Question

Based on the Sporty Cars data, is "road test" a good predictor of Price at the 95% confidence level?

Select one: a. No, the R^2 statistic indicates that only 30% of the variability in price is explained by road test. b. No, the F-statistic indicates that the regression does not explain price significantly at the ninety five percent level. c. No, the t-statistic indicates that the coefficient on road test is not significantly different than zero at the 95% confidence level. d. All of the above are true.

How might the regression model be improved?

Select one:

a. Adding other explanatory variables such as years of age, miles and condition.

b. Adding data, including more observations for both price and road test score.

c. Both A and B could help improve model predictive accuracy.

d. Nothing can be done to improve regression accuracy; the results are final.

Background Information:

Car	Price ($1000s)	Road-Test Score
Chevrolet Cobalt SS	24.5	78
Dodge Caliber SRT4	24.9	56
Ford Mustang GT (V8)	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
Suburu Impreza WRX	25.2	81
Suburu Impreza WRX Sti	37.6	89
Volkswagen GTI	24	83
Volkswagen R32	33.6	83

Please show work in Excel

Answer 1

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.544552012
R Square	0.296536894
Adjusted R Square	0.226190583
Standard Error	4.93624909
Observations	12
ANOVA
	df	SS	MS	F	Significance F
Regression	1	102.7144492	102.7144492	4.215386576	0.067154276
Residual	10	243.6655508	24.36655508
Total	11	346.38
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%
Intercept	2.613101604	12.59191584	0.207522162	0.839767222	-25.44343531	30.66963852
Road-Test Score	0.33144385	0.161432607	2.053140662	0.067154276	-0.028250414	0.691138115

Based on the Sporty Cars data, is "road test" a good predictor of Price at the 95% confidence level?

Select one:

a. No, the R^2 statistic indicates that only 30% of the variability in price is explained by road test.

b. No, the F-statistic indicates that the regression does not explain price significantly at the ninety-five per cent level.

c. No, the t-statistic indicates that the coefficient on-road test is not significantly different than zero at the 95% confidence level.

d. All of the above are true.

All of the above statements are true.

R^2 = 0.296 or 30% of variation in price is explained by the predictor variable road test.

P-value of f-test = 0.06 > 0.05, So its not significant. That means that the model is not significant.

p-value of t-statistic = 0.067>0.05 So its not significant. That means that the coefficient is not significant..

How might the regression model be improved?

Select one:

c. Both A and B could help improve model predictive accuracy.