Classified ads in a newspaper offered several used Mitsubishi Mirage cars for sa
ID: 3149564 • Letter: C
Question
Classified ads in a newspaper offered several used Mitsubishi Mirage cars for sale. Listed below is a random sample of 15 cars showing their ages and the advertised prices:
Age (yrs) 1 1 3 4 4
Price ($) $1399 9 $13495 $12999 $9500 $10495
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Age (yrs) 5 5 6 7 7
Price ($) $8995 $9495 $6999 $6950 $7850
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Age (yrs) 8 8 10 10 13
Price (S) $6999 $5995 $4950 $4495 $2850
COMPUTER OUTPUT (RESULTS)
USED Mitsubishi Mirage PRICES
REGRESSION FUNCTION & ANOVA FOR PRICE
PRICE = 14285.95 - 959.0459 AGE
R-Squared = 0.944333
Adjusted R-Squared = 0.94005
Standard error of estimate = 816.2135
Number of cases used = 15
Analysis of Variance
p-value
Source SS df MS F Value Sig Prob
Regression 1.46918E+08 1 1.46918E+08 220.52950 0.000000
Residual 8.66066E+06 13 666204.50000
Total 1.55578E+08 14
USED Mitsubishi Mirage
REGRESSION COEFFICIENTS FOR PRICE
Two-Sided p-value
Variable Coefficient Std Error t Value Sig Prob
Constant 14285.95000 448.67270 31.84047 0.000000
AGE -959.04590 64.58119 -14.85024 0.000000 *
Use the computer output above to respond to the questions below:
QUESTIONS
How many years will it take for the residual value of this car to drop to zero?
ANSWER
Use the estimated simple linear regression equation to find the expected price of a two-year used Mitsubishi Mirage car
ANSWER
To test for the statistical significance of the relationship, we use the following pair of hypotheses:
Null Hypothesis H: b = 0
Alternative H: b 0
The model being PRICE = b + bAGE
What is your conclusion? Is the relationship statistically significant? Why or why not?
ANSWER
Explanation / Answer
1. How many years will it take for the residual value of this car to drop to zero?
ANSWER
PRICE = 14285.95 - 959.0459 AGE
In this above equation, price is substituted by mean price of the 15 data set. That is
7564.4 = 14285.95 - 959.0459 AGE
=>- 959.0459 AGE=-6721.55
=> Age=7.0085
=> AGE=7
Therefore, the year which give 0 residual value is 7 year.
2. Use the estimated simple linear regression equation to find the expected price of a two-year used Mitsubishi Mirage car
ANSWER
PRICE = 14285.95 - 959.0459 AGE
Using the above linear regression equation the price of two-year old Mitsubishi Mirage car is
PRICE = 14285.95 - 959.0459 *2
=14285.95-1918.0918
=12367.8582
Therefore, the price of the two-year old Mitsubishi Mirage car is $12367.8582.
3. To test for the statistical significance of the relationship, we use the following pair of hypotheses:
Null Hypothesis H: b = 0
Alternative H: b 0
The model being PRICE = b + bAGE
What is your conclusion? Is the relationship statistically significant? Why or why not?
ANSWER
Your writing of the equation is wrong (in the PRICE = b + bAGE). Both the intercept and slope are represented by same symbol “b”. It should write in general form as PRICE = bo + b1AGE.
From the yours regression analysis table bo=14285.95 and b1=- 959.0459 with 0.0000 and 0.0000 p-values respectively and smaller than 0.05 level of significance. Here, we can not accept the null hypothesis for both the intercept and slope; and accept the alternative hypothesis in these two parameters. Hence, we can conclude that both the intercept and age of the car are statistically significant at the mean price of the Mitsubishi Mirage car.