So now that we have a regression model that we feel like it's a good model for prediction, I'm going to show you how we're going to use the output for the purpose of prediction. And for that matter, I'm going to focus on the last table of this output. So, focusing on the last part of this output, these are the parts that are important to my regression equation. So, if I were to write this in regression equation, it would look like this. Y hat is the intercept, and the intercept comes from right here. And I'm going to just round a little, 1.9 plus 2.9 times x1. Promotional budget is x1, and it has a coefficient of 2.9. And I'm going to go down to the time, which has a coefficient of 5.325 times x2 plus market potential has 0.019 and it's x3, and customer rating is 50.32 x4. The coefficient will tell me which one has the highest impact if I could change it. So, for example, if I changed x1 by one value, the total sales would go up by 2.9. And, of course, sales are in thousands. So 2.9 were represent 2,900. So if I look at the coefficient, I will see that this has the highest potential for change, which means if I could get my employees to have a better customer service, if they go from a 3 point rating to 4 point rating, I'm going to see a difference of $50,000 almost. The next thing is the number years that they have been. So, these are the coefficients that are telling me where do I get my most bang for my buck. So if you were going to manipulate one of these variables, you should look for variable that has the highest impact. So now, let me show you how you actually do the prediction. For that, I like to copy values here down. So just, I just copy them, and then I would paste them right here. So, these are the coefficients, and I can enter now different values. So, value one, for example, is going to be, so there is nothing that I would would enter for intercept. But for promotional budget, let's say I'm going to consider someone who has a $5,000 promotional budget. And because my values were in thousands, I'm going to enter this as 5. This person has been with the company for five years. So that would be 60 months, because time with the company has been recorded in number of months. The market potential that they're in has a $8 million market potential. And, again, it is done in thousands. So I'm going to enter this as 8,000. So 8,000 is going to represent 8 million. And this person has a customer rating of 4.3. So if I want to know now what is the prediction, I'm going to record it right here. The prediction is going to be intercept this value plus this value multiplied by this value, and then this with this, and this with this. So the Best thing I can do is, first of all, make a sum product. Sum product is a function in Excel which would do exactly what we want to do. It will take array one, and one by one it will multiply it by its array two and sum them up as it goes along. So, basically, it will take 2.9 multiplied by 5 plus 5.32 times 60 and so on. Now, if I want to repeat this formula over and over again as I change values, one thing that we want to do is that we want to lock the location of our coefficients. So, I'm going to put my cursor back on B28 and then click on F4 and it will lock it. And same thing with B29. I'm going to click on B29 and then say F4 and B32, F4. And in a minute, you will see that now that I have locked it I can just enter new values and I would get new sum products. So this will tell me that the prediction is 1.229 because this was in thousands, so maybe I want to just take this back and multiply it by a 1,000. Even show it in dollars so it would be easier to understand. I'm going to go to home. And so, this would be my prediction. And this is, again, a point estimate of the prediction interval. I'm not giving you the interval, although there is a 95% confidence interval that we have for each one of them. So, we can create a prediction interval, but as I said, Excel doesn't automate that and it's a little cumbersome, so I'm just going to ignore it for now. So now what happens if I said, okay, I'm going to give the same person a little bit more promotional budget? So I'm going to increase the promotional budget from 5,000 to 6,000. So what will happened? Well, you should be able to tell that my sales should go up by the coefficient. The rest of the things are the same. So, it's the same percent with the same number of months. So, I'm just going to copy these. And now, because I have locked my locations of coefficients, it can just take this column and multiply it by values that I see in this column. So I'm going to just drag this out. And you would see that it has gone up. And how much has gone up? It should be by that coefficient, so I'm going to just show it to you that that is the case. If I take the difference between this increase of one with this one, you would get 2.9, exactly like you see here as you would expect it. So if I enter 60, it will go up by 10 times that. So, basically, now we can take this model and make point estimates of our prediction for values that we give.
