The first section of the exam has you evaluate and interpret regression tables. You must be able to write out the regression equation in a manner that would allow you to create an estimate of the independent variable.
Homework #4 had a very good example of this kind of question and we will use it here to prepare for the test. Here is the question from homework #4.
| Independent Variable | Coefficient | Standard Error | T | P |
|---|---|---|---|---|
| \(\beta_1\) African American (1=yes, 0=no) | -241.332 | 38.472 | -6.270 | 0.000 |
| \(\beta_2\) Lives in the South (1=yes, 0=no) | -72.764 | 27.235 | -2.670 | 0.008 |
| \(\beta_3\) Lives in an Urban Area (1=yes, 0=no) | 183.197 | 27.934 | 6.560 | 0.000 |
| \(\beta_4\) Age (in years) | 19.314 | 4.007 | 4.820 | 0.000 |
| \(\beta_0\) Constant | 243.356 | 135.558 | 1.800 | 0.073 |
First, you were asked to interpret coefficients. You will be asked to interpret up to 8 coefficients on the final exam. The coefficients you were asked to interpret on the homework assignment were.
Interpret the coefficient of the constant:
Interpret the coefficients for the “Living in the South” and “Age” independent variables.
After being asked to interpret coefficients, you were asked to write the regression equation and calculate an estimate.
You will be asked to do this for up to four equations on the test. In this case the equation should have looked like the following and we will go step by step.
First, you write out the basic equation with no listed independent variables or coefficient values.
\[Income = \beta_0+ \beta_1*X_1 + \beta_2*X_2 + \beta_3*X_3 + \beta_4*X_4\]
Then you rewrite the equation substituting the value of the \(\beta\) coefficient for the \(\beta\) variable.
\[Income = 243.356 + -241.332*X_1 + -72.764*X_2 + 183.197*X_3 + 19.314*X_4\]
Then you rewrite the equation substituting the independent variable for the \(X_x\)
\[Income = 243.356 + -241.332*(African American) + -72.764*(Lives in the South)\] \[+ 183.197*(Lives in an Urban Area) + 19.314*(Age in Years)\] Finally, you substitute in the numerical value of each independant variable and solve the equation. In homework 4, you were asked to provide the following estimate:
In this description, we set the variable African American to 1, the Lives in the South variable to 0, the Livers in an Urban Area variable to 1, and the Age variable to 30.
\[Income = 243.356 + -241.332*1 + -72.764*0 + 183.197*1 + 19.314*30\]
Calculating this out, we arrive at the following answer.
\[$764.64 = 243.356 -241.332 + 0 + 183.197 + 30*19.314$$\]
A key thing to remember here is to always look at how your variables are measured. Are they in dollars? Are they in years? Are they on a scale of 1 to 7?
No matter what the scale of the variable, always assume that every IV has a value of 0 when interpreting the Constant.
When interpreting the constant, or any other variable, think of it like telling a story. You are describing a person, place, or event. Use your imagination and try to look at the numbers as more than an abstraction. Try to think about WHAT they represent.