and standardized residuals.

12.36 (a) Does the 95 percent confidence interval for the slope include zero? If so, what does it mean? If not, what does it mean? (b) Do a two-tailed t test for zero slope at ? = .05. State the hypotheses, degrees of freedom, and critical value for your test. (c) Interpret the p-value for the slope. (d) Which approach do you prefer, the t test or the p-value? Why? (e) Did the sample support your hypothesis about the sign of the slope?

12.37 (a) Based on the R2 and ANOVA table for your model, how would you assess the fit? (b) Interpret the p-value for the F statistic. (c) Would you say that your model's fit is good enough to be of practical value?

DATA SET G Mileage and Vehicle weight MPG

Vehicle City MPG Weight Vehicle City MPG Weight

Acura CL 20 3,450 Land Rover 17 3,640
Acura TSX 23 3,320 Lexus IS 300 18 3,390
BMW 3 Series 19 3,390 Lincoln Aviator 13 5,000
Buick Century 20 3,350 Mazda MPV 18 3,925
Buick Rendezvous 18 4,230 Mazda 6 19 3,355
Cadillac Seville 18 4,050 Mercedes-Benz S-Class 17 4,195
Chevy Corvette 19 3,255 Mercury Sable 20 3,340
Chevy Silver1500 14 4,935 Mitsubishi Galant 20 3,285
Chevy TrailBlazer 15 4,660 Nissan 350Z 20 3,345
Chrysler Pacifica 17 4,660 Nissan Pathfinder 15 4,270
Dodge Caravan 18 4,210 Nissan Xterra 16 4,315
Dodge Ram 1500 13 5,300 Pontiac Grand Am 25 3,095
Ford Expedition 13 5,900 Pontiac Vibe 28 2,805
Ford Focus 26 2,760 Saturn Ion 24 2,855
GMC Envoy 15 4,660 Subaru Baja 21 3,575
Honda Accord 21 3,390 Suzuki Vitara XL7 17 3,590
Honda Odyssey 18 4,315 Toyota Celica 23 2,570
Hyundai Elantra 24 2,880 Toyota Matrix 26 2,985
Infinity FX 16 4,295 Toyota Sienna 19 4,120
Isuzu Ascender 15 4,965 Volkswagen Jetta 34 3,045
Jaguar XJ8 18 3,805 VolvoC70 20 3,690
Kia Rio 25 2,295

Attachments

Solution Preview

Please see the attached files.

12.28 The given data is a cross-sectional data.
12.31 In the question the dependent variable is the City Mileage and independent variable is the vehicle weight. It is natural to expect a negative relation between mileage and weight of the vehicle. Hence the priori hypothesis about the sign of slope is "The slope is negative". Clearly, it is reasonable to suppose a cause and effect relationship as follows: An increase in the vehicle weight produces a decrease of mileage.
12.35 The results of the regression analysis done by using MS Excel are given below.

SUMMARY OUTPUT

Regression Statistics

Multiple R 0.8252
R Square 0.6809
Adjusted R Square 0.6732
Standard Error 2.4989
Observations 43.0000

ANOVA
df SS MS F Significance F
Regression 1.000 546.438 546.438 87.506 0.000
Residual 41.000 256.027 6.245
Total 42.000 802.465

Coefficients Standard Error t Stat P-value Lower 95% Upper 95%
Intercept 36.634 1.879 19.493 0.000 32.838 40.429
Weight(X) -0.005 0.00049 -9.354 0.000 -0.006 -0.004

The regression Model is Y = 36.634 -0.005 X, where Y denotes the mileage and X denotes vehicle weight

RESIDUAL OUTPUT
Observation Predicted ...

Solution Summary

An analysis for mileage and vehicle weight versus mile per gallon data is examined.

$2.19