Okay let's continue with our study of multiple regression. So you recall at the end of the last video, we found the unemployment rate had a high P value, so we should throw it out. Okay so with Finland out right here, and we got unemployment out right here. So notice there's no Finland, and we've deleted the unemployment rate column. So we can run this regression again and then we can try it, and we'll see that this will, Be a decent regression that we can use and gain some insights into predicting computer sales in Europe. Okay. So now what I'm going to do is I'm going to predict the same data set. And the input range will be two columns now. And let's call it Mukeregression2. And we can click residuals here. So we've got 20 data points. Okay, and so this is looking good, I believe. Okay, so let's interpret the equation we got. Look at the P values. Okay. So this says, we can predict computer spent per person right here. We predicted to be -38.48 + 0.00172*GNP per capita +15.31 times the EDPERCENTAGE. Okay, are these independent P-values significant? Yes. Look at those P-values. We don't care about the intercept. But P values for each independent variable, way less than 0.1. We got 0.01 and 0.02, which are less than 0.1. So they're both important. There's one chance in a hundred, that's 0.001. I got that wrong. There's like 1 chance in 1000 that GNP doesn't help you predict computer sales after knowing education spend. And only 3% chance education spend doesn't help you after knowing GNP. So the question is, how good is this equation for forecasting? What use is it? The two numbers that help you there are these two. So, the R-squared of 74%, and then we'll look at out lackers. Okay, that, basically, says our equation explains 74% of the variation in computer spent. There's 26% not explained. Is that a good R-squared? It's hard to tell. Okay, it's hard to tell if it's a good or a bad or a square. Really, what's more important is the standard error. Okay, so the standard error is 29. That means, again, 68% of forecast accurate within $58 per year. Sorry, within 29. 95% accurate. Within $58. So are there any outliers? Well let's see if there's any of our observations where the error is off by more than $58. I think there's one. I think it's Switzerland, 18th observation here. So the 18th observation third from the bottom is Switzerland. Now that's not a horrible outlier. It's not more than three standard deviations. So I'm not going to throw it out. Again, that would be a judgment call there. But we'll leave it in. So how do you interpret these coefficients? After adjusting for GNP, 1% more GNP spent on education Yields $15 more in computer sales. And if you do this per 1,000, if I multiply this coefficient by 1,000, it will tell you a bit more. A $1,000 increase in GNP. This is all interpreted after adjusting for the other variables. The phrase is ceteris paribus. Means basically, about two bucks more spent on computers per year. And we'd expect 95% of our forecast to be accurate within $58. Is that good enough? Well, it's the best you can do. Okay, so now we'll get back to sports in the next video. Where we talk about linear weights, which is a very important topic in really all sports. Football, basketball, particularly basketball, but mostly baseball. But we've learned about regression to understand linear weights and we'll get back to that in the next video.