Welcome back, in this lesson, I'm going to illustrate a point with a symbolic asset that has two marketing variables, advertising and price. Based on this data set, we'll answer the questions, does price in advertising have impact on sales? Are they significant? And what percentage of sales variations can be explained by my model? Here's the data that we'll be using. We have columns for price, advertisings, and sales. I did this regression and got the following results. From these results, I can see three things. One is that all my parameter estimates are significant. How do I know that? I know that for two reasons. One, the T-values are all above 1.96, which means that I can say that, with 95% confidence level, that those parameters are statistically speaking, different from zero. The last column of the table also gives me another indication of this, all these variables are below 5%, and those are what we call the P-values. Usually, the heuristics to assess whether a variable is significant or not, is that the P-value should be below 5% when you work at the 95% confidence level. Before going any further, remember that we're trying to measure the impact of price and advertising on sales. And with that, we work on to assumptions, that first advertising will have a positive impact on sales, and that price should have a negative or no impact on sales. So with that in mind, here are two other things that I can say by looking at the bottom of the table. I find that, indeed, price has a negative impact on sales because the parameter estimate is -1.22. And I can see that advertising has a positive impact on sales, because the coefficient is equal to 0.24, which is positive. So these results are meaningful. I have to point this out because that's not always the case. Remember, that those numbers, or whatever numbers you have in your tables, are just statistical constructs. It's always important for researchers to ask whether these numbers make sense or not. The primary goal of the researcher is to find managerial insights. If your results contradict, basic business knowledge, like the assumption that price would reduce sales or that advertisings would increase sales, then there is something wrong and you want to refine your model. Beyond the points I just mentioned, you also want to know what is a predictive value of the model. How well does the model explain sales variations? And to assess that, I'm going to look at something called the adjusted R-square, which is at the top of the table. Here, it's about 96%, which means that about 96% of sales variations can be explained by model. Usually, the R-square pr adjusted R-square is going to be between 0 and 1. The closer it is to 1, the better it is, because it means that your model is very good at explaining the sales variations. The question often arises, what is a good number? If you get 20%, is that good or is that bad? That's really up to you to decide. If you get an R-square that is very high, that is very good, but I wouldn't dismiss result that have a low R-square as long as the variables are statistically significant.