Speaker 1:	Let me introduce you to regression through the data in the game. I go to customer orders. There are two sets of data here, plot job arrivals, plot rejected jobs. Job arrivals are those that we have accepted. Rejected job, rejected due to limit on our working process. Here in this data that I have, I have not rejected any job. If I had, I should add it to the job arrives. I go to Job arrivals, download it into an Excel sheet, enable content. Here I mark this data, insert scatter graph. I talk about three ways of doing regression, the easiest way, the worst way, and the best way. This is the easiest way. I write click on this at trend line, linear trend line, display equation on the chart, display R^2. Everything is here. Here is our slope of the line, and here is the intercept. Here is R^2. It shows if this line is a good fit to this data. R^2 is between 0-1. If it is close to one, it's very good, close to zero, not good. This was the easiest way. The worst way, data analysis. If you don't have data analysis, you can just add it exactly the same as the way you added solve data analysis. Go down to regression. Where is your Y range? Here, that is my Y range? Where is your X range? Here is my range. Do you want the output on a new sheet or on this sheet? I want this sheet, I want it here and the data is prepared. This is intercept. The same intercept as we had it here. This is slope This is R^2, the same R^2 as we had it here. This is multiple R. Multiple R is also called correlation coefficient. R^2 also is called coefficient of determination. R^2 is equal to correlation coefficient to the power of two. Multiple R is a square root of R^2. Because the relationship could be positive or negative. In this case, the relationship is positive, but it could have been negative. I should also write here sign of this one. Here it is positive, but if it was negative, I have a negative sine. I can also go here and type equal to correl and for correl ask me for Y values, X values, this way. Of course, this is equal to this to the power of two. Coefficient of determination or R^2 moves from 0-1. Correlation coefficient goes from negative one to positive one. From zero to positive one, from negative one to positive one. This is coefficient of determination, and this is correlation coefficient. Therefore, if I tell you which one shows a better relationship, a coefficient of determination of 0.9 or a correlation coefficient of negative 0.99. Which one is better? This one is better while it is negative because if we square it, it will be a number very close to one compared to 0.9. Remember this if I give you correlation coefficient to compare it with coefficient of determination, you need to square correlation coefficient and then compare it because negative 0.99 correlation coefficient is as good as positive. Other things that we may consider in this table is we want this P value to be as small as possible, less than or equal to say 0.025 or even less than or equal to 0.001. The smaller, the better. The larger, the better. The larger, the better. Larger, but this one, it's absolute value because negative 0.9 is as good as positive 0.9. Why this is not a good approach? Because if I change my data here, if I make this 300, nothing happens in this table. Each time I change my data, I must recalculate this table. Now let's go for the best approach. Intercept equal to intercept of these data, these are my Y values. These are my X values. That is the same thing we found over there. Now, I come here slope. Equal to slope. Y values, X values. That is slope which we got. However, I could go here. I could mark this a four, lock it, and then copy this down, and then go here, mark this instead of intercept and type slope. Then I can copy this down. Double click on it, and type RSQ. I can double click on it. Mark this ST I really don't remember it. STEYX enter. This is R^2, and this is standard error. Standard error is something like MSE. It is a little bit different, but we can just assume it as MSE. When we say we have the forecast for the next period, indeed, in moving average in exponential smoothing and in regression, that is average of forecast and then we accompany average of forecast with standard deviation of forecast. This is standard deviation of forecast. Now, let's forecast for all periods equal to intercept and lock it plus slope and lock it times period. That is our forecast for period one, and this is our forecast for period 51, 52, and 53. Now I can come here "Control" "Shift" down, insert, scatter graph. I can come here, "Control" "Shift" down, copy, paste, and that is my regression line. Our forecast for next period follows normal distribution. Its average is down here. For period 51, average is five, about five. In the standard deviation is this much 1.7. That is more information about future. It was the case in moving average and exponential smoothing too. What we define as our forecast is indeed our average forecast, and then we have standard deviation. In moving average, we did 1.25 MD oR^2 root of MSC, the same for exponential and this standard order or has some meaning similar to that MSC with minor difference, and that goes to degrees of freedom. Thank you very much for paying attention to this talk.