Nonlinear Modeling using the Equation Editor
Lesson
In the previous tutorials, you learned about linear functions and the mechanics of modeling them on Tuva. The slope of the function in linear models stays the same, that is, the effect of the x-attribute on the y-attribute remains the same in every step. In contrast, the slope of a nonlinear model changes, that is, the effect varies with each step. ![]700 ![]700 You can use the function editor to model the relationship between two quantitative attributes or variables. The mechanics are simple: drag and drop two quantitative attributes on the x and y axes, and fit a curve to approximate the relationship between the two attributes. Step 1: Create the Scatterplot and Open the Modeling Card Drag and drop quantitative attributes on both the x and y axes to create a scatterplot. !--- Note: If you do not plot both an x and y attribute, the f(x) functionally will not allow you to plot a curve. ---!{border-color:#008000;text-align:left;} To model the relationship (which in this context is between roller coaster height and speed), choose :ti[ti-f-of-x] from the toolbar to open the modeling card. The modeling card will appear on the left-hand side of your screen. ![]700 Step 2: Form Your Function In the modeling card, you can either enter the function in the editor, or choose the desired function form from the drop-down menu. If you choose a function from the drop-down menu, you may need to adjust the function for your own context. ![]700 When you have done this, two things happen: 1. Your function will appear on the graph. If it doesn’t, you will need to estimate the range of the parameter to get it in the viewing window, and/or zoom out. 2. The parameter (a in this case) appears as a slider below the function editor in the modeling card. ![]700 Step 3: Tweak the Parameter You can change the value of a parameter by dragging the slider pointer. As you do this, the curve will move. The default lower bound of the slider is -10 and the default upper bound is +10. You can tweak the minimum and maximum values by clicking on them and inputting the desired value. Hit enter to submit the maximum and minimum values. Alternatively, you can type in a new value for the parameter and press enter. ![]700 Additionally, if you feel that you need to make very small or large changes to the parameter value, click on the upper range of the slider and adjust the steps to the desired value. Step 4: Finding the Right Fit Continue to tweak the parameter value until you get the closest possible fit. In this case, you get a reasonable fit at 4.5. ![]700 You can read the details of the function from the :ti[ti-summary-view]. In the interactive tutorial that follows, you will use the equation editor to fit nonlinear data on dinosaurs on your own. You will also learn to tackle situations where the curve does not appear in the graphing area after inputting the function in the editor.
Topics and standards: Nonlinear Models, Tutorial