Question

AutoReports is a consumer magazine that reports on the cost of maintaining various types of automobiles. The magazine collected the data found in the file Dat9-16.xls on your data disk describing the annual maintenance cost of a certain type of luxury imported automobile along with the age of the car (in years).

a. Prepare a scatter plot of these data.

b. Let Y = Maintenance Cost and X = Age. Fit the following regression model to the data:

Ŷi = b0 + b1X1i

Plot the maintenance costs that are estimated by this model along with the actual costs in the sample. How well does this model fit the data?

c. Fit the following regression model to the data:

Ŷi = b0 + b1X1i + b2X2i

Where X2i = X21i. Plot the maintenance costs that are estimated by this model along with the actual costs in the sample. How well does this model fit the data?

d. Fit the following regression model to this data:

Ŷi = b0 + b1X1i + b2X2i + b3X3i

Where X2i = X21i and X3i = X31i. Plot the maintenance costs that are estimated by this model along with the actual costs in the sample. How well does this model fit the data?

Answer 1

Age	Age^2	Age^3	Maintenance Cost	Linear	Quadratic	Cubic
1	1	1	100	175.46512	214.51923	115.08052
2	4	16	375	296.15449	303.12843	342.28298
2	4	16	325	296.15449	303.12843	342.28298
3	9	81	455	416.84385	403.73283	466.38458
3	9	81	520	416.84385	403.73283	466.38458
4	16	256	485	537.53322	516.33242	528.03634
4	16	256	530	537.53322	516.33242	528.03634
5	25	625	595	658.22259	640.9272	584.14975
5	25	625	515	658.22259	640.9272	584.14975
6	36	1296	700	778.91196	777.51717	707.89667
6	36	1296	800	778.91196	777.51717	707.89667
7	49	2401	1000	899.60133	926.10234	988.70941
7	49	2401	950	899.60133	926.10234	988.70941

Scatter plot a

Part b, c, d

 

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.950898163
R Square	0.904207317
Adjusted R Square	0.895498891
Standard Error	80.59932464
Observations	13
ANOVA
	df	SS	MS	F	Significance F
Regression	1	674514.3145	674514.3145	103.8313176	6.12492E-07
Residual	11	71458.76246	6496.251133
Total	12	745973.0769
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%	Lower 95.000%	Upper 95.000%
Intercept	54.77574751	54.87003772	0.998281572	0.339596592	-65.99245233	175.5439474	-65.99245233	175.5439474
X Variable 1	120.6893688	11.84417548	10.18976534	6.12492E-07	94.62050111	146.7582364	94.62050111	146.7582364

 

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.954326142
R Square	0.910738385
Adjusted R Square	0.892886062
Standard Error	81.60071181
Observations	13
ANOVA
	df	SS	MS	F	Significance F
Regression	2	679386.3152	339693.1576	51.01511908	5.66661E-06
Residual	10	66586.76168	6658.676168
Total	12	745973.0769
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%	Lower 95.000%	Upper 95.000%
Intercept	137.9052198	111.9408347	1.231947395	0.246150736	-111.5145464	387.3249859	-111.5145464	387.3249859
X Variable 1	70.61641484	59.75431279	1.181779382	0.264633471	-62.5245141	203.7573438	-62.5245141	203.7573438
X Variable 2	5.997596154	7.011605803	0.855381253	0.412365513	-9.625237854	21.62043016	-9.625237854	21.62043016

 

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.98546528
R Square	0.97114182
Adjusted R Square	0.96152243
Standard Error	48.9074227
Observations	13
ANOVA
	df	SS	MS	F	Significance F
Regression	3	724445.6529	241481.8843	100.9566663	3.01162E-07
Residual	9	21527.42398	2391.935998
Total	12	745973.0769
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%	Lower 95.000%	Upper 95.000%
Intercept	-239.61344	109.8493378	-2.181291596	0.057054284	-488.110093	8.883218391	-488.110093	8.883218391
X Variable 1	422.504812	88.63291184	4.766906591	0.001019768	222.0030825	623.0065409	222.0030825	623.0065409
X Variable 2	-68.48837	17.66860142	-3.876275687	0.00375266	-108.4575538	-28.51918638	-108.4575538	-28.51918638
X Variable 3	0.67751741	0.156099976	4.34027877	0.001876701	0.324394463	1.030640357	0.324394463	1.030640357