Creating and Estimating Nonlinear Models on Tuva
Lesson
In this tutorial, students explore the Dinosaurs dataset to learn how to create nonlinear models on Tuva. ![]720
In this tutorial, you will explore the Dinosaurs dataset to learn how to create nonlinear models on Tuva. ![]720 When you fit a movable line to a scatter plot, you approximated the relationship between the two attributes. You may have used certain criteria to get the best possible fit. A few of these criteria could be: Roughly, are there the same number of data points on either side of the line? Are the dots, more or less evenly distributed around the line? Is the average distance from your line to each of the data points as small as possible? You did an eyeball estimation to assess the fit but if you were to compare the equation of your line with another person's model for the same data, it is highly likely that the two equations would differ. While eyeballing a line works reasonably well, statisticians use a variety of standard methods and criteria for fitting a line to data that give them comparable models. One such method uses the Least-Squares line also known as the Least Squares Regression Line (LSRL). ![]700 Before we dive into what that means, we will take a look at the mechanics of adding the line to a scatter plot and using it to model the relationship between two attributes. Adding a Single Least Squares Line (LSRL): Step 1: Add the LSRL from the Model Data Menu Once you have created your scatter plot, you need to choose the :ti[least-squares-line] from the toolbar to add it to the scatter plot. ![]700 Step 2: View the Equation of the LSRL Now that the least squares line is added to the plot, you may view the equation and its components in one of two ways, by hovering on the line to view the equation or by opening the :ti[ti-summary-view] and seeing its parameters listed in the table. ![]700 You can also add multiple LSRLs to your graph. Adding Multiple Least Squares Lines: Within a scatter plot, Tuva allows you to separate data points by category. How? You simply add a categorical attribute to the legend. Additionally, you can generate a least squares line for each of these categories. Here are the steps: Step 1: Create a Scatter Plot with a Categorical Attribute in the Legend Area Once you have created a scatter plot, you need to select a categorical attribute by single-clicking it in the :ti[case-card] or by dragging and dropping it in the legend area directly. ![]700 Step 2: Add Multiple Least Squares Lines Next, you need to choose :ti[least-squares-line-by-category] from the toolbar to add multiple least squares lines to the scatterplot. ![]700 Step 3: View the Equation of the Lines Now that the least squares lines are added to the plot, you may view the equation and its components in one of two ways, by hovering on the line to view the equation or by opening the :ti[ti-summary-view] and seeing its parameters listed in the table. ![]700 In the interactive tutorial that follows, you will explore data on Dinosaurs to learn the different ways you can use the least squares line to model the relationship between two attributes. You will also learn to use the context menu, display the sum of the squared residuals for the line and work with the :ti[ti-summary-view].
Topics and standards: Nonlinear Models, Quadratic Models, Tutorial