Sporty cars are designed to provide better handling, acceleration, and a more re

Question

Sporty cars are designed to provide better handling, acceleration, and a more responsive driving experience than a typical sedan. But, even within this select group of cars, performance as well as price can vary. Consumer Reports provided road- test scores and prices for the following 10 sporty cars. Prices are in thousands of dollars and road- test scores are based on a 0– 100 rating scale, with higher values indicating better performance.

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e) Another sporty car that Consumer Reports tested is the BMW 135i; the price for this car was $ 36,700. Predict the road- test score for the BMW 135i using the estimated regression equation developed

f) Find the 98% Confidence and Prediction Intervals for the BMW 135i in part (e).

g) Conduct p-Value as well as Critical-Value based Hypothesis Tests to determine the significance of regression. Use = 0.01. Is the regression statistically significant?

Please show detailed, step by step workings. If you use an Excel formula, please list the formula and method.

Car Price ($1000s) Road-Test Score Chevrolet Cobalt SS 24.5 78 Dodge Caliber SRT4 24.9 56 Ford Mustang GT 29 73 Honda Civic Si 21.7 78 Mazda RX-8 31.3 86 Mini Cooper S 26.4 74 Mitsubishi Lancer Evolution GSR 38.1 83 Nissan Sentra SE-R Spec V 23.3 66 Subaru Impreza WRX 25.2 81 Subaru Impreza WRX STI 37.6

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Explanation / Answer

Regression Analysis: Road-Test Score versus Price ($1000s)

The regression equation is
Road-Test Score = 47.9 + 1.01 Price ($1000s)

Predictor Coef SE Coef T P
Constant 47.86 13.83 3.46 0.009
Price ($1000s) 1.0120 0.4813 2.10 0.069

S = 8.33259 R-Sq = 35.6% R-Sq(adj) = 27.5%

Analysis of Variance

Source DF SS MS F P
Regression 1 306.94 306.94 4.42 0.069
Residual Error 8 555.46 69.43
Total 9 862.40

Unusual Observations

Price Road-Test
Obs ($1000s) Score Fit SE Fit Residual St Resid
2 24.9 56.00 73.06 3.08 -17.06 -2.20R

Predicted Values for New Observations

New Obs Fit SE Fit 98% CI 98% PI
1 184.48 51.47 (35.39, 333.57) (33.45, 335.51)

P-value 0.069 > 0.01 We do not reject the null hypothesis. we conclude that regression statistically not significant.

Hope this will be helpful. Thanks and God bless you.

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