You collect some new data regarding Excavators, Inc. and wonder if this new information may be useful in your modeling efforts.
Year Sales (in $millions) # Workers Sunny Days GDP
2005 15.2 36 130 10.3
2006 15.7 41 211 10.6
2007 16.4 44 145 11.1
2008 17.2 44 156 11.9
2009 19.1 52 200 12.6
2010 20.1 63 138 13.4
2011 22.8 85 185 14.1
2012 24.2 88 140 15.0
2013 19.4 65 138 15.5
2014 18.8 72 160 16.0
2015 20.0 80 155 17.0
Run a simple linear regression, using Sales as the dependent variable, and # of Workers the independent variable. State your results both quantitatively (give the equation) and qualitatively (provide the explanation of the equation).
Setup and perform the hypothesis test of the coefficient on # of Workers. (choose your own value for alpha)
Run a multiple regression analysis on the above data. Use “number of workers” and “sunny days” as the only independent variables, thus you will have just two independent variables on the right hand side of the equation. State your results both quantitatively (give the equation) and qualitatively (provide the explanation of the equation).
Perform a Global F-test and state your results. (show the null and alternative hypotheses and your choice of alpha)
Discuss the value of R-squared. What does it tell you? How is it calculated?
2. After performing your analysis in question #3, you start wondering if there is any way you can “improve” your model. Specifically, you want to test the “usefulness” of adding two more variables to the right hand side (independent variables) of the equation.
You find that you could add “Roger” as an independent variable. “Roger” will be a qualitative variable that is used to define the presence of employee Roger Slane at Excavators Inc. Looking through company records you find that “Roger” has been employed by the company only over the last five years. Add “Roger” as an independent variable. Enter “0” for the years that Roger was not employed by the company. Enter a value of “1” for the years that Roger was employed by the company.
Also, you add a variable that represents the national economy. You call it, “GDP.” The GDP information is found in the table in problem #3.
Perform the new regression analysis with all four independent variables. State your results both quanitatively (write the equations) and again utilizing the context of the model (in words). Explain the new value of R-squared. Also peform a Global F-test and state the results.
AND, perform a comparison F-test, comparing this new 4-variable model to the 2-variable model found in #3 above. State the results of your test.