 Hi there. In this screencast we're going to learn how to use GeoGebra to plot a set of data points, find a curve that fits the data plot, and then export the curve back into the graphics view so that we can work with it. I have here a set of data that represent the height of a child over a period of six years. The independent variable here is age, and the dependent variable is height, and I'm measuring that in meters. Let's suppose I want to guess how tall this kid will be when she's 18. For this, I would need to find a function that models my data in some way that I can then use to forecast the child's height for the future. GeoGebra can actually do all of this, as we will see. Let's first enter these data into GeoGebra and then plot the data points. In GeoGebra, open up the spreadsheet view by going to View, then Spreadsheet. Then enter in the independent variable, which in this case is age, into one column, and the dependent variable, which here is height, into the adjoining column. To make a plot of the data points, go into the spreadsheet and highlight the cells you want to plot, which in my case is all of them. Then go to the third icon on the left, click on the down arrow, and select Create List of Points. You can just click Create here now to accept the defaults. The points now appear as ordered pairs in the graphics view. This kind of plot of discrete data points is known as a scatter plot. I noticed that my scatter plot has a pretty definite shape to it, so I'm wondering if I can find a function whose graph goes more or less through these points. In other words, I would like to fit the data with a curve. Finding a curve that's a good fit to a data plot is a process known as regression analysis. To find a curve that fits the data, highlight the cells in the spreadsheet view. Then go to the second icon on the left, and click the down arrow, then select Two Variable Regression Analysis. Verify that the points are correct here, and then click Analyze. This opens up a new window that shows a copy of your data plot. We can play around with different kinds of functions to see which one looks best as a fit to our data by using the pull-down menu labeled Regression Model. For example, here's what a line of best fit looks like. It doesn't hit all the data points, but it's the best fit through the data that a line can possibly have. The formula for this line is displayed below the graph. We can also select other kinds of functions to see how different shapes look. For example, the polynomial fit gives me a second degree or quadratic polynomial that is a really good fit. I can adjust the degree of the polynomial here, so if I wanted a cubic instead of a quadratic, I would just dial this up to three and then everything updates. Now, given that this is a set of height values for a child, I know that the heights will eventually level off and not increase or decrease as time passes. A polynomial may not be the most sensible function to fit the data with, since a polynomial either increases or decreases to plus or minus infinity as we go to the right. Instead, I'm going to choose a logarithmic function, which, while it still increases to infinity as time gets large, the rate of increase is very, very slow, so it behaves much like my height values. Even though this log function doesn't fit the data as well as the other functions, if I want to make predictions for the child's height in the future, this might be the right model to choose. Now notice on the data analysis window, I can enter in an independent variable value and have GeoGebra use the model to compute the y value. So this logarithmic model would say that the child will be 1.9841 meters tall at age 18. Let's now define this function back in the main GeoGebra window so that we can work with it like any other function. I could type the formula by hand using the input bar, but there's no need for that. Instead, go up to this button here that looks like an arrow coming out of a square. Click and then select copy to graphics view. Back in the main GeoGebra window, the model is now available for me as a function and its graph appears on the graphics view. For example, I could type g of 18 to estimate the child's height when she is 18. Or I could type g prime of 10 to get the rate at which the child's height is changing when she's 10, which in this case is 0.1 meters per year. For that matter, I could plot the entire derivative of the height model to get a sense of the overall growth behavior over time. Anything that I can ordinarily do with a function I can now do with the model because I have defined the model as a function. So that's how to enter, plot, and analyze data in GeoGebra. Thanks for watching.