Question

In: Statistics and Probability

A social scientist would like to analyze the relationship between educational attainment (in years of higher...

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^ _______ $

Solutions

Expert Solution

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!


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