Question

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 regression equation for the model: Salary = β0 + β1Education + ε.

What is the coefficient for β1? ______ thousand. (Enter your answers in thousands rounded to 2 decimal places. The data is ALREADY in thousands. If you got 34.8763 for your answer, you would round that number to 34.88. The teacher's salary would be 34,880. This question is asking you to enter 34.88 ) (Enter your answers in thousands rounded to 2 decimal places.)

Answer #1

Line of Regression Y on X i.e Y = bo + b1 X |
||||

X | Y | (Xi - Mean)^2 | (Yi - Mean)^2 | (Xi-Mean)*(Yi-Mean) |

3 | 40 | 1 | 415.14 | 20.38 |

4 | 53 | 0 | 54.39 | 0 |

6 | 80 | 4 | 385.14 | 39.25 |

2 | 42 | 4 | 337.64 | 36.75 |

5 | 70 | 1 | 92.64 | 9.63 |

4 | 50 | 0 | 107.64 | 0 |

8 | 110 | 16 | 2462.64 | 198.5 |

0 | 38 | 16 | 500.64 | 89.5 |

calculation procedure for regression

mean of X = ∑ X / n = 4

mean of Y = ∑ Y / n = 60.375

∑ (Xi - Mean)^2 = 42

∑ (Yi - Mean)^2 = 4355.87

∑ (Xi-Mean)*(Yi-Mean) = 394.01

b1 = ∑ (Xi-Mean)*(Yi-Mean) / ∑ (Xi - Mean)^2

= 394.01 / 42

= 9.38

bo = ∑ Y / n - b1 * ∑ X / n

bo = 60.375 - 9.38*4 = 22.85

value of regression equation is, Y = bo + b1 X

Y'=22.85+9.38* X

the coefficient for β1 =9.38

A college professor would like to analyze the relationship
between educational attainment and salary. She 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
41
46
59
49
68
43
95
49
a.
Find the sample regression equation for the model: Salary =
β0 + β1Education +
ε. (Round intermediate calculations to 4 decimal
places. Enter your...

A social scientist would like to analyze the relationship
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Salary
Education
34
3
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1
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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
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Salary
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40
4
73
1
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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
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8
38
0
42
3
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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.)
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As Education increases by...

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
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between educational attainment (in years of higher education) and
annual salary (in $1,000s). He collects data on 20 individuals. A
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Salary
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42
6
48
7
82
1
46
3
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1
54
5
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6
42
0
38
4
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6
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2
44
7
67
5
64
7
143
12
43
0
76
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64
4
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between educational attainment (in years of higher education) and
annual salary (in $1,000s). He collects data on 20 individuals. A
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Salary
Education
40
3
53
4
80
6
42
2
70
5
50
4
110
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38
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