Question

In: Statistics and Probability

Mileage and Vehicle Weight  (n = 73 vehicles) Vehicle Weight City MPG Acura TL 3968 20 Audi...

Mileage and Vehicle Weight  (n = 73 vehicles)
Vehicle Weight City MPG
Acura TL 3968 20
Audi A5 3583 22
BMW 4 Series 428i 3470 22
BMW X1 sDrive28i 3527 23
Buice LaCrosse 3990 18
Buick Enclave 4724 17
Buick Regal 3692 21
Cadillac ATS 3315 22
Cadillac CTS 3616 20
Cadillac Escalade 5527 14
Chevrolet Camaro 1SS 3719 16
Chevrolet Cruze LS 3097 26
Chevrolet Impala LTZ 3800 19
Chevrolet Malibu 2LT 3532 25
Chevrolet Spark LS 2269 31
Chevrolet Suburban LTZ 5674 15
Chrysler 200 Touring LX 3402 20
Chrysler 300 S 4029 19
Dodge Charger SXT 3996 19
Dodge Dart Limited 3242 23
Fiat 500 Sport 2434 31
Ford Fiesta S 2575 29
Ford Focus  SE 2960 27
Ford Mustang GT 3618 15
Ford Taurus 4054 19
Honda Accord LX 3192 24
Honda CRV LX 3305 23
Hyundai Azera Limited 3605 19
Hyundai Genesis 5.0 4240 15
Hyundai Santa Fe GLS 3933 18
Infiniti Q60 3633 19
Infiniti QX50 3790 17
Jaguar F-Type 3477 20
Jeep Compass Limited 3258 21
Jeep Grand Cherokee Limited 4685 17
Kia Forte LX 2776 25
Kia Soul 2615 24
Kia Sportage LX 3186 21
Land Rover Range Rover Sport 5137 13
Lexus IS 250 3461 21
Lexus LS 460 4233 16
Lexus RX 350 4178 18
Lincoln MKT 4702 17
Lincoln MKZ 3713 22
Lincoln Navigator 5794 14
Mazda 2 2306 28
Mazda CX-5 Sport 3194 26
Mercedes-Benz C-250 3428 22
Mercedes-Benz CL600 4894 12
Mercedes-Benz ML350 4751 17
Mini-Cooper 2605 29
Mitsubishi Outlander Sport SE 3296 25
Nissan Armada SV 5267 13
Nissan Cube S 2789 25
Nissan Maxima SV 3570 19
Nissan Murano SV 4011 18
Nissan Versa S 2363 27
Porsche Cayenne 4398 15
Scion FR-S 2806 25
Scion iQ 2127 36
Scion XD 2665 27
Suburu Forester 2.5i Limited 3419 24
Suburu Legacy 2.5i Limited 3427 24
Toyota Camry XLE 3280 25
Toyota Land Cruiser 5765 13
Toyota RAV4 XLE 3465 24
Toyota Yaris 2295 30
Volkswagen Beetle 2.5L 3038 22
Volkswagen Jetta SE 3070 25
Volkswagen Toureg V6 Sport 4711 17
Volkswagen Passat SE 3230 24
Volvo S60 T5 3528 21
Volvo XC90 4667 16

a. Interpret the slope. Does the intercept have meaning, given the range of the data?

b. Based on the R2 and ANOVA table for your model, how would you assess the fit? Interpret the p-value for the Fstatistic. Would you say that your model’s fit is good enough to be of practical value?

c. Is an autocorrelation test appropriate for your data? If so, perform an eyeball inspection of residual plot against observation order or a runs test.

d. Use MegaStat or Minitab to generate 95 percent confidence and prediction intervals for various X-values.

e. Use MegaStat or Minitab to identify observations with high leverage.

Solutions

Expert Solution

Minitab output:

a. As weight is increased by 1 unit, expected City MPG is decreased by 0.00517 unit. Intercept has no real interpretation since when weight is zero the expected City MPG is 40.1 unit which is meaningless.

b. R-sq=80% i.e. 80% of total variation in City MPG is explained by this regression equation. Moreover from ANOVA table, we see that p-value<0.05, so the these two variables are linearly related significantly. Hence we can conclude that the fitting is good.

c.

From the above plot, we see the residuals bounce randomly around the residual = 0 line as we would hope so. In general, residuals exhibiting normal random noise around the residual = 0 line suggest that there is no serial correlation.

d.

e.

Unusual Observations:

orchestra answered 1 year ago
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