Question

Use the advertised prices for a used car of a particular model to create a linear model for the relationship between a​ car's Year and its Price. Complete parts a through e.

Year   Price ($)
1994   11,538
1994   12,333
1994   10,436
1994   11,995
1995   14,567
1995   14,658
1995   13,656
1995   15,199
1996   16,192
1996   17,039
1996   19,074
1997   19,823
1997   19,249
1997   19,242
1997   20,577

​a) Find the equation of the regression line.

Price=___ + _____ year

b) Explain the meaning of the slope of the line. Select the correct choice below and fill in the answer box to complete your choice. ​(Round to the nearest integer as​ needed.)

A.The slope of ___indicates the Year when the Price of a used car of this model will be​ $0.

B.The slope of ___ is meaningless and should not be interpreted.

C.The slope indicates that for every one Year increase or one Year newer​ model, the Price increases by

​___.

D.The slope indicates that for every one Year increase or one Year newer​ model, the Price decreases by

​___.

​c) Explain the meaning of the intercept of the line. Select the correct choice below and fill in the answer box to complete your choice.

A.The intercept indicates that cars of this model increase in price by ___ per Year.

B.The intercept of ___ indicates the Price at Year 0.

C.The intercept of ____ indicates the Year when the Price of a used car of this model will be​ $0.

D.The intercept of ____ is meaningless and should not be interpreted.

d) If you want to sell a used car of this particular model from 1997​, what price seems​ appropriate?

​e) You have a chance to buy one of two cars. They are about the same age and appear to be in equally good condition. Would you rather buy the one with a positive residual or the one with a negative​ residual? Explain.

You would rather buy the car with a ____ residual because this indicates that the actual price is ____than the predicted price. This is important because the two cars have the same ____price, since they are the same age and​ condition, so the one with the lower ____price is a better purchase.

Answer 1

Using Excel<data <megastat<correlation/regression<regression

Here is the output:

Regression Analysis
	r²	0.941
	r	0.970
	Std. Error	845.581
	n	15
	k	1
	Dep. Var.	price
ANOVA table
Source	SS	df	MS	F	p-value
Regression	14,69,42,823.7480	1	14,69,42,823.7480	205.51	2.41E-09
Residual	92,95,098.6520	13	7,15,007.5886
Total	15,62,37,922.4000	14
Regression output					confidence interval
variables	coefficients	std. error	t (df=13)	p-value	95% lower	95% upper
Intercept	-54,29,552.5541	379839.08	-14.29	0.00	-6250145.00	-4608960.10
Year	2,728.8142	190.3510	14.336	2.41E-09	2,317.5859	3,140.0425

a)

Price=-5429553 + 2729 year

b)

Option C

The slope indicates that for every one Year increase or one Year newer​ model, the Price increases by 2729

c) The intercept of -5429553 is meaningless and should not be interpreted.

d) 1997​

Price=-5429553 + 2729 year

= -5429553 + 2729 *1997

= 20260

Answer 20260.

e)

You would rather buy the car with a negative residual because this indicates that the actual price is below than the predicted price. This is important because the two cars have the same predicted price, since they are the same age and​ condition, so the one with the lower actual price is a better purchase.