Question

A social scientist would Ilike to analyze the relationship between educational attainment and salary. He collects a sample data, where "Education" refers to years of higher education and "Salary" is the individual's salary in thousands of dollars. The summary statistics are as follow:

EDUCATION MEAN 4 ST DEV 2.45

SALARY MEAN 60.34 ST DEV 24

mean | st dev |

4 | 2.45 |

60.34 | 24.95 |

According to the data, the correlation coefficient between "Education" and "Salary" is 0.9212

a. Find a linear equation to predict the "Salary" from the "Education"

b. Find the coefficient of determination and explain the meaning of it.

C. Suppose an individual has completed 7 years education, predict his salary based on the linear regression model.

d. Interpret the slope and intercept of the regression line

Answer #1

Explanatory variable(X) - education and dependent variable(Y) - salary

The value of estimated slope

The value of estimated y intercept

a) The estimated linear regression equation is :

Salary = 22.8152 + 9.38120*Education

b) The coefficient of determination R^{2} =
0.9212^{2}= 0.8486

84.86% variation in salary can be explained by the above regression equation using education as predictor.

c) The predicted salary for an individual with 7 years education = (22.8152 + 9.38120*7) K = 88483.6 dollars

d) Interpretation of the slope : For a number of years of education increase, predicted salary will increase 9.38120 thousand dollars.

Interpretation of the intercept : When number of years of education = 0, predicted salary = 60.34 thousand dollars.

A social scientist would like to analyze the relationship
between educational attainment and salary. He collects the
following sample data, where Education refers to years of higher
education and Salary is the individual’s annual salary (in
$1,000s):
Education 3 4 6 2 5 4 8 0
Salary 40 53 80 42 70 50 110 38
Data is in the spreadsheet.
Use the Regression tool in Data Analysis to find the sample
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A college professor would like to analyze the relationship
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Education
3
4
6
2
5
4
8
0
Salary
41
46
59
49
68
43
95
49
a.
Find the sample regression equation for the model: Salary =
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ε. (Round intermediate calculations to 4 decimal
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A social scientist would like to analyze the relationship
between educational attainment (in years of higher education) and
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portion of the data is as follows:
Salary
Education
42
6
48
7
82
1
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a. Find...

A social scientist would like to analyze the relationship
between educational attainment (in years of higher education) and
annual salary (in $1,000s). He collects data on 20 individuals. A
portion of the data is as follows:
Salary
Education
40
3
53
4
80
6
42
2
70
5
50
4
110
8
38
0
42
3
55
4
85
6
40
2
70
5
60
4
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0
75
5
65
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8
38
0
a. Find...

A social scientist would like to analyze the relationship
between educational attainment (in years of higher education) and
annual salary (in $1,000s). He collects data on 20 individuals. A
portion of the data is as follows:
Salary
Education
34
3
66
1
89
4
56
3
71
7
80
2
111
7
51
0
23
7
36
2
100
1
35
1
71
6
68
9
163
5
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0
86
5
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4
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9
33
0
a. Find...

A social scientist would like to analyze the relationship
between educational attainment (in years of higher education) and
annual salary (in $1,000s). He collects data on 20 individuals. A
portion of the data is as follows:
Salary
Education
42
6
48
7
⋮
⋮
42
0
a. Find the sample regression equation for the
model: Salary = β0 +
β1Education + ε. (Round
answers to 3 decimal places.)
Salaryˆ= _(answer)__ + __(answer)__ Education
b. Interpret the coefficient for Education.
As...

A social scientist would like to analyze the relationship
between educational attainment (in years of higher education) and
annual salary (in $1,000s). He collects data on 20 individuals. A
portion of the data is as follows:
Salary
Education
35
4
71
1
84
3
52
3
70
7
80
5
107
9
55
0
23
4
33
6
102
6
40
4
67
2
68
5
163
9
55
0
83
8
56
3
125
11
31
0
What is...

A social scientist would like to analyze the relationship
between educational attainment (in years of higher education) and
annual salary (in $1,000s). He collects data on 20 individuals. A
portion of the data is as follows:
Salary
Education
40
4
73
1
⋮
⋮
25
0
Salary
Education
40
4
73
1
99
7
57
1
83
8
76
4
109
6
49
0
31
4
32
4
91
2
40
4
65
6
71
2
166
5
61
0...

A social scientist would like to analyze the relationship
between educational attainment (in years of higher education) and
annual salary (in $1,000s). He collects data on 20 individuals. A
portion of the data is as follows:
Salary
Education
40
3
53
4
⋮
⋮
38
0
Salary
Education
40
3
53
4
80
6
42
2
70
5
50
4
110
8
38
0
42
3
55
4
85
6
40
2
70
5
60
4
140
8
40
0...

20. A social scientist would like to analyze the relationship
between educational attainment (in years of higher education) and
annual salary (in $1,000s). He collects data on 20 individuals. A
portion of the data is as follows:
Salary
Education
35
1
67
6
⋮
⋮
32
0
a. Find the sample regression equation for the
model: Salary = β0 +
β1Education + ε. (Round
answers to 2 decimal places.)
Salaryˆ=Salary^= + Education
b. Interpret the coefficient for Education.
As Education increases by...

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