INSTRUCTOR: I'd like to show you how to enter data points and also to calculate a logistical function regression in Desmos. So here we are in desmos.com. And we go to the graphs. And the default axes have labels on them. You can see that they are evenly spaced in the x and y directions. And that may or may not be what we need for our data. 

So when we want to enter the data, we can insert a table here that has an x and a y column. And I can actually plug in the coordinates. So if my first point is the point 0 and then the y-coordinate is 6.1, I can enter that data. And as I hit Enter, it will take me to future rows. But if I already have the data entered in a table elsewhere, I can use that information. So I'm going to erase that. 

But I have this data table in an Excel spreadsheet. And so I'm going to highlight the data I left off the labels, but I've copied the data. And now when I go back into Desmos and paste it, you can see that all the data appears here. Now, one of the things that it sometimes will do, depending-- it says it zoomed to fit your data. And so the axes have been automatically adjusted. 

There are some times when you're graphing in Desmos when it does not automatically adjust for you. And if that's the case, you can go to the settings with the wrench here, and you can manually select what you want for your data, for example, on the x-axis, if I wanted it, instead of starting at negative 10, perhaps, I wanted to start it at negative 5. 

Then in the y direction, if I wanted to change the starting place of the y-axis, instead of being at negative 133, perhaps I wanted to begin at negative 200, I could change that as well. The scale shrinks slightly. You don't actually see the number 200 here because my screencast window has cut off the label that's on that axis. 

Next, if we want to perform the regression on that, we should type the regression equation in one of these boxes over here. So I'll type it in box number 2. And because my coordinates are labeled x1 and y1, I'm going to say that y1-- and for regression, I'll use the squiggly. And the regression equation looks like this. c divided by 1 plus a times e. And I'm going to explicitly put the times symbol in there, raised to the power negative b times x1. And x1 is the input variable. 

And you can see that we get this nice-looking curve here. And I'll just move it up so that you can see the regression curve that goes through the data points. And it's got a very, very high r squared value of one. And when you look at the points, they don't quite exactly fit all on the curve. This one's lying a little below the line. 

So you might expect it to have an r squared value of slightly less than 1. But what we're seeing here is that the rounding, it's probably 0.9999 or whatever decimal place, wherever they round it, which is typically to three significant figures or to the nearest thousandth, that it does round off to 1. 

If we were to skew one of these data points and make it different-- so let's make this, let's say, 800-- we can see now that our r squared value-- hiding this keypad-- has now changed. And it is not quite the value of 1, but it's 0.985. And again, because we put that additional data point up there, it caused the curve to try to move up and some of the points to fall off the line.