A social scientist would like to analyze the relationship between educational attainment (in years of higher education) and annu
al 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 $
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.
