# Least-Squares Background Part 4 — Making Predictions

In this Article, I discuss another key use of the regression coefficients, namely to make predictions. This article is part 4 of a 5 part series briefly reviewing some aspects of regular linear least-squares regression. Some background with respect to least-squares regression will be used to motivate interpretation of the logistic regression output. Part 1 of this review series discusses the three main sections of the least-squares regression output and provides an example using the Kid Creative data. Part 2 discusses using the regression coefficient table to determine what variables matter. Part 3 discusses assessing the impact of each of the variables using the regression coefficients.

## 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.