 Mathematics
George Washington University Toyota Corollas Confidence Interval Homework

George Washington University

### Question Description

Can you help me understand this Statistics question?

I will post you some links below for the answers but I am not sure if it is correct. Also I will attach the Question and the power point for the lecture

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32. Used cars 2010 Vehix.com offered several used Toyota Corollas for sale. Listed below are the ages of the cars and the advertised prices. a) b) c) d) Make a scatterplot for these data. Do you think a linear model is appropriate? Explain. Find the equation of the regression line. Check the residuals to see if the conditions for inference are met. 34. Used cars 2010, again based on the analysis of used car prices you did for Exercise 32, create a 95% confidence interval for the slope of the regression line and explain you’re your interval means in context. Extra Problem: Develop the confidence interval for the predicted mean value of a car that is 6 years old and the prediction interval for such a car. (Slides 77-79) Home work Problem 32 (Review slides 2 through 19. Also, age of car is the x-variable, price is the yvariable) Problem 34 (Review slides 51 through 63, and assume for this problem we are doing a 95% confidence interval for the slope of the regression line) Extra Problem: Develop the confidence interval for the predicted mean value of a car that is 6 years old and the prediction interval for such a car. (Slides 77-79) ...
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32. Used cars 2010 Vehix.com offered several used Toyota Corollas for sale. Listed below are
the ages of the cars and the advertised prices.

a) Make a scatterplot for these data.

Price Vs Age
18000
16000
14000

Price (\$)

12000
10000
8000
6000
4000
2000
0
0

2

4

6

8

10

12

14

Age (Yr)

b) Do you think a linear model is appropriate? Explain.
A linear model is appropriate as the scatterplot shows evidence of a linear relationship between
the variables.
c) Find the equation of the regression line.
Excel

Price Vs Age
18000
16000
14000

Price (\$)

12000
10000
8000

6000
4000

y = -1085.9x + 16567

2000
0
0

2

4

6

8

10

12

14

Age (Yr)

Manual:

Sum =

X
1
1
2
3
3
4
4
5
6
6
7
8
8
9
10
12
89

Y
15988
13988
14488
10995
13998
13622
12810
9988
9995
11988
8990
9488
8995
5990
4100
2995
168418

X*Y
15988
13988
28976
32985
41994
54488
51240
49940
59970
71928
62930
75904
71960
53910
41000
35940
763141

X2
1
1
4
9
9
16
16
25
36
36
49
64
64
81
100
144
655

Y2
255616144
195664144
209902144
120890025
195944004
185558884
164096100
99760144
99900025
143712144
80820100
90022144
80910025
35880100
16810000
8970025
1984456152

The equation is: Y = -1085.95x + 16566.72

d) Check the residuals to see if the conditions for inference are met.

The above fit line shows that the assumption of homoscedasticity is met as points appear to be
evenly distributed around the fit line.

The above fit line shows that the assumption of normality is met as the residuals of the
34. Used cars 2010, again based on the analysis of used car prices you did for Exercise 32,
create a 95% confidence interval for the slope of the regression line and explain you’re your
interval means in context.
Excel
SUMMARY OUTPUT
Regression Statistics
Multiple R
0.94397
R Square
0.891079
Square
0.883299
Standard Error
1283.27
Observations
16
ANOVA
df
Regression
Residual
Total

1
14
15

Coefficients
16566.72
-1085.95

Intercept
Age(X)

SS
1.89E+08
23054960
2.12E+08

MS
F
1.89E+08 114.5338
1646783

Standard
Error
t S... mickeygabz (5240)
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