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# Regression Equation

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Fred is the manager of human resources at St. Luke Hospital. As part of his yearly report to the president of the medical center, he is required to present an analysis of the salaried employees. Because there are over 1,000 employees, he does not have the staff to gather information on each employee, so he selects a random sample of 30. For each employee, he records monthly salary; service at St. Luke's, in months; sex (1 = male, 0 = female); and whether the employee has a technical or clerical job. Those with technical are coded 1, those with clerical are coded 0.

File Attached.

a) determine the regression equation, using salary as the dependent variable and the other four variables as independent variables.
b) What is the value of R squared? Comment on this value.
c) Conduct a global test of hypothesis to determine whether any of the independent variables are different from 0.
d) Conduct an individual test to determine whether any of the independent variables can be dropped.
e) Rerun the regression equation, using only the independent variables that are significant. How much more does a man earn per month than a woman? Does it make a difference whether the employee has a technical or clerical job?

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##### Solution Summary

Fred is the manager of human resources at St. Luke Hospital. As part of his yearly report to the president of the medical center, he is required to present an analysis of the salaried employees. Because there are over 1,000 employees, he does not have the staff to gather information on each employee, so he selects a random sample of 30. For each employee, he records monthly salary; service at St. Luke's, in months; sex (1 = male, 0 = female); and whether the employee has a technical or clerical job. Those with technical are coded 1, those with clerical are coded 0.

File Attached.

a) determine the regression equation, using salary as the dependent variable and the other four variables as independent variables.
b) What is the value of R squared? Comment on this value.
c) Conduct a global test of hypothesis to determine whether any of the independent variables are different from 0.
d) Conduct an individual test to determine whether any of the independent variables can be dropped.
e) Rerun the regression equation, using only the independent variables that are significant. How much more does a man earn per month than a woman? Does it make a difference whether the employee has a technical or clerical job?

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##### Solution Preview

a) the regression equation should be:
<br>W = a + b*Service + c*Age + d*Male + e*Tech + U
<br>Where W is monthly salary; Service is service at St. Luke's, in month; Male is dummy variable and =1for male, =0 for female; Tech is dummy variable and = 1 for technical job, =0 for clerical job; "a" is our intercept.
<br>Using OLS, we can calculate the relative coefficients of a, b, c, d, and e.
<br>Coefficients
<br> Coefficients
<br> B Std. ...

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