Question

The Toyota Camry is one of the best-selling cars in North America. The cost of a previously owned Camry depends on many factors, including the model year, mileage, and condition. To investigate the relationship between the car’s mileage and the sales price for Camrys, the following data show the mileage and sale price for 19 sales (PriceHub web site, February 24, 2012).

	Miles (1,000s)		Price ($1,000s)
	22		16.2
	29		16.0
	36		13.8
	47		11.5
	63		12.5
	77		12.9
	73		11.2
	87		13.0
	92		11.8
	101		10.8
	110		8.3
	28		12.5
	59		11.1
	68		15.0
	68		12.2
	91		13.0
	42		15.6
	65		12.7
	110		8.3

(d)	How much of the variation in the sample values of price does the model estimated in part (b) explain?
	If required, round your answer to two decimal places.
	%
(e)	For the model estimated in part (b), calculate the predicted price and residual for each automobile in the data. Identify the two automobiles that were the biggest bargains.
	If required, round your answer to the nearest whole number.
	The best bargain is the Camry # in the data set, which has  miles, and sells for $ less than its predicted price. The second best bargain is the Camry # in the data set, which has  miles, and sells for $ less than its predicted price.
(f)	Suppose that you are considering purchasing a previously owned Camry that has been driven 30,000 miles. Use the estimated regression equation developed in part (b) to predict the price for this car.
	If required, round your answer to one decimal place. Do not round intermediate calculations.
	Predicted price: $
	Is this the price you would offer the seller?
	- Select answer -Yes or No?
	Explain.

Answer 1

Answer:

By using gievn data,

(D)

The R-square is known as coefficient of determination,which indicates the proportion of the total variation explained by the regression line.According to the regression output obtained in the part(b),the R-square value is 0.5386.It means that 53.86% of thevariation in response variable(car price) is explained by explanatory variable(Car mileage) in the regression equation and rest 46.12% of the variationremains unexplained.

(E)

There exists a negative relationship between price and miles.

As miles travelled increases,price decreases and vice versa

Linear regression in excel is follows bellow,

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.733933
R Square	0.538657
Adjusted R Square	0.51152
Standard Error	1.541377
Observations	19
ANOVA
	df	SS	MS	F	Significance F
Regression	1	47.15804	47.15804	19.84897	0.000348
Residual	17	40.38933	2.375843
Total	18	87.54737
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%
Intercept	16.46976	0.948764	17.35917	2.99E-12	14.46804	18.47147
Miles	-0.05877	0.013192	-4.45522	0.000348	-0.08661	-0.03094

Regression equation is

price=16.46976-0.05877*miles

For the question is

calculate the predicted price and residual for each automobile in the data.

ANSWER is

RESIDUAL OUTPUT
Observation	Predicted Price	Residuals
1	15.17672853	1.023271468
2	14.76531101	1.234688992
3	14.35389349	-0.553893485
4	13.70738023	-2.207380235
5	12.76699732	-0.266997324
6	11.94416228	0.955837722
7	12.17925801	-0.979258006
8	11.35642296	1.643577041
9	11.0625533	0.7374467
10	10.53358791	0.266412087
11	10.00462253	-1.704622526
12	14.82408494	-2.32408494
13	13.00209305	-1.902093052
14	12.47312766	2.526872335
15	12.47312766	-0.273127665
16	11.12132723	1.878672768
17	14.00124989	1.598750106
18	12.64944946	0.050550539
19	10.00462253	-1.704622526

Miles	observed Price	Predicted Price	Residuals
101	10.8	10.53359	0.266412
110	8.3	10.00462	-1.70462

bargain means less price is

The best bargain is the Camry #.........in the data set, which has……..miles, and sells for $............less than its predicted price.

110000 miles and sells for -266 less than predicted

The second best bargain is the Camry #........in the data set, which has……..miles, and sells for $........less than its predicted price.

101000 and sells for $...1705.....less than its predicted price.

(F)

Suppose that you are considering purchasing a previously owned Camry that has been driven 80,000 miles. Use the estimated regression equation mentioned above to predict the price for this car. If required, round your answer to one decimal place. Do not round intermediate calculations.

Predicted price: $.....

Price =16.46976-0.05877*miles

=6.46976-0.05877*80

= 1.76816

= 1.76816*1000

=1768.16

=1768.2

Predicted price=1768.2