Coefficient Table Use #3: Making Predictions
When we use regular least-squares regression, we obtain a linear equation that is intended to predict the expected (average) value of the dependent variable given the values of the -variables. In notation, we obtain the equation for the least-squares regression line:
If we want to make a prediction of the value of for a given set of values for the variables, we can just plug the -values and the regression coefficients (the ‘s) into the regression equation.
Using the least-squares regression example based on the Kid Creative data discussed in Part 1, suppose I wanted to predict the Household Income for a person with the following characteristics:
- Gender Male: IsFemale =
- Married: IsMarried =
- College Educated: HasCollege =
- Not a Professional: IsProfessional =
- Not Retired: IsRetired =
- Employed: Unemployed =
- Five years of Residency in Current City: ResLength =
- Dual Income: Dual =
- Has Children: Minors =
- Rents Home: Own =
- Lives in a house: House =
- Race is white: White =
- First language is English: English =
- No previous purchases: PrevParent = and PrevChild =
To predict the Household Income for this person, I simply plug these -values into the least-squares regression equation. To do so, I need the regression coefficients. The table below shows the regression coefficients pulled from the coefficient output table for the KidCreative Household Income least-squares regression example (click here to see the entire regression output).
Using these regression coefficients and the particular -values given above, the predicted household income is:
I certainly do not want to type all of this into a calculator, so I am going to compute the prediction using Excel. Here is the section of the Excel worksheet that I used:
Thus, the expected household income predicted by the least-square regression for a person with the -variable values listed above is about $42,300.
Prediction is one of the most important uses of the regression coefficient table. In the last part of this background series, I will discuss assessing the statistical uncertainty with respect to the regression coefficient and will briefly touch on the uncertainty with respect to predictions. Click here to proceed to Part 5.
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