Question

Age and Price data for a sample of 12 cars

Age (years) 5 4 5 5 7 6 6 2 7 7 8 9

Price(Hundreds) 95 100 75 82 89 98 66 95 179 72 49 84

At the 1% significance level do the data provides sufficient evidence to conclude that age and price of cars are negatively correlated. a) Perform a hypothesis test ( 6 points)

- State Null and alternative Hypothesis

- Test Statistics

- P-value approach

- Conclusion:

- Find the line of best-fit (2 points)

- Explain what is in terms of age and price.( 2 points)

Answer #1

(For computing correlation, I have used R code:

x=c(5,4,5,5,7,6,6,2,7,7,8,9)

y=c(95,100,75,82,89,98,66,95,179,72,49,84)

#x=Age, y=Price

round(cor(x,y),4)

)

For finding regression equation I have used R code:

x=c(5,4,5,5,7,6,6,2,7,7,8,9)

y=c(95,100,75,82,89,98,66,95,179,72,49,84)

#x=Age, y=Price

m=lm(y~x)

round(m$coefficients,4)

m1=lm(x~y)

round(m1$coefficients,4)

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between 1 and 6 years old. Here, x denotes age, in years, and y
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complete parts (a) through (g).
x
6
6
6
2
2
5
4
5
1
4
y
290
290
285
420
394
315
355
333
425
335
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Student Grades
Student
Test
Grade
1
76
62
2
84
90
3
79
68
4
88
84
5
76
58
6
66
79
7
75
73
8
94
93
9
66
65
10
92
86
11
80
53
12
87
83
13
86
49
14
63
72
15
92
87
16
75
89
17
69
81
18
92
94
19
79
78
20
60
71
21
68
84
22
71
74
23
61
74
24
68
54
25
76
97...

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70
2
80
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66
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74
5
64
6
76
7
72
8
83
9
82
10
76
11
84
12
80

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y: 280,285,305,425,389,325,355,328,415,330
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(5
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Day
Stock Price:
1
84
2
87
3
84
4
88
5
85
6
90
7
91
8
83
9
82
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86
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1
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