Question

DATE FILE MPG2

Mfgr/Model	HPMax	CityMPG
Acura Integra	140	25
Acura Legend	200	18
Audi 90	172	20
Audi 100	172	19
BMW 535i	208	22
Buick Century	110	22
Buick LeSabre	170	19
Buick Roadmaster	180	16
Buick Riviera	170	19
Cadillac DeVille	200	16
Cadillac Seville	295	16
Chevrolet Cavalier	110	25
Chevrolet Corsica	110	25
Chevrolet Camaro	160	19
Chevrolet Lumina	110	21
Chevrolet Lumina APV	170	18
Chevrolet Astro	165	15
Chevrolet Caprice	170	17
Chevrolet Corvette	300	17
Chrysler Concorde	153	20
Chrysler LeBaron	141	23
Chrysler Imperial	147	20
Dodge Colt	92	29
Dodge Shadow	93	23
Dodge Spirit	100	22
Dodge Caravan	142	17
Dodge Dynasty	100	21
Dodge Stealth	300	18
Eagle Summit	92	29
Eagle Vision	214	20
Ford Festiva	63	31
Ford Escort	127	23
Ford Tempo	96	22
Ford Mustang	105	22
Ford Probe	115	24
Ford Aerostar	145	15
Ford Taurus	140	21
Ford Crown Victoria	190	18
Geo Metro	55	46
Geo Storm	90	30
Honda Prelude	160	24
Honda Civic	102	42
Honda Accord	140	24
Hyundai Excel	81	29
Hyundai Elantra	124	22
Hyundai Scoupe	92	26
Hyundai Sonata	128	20
Infiniti Q45	278	17
Lexus ES300	185	18
Lexus SC300	225	18
Lincoln Continental	160	17
Lincoln Town Car	210	18
Mazda 323	82	29
Mazda Protege	103	28
Mazda 626	164	26
Mazda MPV	155	18
Mazda RX-7	255	17
Mercedes-Benz 190E	130	20
Mercedes-Benz 300E	217	19
Mercury Capri	100	23
Mercury Cougar	140	19
Mitsubishi Mirage	92	29
Mitsubishi Diamante	202	18
Nissan Sentra	110	29
Nissan Altima	150	24
Nissan Quest	151	17
Nissan Maxima	160	21
Oldsmobile Achieva	155	24
Oldsmobile Cutlass Ciera	110	23
Oldsmobile Silhouette	170	18
Oldsmobile Eighty-Eight	170	19
Plymouth Laser	92	23
Pontiac LeMans	74	31
Pontiac Sunbird	110	23
Pontiac Firebird	160	19
Pontiac Grand Prix	200	19
Pontiac Bonneville	170	19
Saab 900	140	20
Saturn SL	85	28
Subaru Justy	73	33
Subaru Loyale	90	25
Subaru Legacy	130	23
Suzuki Swift	70	39
Toyota Tercel	82	32
Toyota Celica	135	25
Toyota Camry	130	22
Toyota Previa	138	18
Volkswagen Fox	81	25
Volkswagen Eurovan	109	17
Volkswagen Passat	134	21
Volkswagen Corrado	178	18
Volvo 240	114	21
Volvo 850	168	20

Use Data Set G, Mileage and Vehicle Weight, on page 536 of your textbook to answer the following questions. The data are found in the Excel Data file, MPG2, which is posted on Canvas under Modules under Chapter 12 Textbook data. The first column (Weight) is X, or the independent, variable and the second column (City MPG) is Y, or the dependent, variable. Use MINITAB to obtain the simple regression equation, confidence interval, prediction interval, and required graphs. Insert tables and graphs in your report as appropriate.

Use Minitab and produce the appropriate output to answer the following questions. Attach the output.

1. Construct a scatter plot. Recalling what scatter plots are used for, write a couple of sentences addressing what you observed from the plot. Be sure to relate your observations to the purpose of using scatter plots in regression. (4 points)

2. Can we conclude that Weight of a vehicle helps in predicting City MPG? Follow the 7 steps for hypothesis testing. (12 points)

3. Find the sample regression equation and interpret the coefficients. Remember your interpretations should be in terms of the problem. (4 points)

4. Find the coefficient of determination, and interpret its value. (2 points)

5. Use residual analysis to check the validity of the model and fully explain your findings and conclusions. (6 points)

6. Estimate with 95% confidence the average City MPG all vehicles with a Weight of 3500 lbs. Predict with 95% confidence the City MPG for an individual vehicle with a weight of 3500 lbs. Write at least one sentence using your confidence interval and at least one sentence using your prediction interval. (10 points)

7. Verify that the p-value for the F is the same as the slope t statistic’s p-value, and show that t2 = F. (2 points)

Answer 1

Question 1

Required scatter plot is given as below:

From above scatter diagram, it is observed that there is a negative relationship exists between the given two variables HPMax and CityMPG.

Question 2

By using given data, a Minitab output for correlation coefficient is given as below:

Correlations: HPMax, CityMPG

Pearson correlation of HPMax and CityMPG = -0.673

P-Value = 0.000

H₀: ρ = 0 versus H_a: ρ ≠ 0

We are given

α = 0.05

Correlation coefficient = r = -0.673

P-value = 0.00

P-value < α = 0.05

So, we reject the null hypothesis

There is sufficient evidence to conclude that weight of a vehicle helps in predicting city MPG.

Question 3

Here, we have to find the regression equation for the prediction of the dependent variable City MPG based on the independent variable HP Max. Required regression model by using excel is given as below:

Regression Statistics
Multiple R	0.672636151
R Square	0.452439391
Adjusted R Square	0.446422242
Standard Error	4.181297473
Observations	93
ANOVA
	df	SS	MS	F	Significance F
Regression	1	1314.594274	1314.594274	75.19164813	1.53684E-13
Residual	91	1590.975619	17.48324856
Total	92	2905.569892
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%
Intercept	32.74627911	1.273229053	25.71907941	1.60204E-43	30.21716606	35.27539216
HPMax	-0.072174339	0.008323347	-8.671311788	1.53684E-13	-0.088707645	-0.055641032

The regression equation is given as below:

City MPG = 32.7463 – 0.0722*HP Max

Y = 32.7463 – 0.0722*X

Slope = -0.0722

There is a decrement of 0.0722 in the city MPG as per one unit increase in HP max.

Y-intercept = 32.7463

The value of city MPG is 32.7463 when value for HP Max is zero.

Question 4

The value of coefficient of determination or the value of R square is given as 0.452439391, which means about 45.24% of the variation in the dependent variable City MPG is explained by independent variable HP Max.