In: Statistics and Probability
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 | 5 | ||||
59 | 5 | ||||
⋮ | ⋮ | ||||
37 | 0 | ||||
a. Find the sample regression equation for the model: Salary = β0 + β1Education + ε. (Round answers to 2 decimal places.)
Salaryˆ=Salary^= __________ + __________ Education
c. What is the predicted salary for an individual who completed 9 years of higher education? (Round coefficient estimates to at least 4 decimal places and final answer to the nearest whole number.)
SalaryˆSalary^ _______ $
Since are only provided a portion of the model, I am assuming you want the regression model for only this small subset of the data. If not let me know in comments and I will update the answer accordingly.
These are the data that have been provided for the dependent and independent variables:
Obs. | X | Y |
1 | 5 | 35 |
2 | 5 | 59 |
3 | 0 | 37 |
Now, with the provided sample values of the predictor and the response variable, we need to construct the following table to compute the estimated regression coefficients:
The sum of squares obtained from the table above are:
The slope and y-intercept coefficients are computed using the following formulas:
Therefore, the regression equation is:
(ii)
When X = 9 then
Please let me know in comments if anything is unclear. Will reply ASAP. Please upvote if satisfied!