Question

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
56 0
86 5
58 4
128 9
33 0
Salary Education
34 3
66 1
⋮ ⋮
33 0
a. Find the sample regression equation for the model: Salary = β0 + β1Education + ε. (Round answers to 2 decimal places.) Salaryˆ= + Education
b. Interpret the coefficient for Education.
As Education increases by 1 unit, an individual’s annual salary is predicted to increase by $4,690.
As Education increases by 1 unit, an individual’s annual salary is predicted to decrease by $4,690.
As Education increases by 1 unit, an individual’s annual salary is predicted to decrease by $8,590.
As Education increases by 1 unit, an individual’s annual salary is predicted to increase by $8,590.
c. What is the predicted salary for an individual who completed 7 years of higher education? (Round coefficient estimates to at least 4 decimal places and final answer to the nearest whole number.)
Salaryˆ $

Answer 1

Answer:

y = 4.69X + 52.93 ;

As Education increases by 1 unit, an individual’s annual salary is predicted to increase by $4,690. ;

$86000

Step-by-step explanation:

Given the data:

X:

34

66

89

56

71

80

111

51

23

36

100

35

71

68

163

56

86

58

128

33

Y:

3

1

4

3

7

2

7

0

7

2

1

1

6

9

5

0

5

4

9

0

The regression equation obtained using a linear regression calculator :

y = 4.689X + 52.93182

Where ;

y = Salary ; x = Educational attainment

Slope is the Coefficient of x = 4.689

Intercept = 52.93

The slope value in thousand = 4.689 * 1000 = 4689 = 4690 (the slope is interpreted to the mean the change in y value per unit change in the value of x)

Therefore, salary increases by about $4690 for every unit increase.

If x = 7

y = 4.689(7) + 52.93182

y = 32.823 + 52.93182

y = 85.7548

Salary =, $86,000