Predict values with regression analysis

- [Narrator] Let's talk about a specific example using regression analysis. In this case, we're looking at predicting the estimated home heating oil use by a particular customer, based on three different factors. A variable that we call the intercept, the temperature outside, and the level of insulation in the customer's house. Let's focus on these bottom three rows in the table, and in particular, focus on the column labeled Coefficients. These coefficients tell us the impact on home heating oil use in a particular month given the temperature outside and the insulation level of the person's house.

Now, let's see how we would use this in a prediction. There's three steps to the prediction, run the regression, which I showed you the output from the previous slide, then we're going to save those coefficients. That was those last three rows of data. For example, this will help us to measure the impact for each additional inch of insulation in a person's house. And then, finally, we're going to use those coefficients and our expected value for the future to get a prediction.

For example, if we were trying to forecast home heating oil use for a particular individual, we'd use our coefficients. In this case, for temperature, that's 5.436, and our expected value for what the temperature is going to be in the future. Maybe it's going to be 40 degrees outside. We'd put in 40 where we have Temperature, and we'd put in the level of insulation in the person's house where we have Insulation labeled. We then crank through the math and this puts out the level of estimated home heating oil that the person will consume.

Now, of course, this isn't going to be perfect. There will always be some small error associated with a particular prediction. Regressions help us to minimize that error, and moreover, particular points in the regression are going to tell us what the expected error will be and whether or not we have a good prediction. So let's use this concept and take it back to what we talked about previously while we were discussing the impact of sales culture on a company's revenue.

This regression shows us again the impact on sales from a variety of different variables related to a company. The sales culture of the firm, but then a variety of other baseline characteristics like the total debt for the firm, the amount of capex they, have etc. Our coefficient of 1.57 on culture told us that one dollar invested in sales culture yielded one dollar and 57 cents in additional sales.

The R squared value, or R-sq, that you see at the top, tells us how effective our prediction is. In particular, those numbers tell us the percentage of the time that we can perfectly predict our sales based on all these different variables. In this case, for the overall regression, we can perfectly predict sales 30.3% of the time. That's what that 0.3030 tells us.

Just less that one third of the time, we can perfectly predict sales given these other factors. Now, even when we can't perfectly predict sales, we will still have only a small error term if we've done a good job of building our regression. The second column here, P greater than t, tells us whether or not we've done a good job in picking our variables. As long as those numbers are small and close to zero, that indicates that those particular variables are effective in helping us make predictions.