Speaker 1:	Suppose we have a web based business, and suppose these our price, and corresponding sales in a couple of days. For example, here, I have set the price to 89 and I have sold 30 huge units. Here I have set it to 60 and I have sold 50. Now suppose we like to develop a linear curve, to represent this demand. Here I select my data, insert, scatter graph, add chart element, access title, primary horizontal. I'll go here, and I say equal to sales. Add chart element, vertical, I go over there, say equal to price. For chart title, equal to price and quotation mark space versus space, quotation mark, and sales, and I enter price versus sales. Then I come here and say equal to price veses sales. I have this data. I will go over here and I type "Add Trendline" and I select "Linear trend line". I say display equation on the line. Therefore, the equation is telling me, that price is equal to 175-2.5 sales. If sales is zero, price is 175. If price is zero, sales is 175/2.5. A display R^2 R^2 here is a large number. R^2 coefficient of determination is something 0-1, which is always positive. The closer to one, the better if our Theta would have been like this, then the trend line, that I may have fit to this red points, would have been something like this, with a small value of cofficient of determination. What small value says is if you have x, if you have x, you cannot estimate y by precision because this x and this x are equal, but they do have entirely two different y values. The closer the dots to a line, the higher the cofficient of determination. These points, if we fit aligned to them, have a high coefficient of determination. These points, we'll have a high coefficient of determination, close to one. The equation of the line, tells us that the line will intersect y axis in about 175, and then with slope of -2.5 will go down. In general, we show the equation of a line with y=b_0+b_1x, b_0, is intersect, b_1, is the slope. In this case, in the case of the relationship between price and quantity, the slope is negative. The higher the price, the lower the sales. Now let's compute this equation in a different way. I come here, I type "P" here, I type "Q" here, I type "Intercept". Ask me what are your y values? I say, these are my y values. Then it will ask what are your x values? I say these are x values and then I say, let me know where this line cuts the y axis, it tells me in 175. This was my intercept, slope. I will click on my comma and my xs and enter. I will tell me with the slope of -2.5, it will go down. Let's see what this 1.75 means. Where the line cuts the y axis, that means if you put price equal to that value, which is 175 in our case, if you set it, you sell nothing. Then because it comes down with that slope, then I go here. If I am at 175, and if I come down at slope of -2.5 and therefore I divided by negative of -2.5. I say, if I set my y=0, what will happen? I will have 0=-2.5+-2.5x+175. Therefore, if I take -2.5x to the left hand side, I will have 2.5x=175. What I did here, I said, what would be if I divide 175 by negative of -2.5, which is +2.5, and then it will give me this number. What this means, it says, even if you set your price equal to zero, the max you can do is to sell 70 units. Now, what is the meaning of this 70 units? Even if you set the price equal to zero, at most, you can sell 70 units. That means your site is visited 70 times and not more. If we set price to 175, we sell nothing. If we set price equal to zero, we sell 70. Before going any further, let me provide you with another interesting application of this trend line and as we refer to it, regression line. This is the data I have with respect to volume of production, and total cost. Now I come here, I mark this data, insert this line. This is a scattered graph of that data. Then I go and right click on it as before and say "Add Trendline" and that would be linear trend line, and I say display the equation. Display R^2. The equation and R^2 are shown over there. Go to total cost, and quotation mark space versus that space quotation mark and Q. Total cost versus Q, go here, say equal to this and that is my graph. Using this graph, I also write the formula here, which is equal to intercept of y values, which are my total cost and x values, which are my volume of production, enter, that is my intercept. I also go there I see slope and y values, x values. These are those coefficients of my regression line. As we can see, it is 1200+16x, and here is my 1,200 and is my slope. Now because it is total cost, I can say my 1,200 is estimate of fixed cost and 16 is my estimate of variable cost. R, as we see here is high. High R is good. That means changes in x can be explained in terms of changes in y. I have created three different curves here to show you what are the differences between different R values. Let me take this one over there. This is the data over there. As we see, R^2=0.86. This is another set of data still in the same column, another set. In all of these, R is high, is closer to one than zero. Therefore, we say a significant portion of changes in y can be explained in changes of x. R^2 here is positive, close to one. Now let me take you to this example. Here, this is the first column and the third column. Here, again, we have a good R. While the relationship is negative, R is still good and close to one negative and positive slope of the line, it doesn't matter. What it matters is whether this line can express those numbers reasonably. Now I provide you with a situation when R is closer to zero. Look at here. These numbers, we cannot represent the changes in y in terms of changes in x. For example, this x and this x and this x all have more or less the same y. The left one is an example when B_1 slope of the line is positive, but those dots are in line with each other. R always comes out hi, 0.91, 0.86, 0.97, and so on and so forth. The relationship between x and y in the second graph is also good, but the relationship is negative as x goes up, y comes down, but changes in y can be reasonably explained in terms of changes in x. However, in this third line, R^2 is quite close to zero. That means relationship between x and y cannot be explained. Changes in y cannot be explained in terms of changes in x. Good, not good. you may ask how these regression lines are drawn. We find a regression line. The best regression line is a line for which the difference between what we see on the line and what we see in real life is minimized. For example, for this x, I observe this y, but on the regressional, I have this one. For this x, I observe this y, but on regression line, I have this one. Therefore, if we find the actual value of y when we put when we had it for specific x, and if we compute y in terms of the value of x and the line, the best line is a line for which the square of these gaps is minimized and that is why they call it list square method. In all three examples, the lines are the best lines. The sum of the squares of the gap between actual observation and the value computed under regression line for a specific x is minimized. But this one, this relationship is reasonable. This one is reasonable, and this one is not reasonable.