Determine how well the graph of the equation fits the scatter plot.ĥ.2.1 Use the logistic regression equation to estimate the number of people who knew the rumor on the fifth day and compare the estimate to the actual number given in the data. The logistic regression equation is stored in Y 1. The logistic equation that best fits the data is approximately , as shown at the top of the screen, and the values for the coefficients a, b, and c are shown below the equation. The form of the logistic regression equation is , and Y 1 is found in the Function submenu in the VARS Y-VARS submenu. Paste the Logistic command to the Home screen by pressingĬomplete the command Logistic L 1, L 2, Y 1 by adding L 1, L 2, and Y 1. The TI-83 can generate a logistic regression equation that best fits the data. Generating the Logistic Regression Equation The value of c is the upper limit of the size of y and y = c is aĪ line y = c is a horizontal asymptote for the graph of a function if the y-values approach c as the x-values approach positive or negative infinity. Then press 7 to choose the residuals: The term RESID will then appear next to. Then scroll down to YList and press 2nd and then press STAT. Hover over the On option and press press ENTER. Each logistic graph has the same general shape as the data shown above and represents a function of the formĢ.71828. In the new screen that appears, press ENTER on the first plot option. When the data points have a shape like this, it is reasonable to try to find a logistic regression equation to fit the data.Ī logistic function models a growth situation that has limited future growth due to a fixed area, food supply, or other factors. To do that, the data must be entered into lists in the Stat/List editor.Įnter the "Day" values in L1 and the "Number Who Know" in L2.ĭefine a scatter plot of the data using squares for the Mark type and display the scatter plot in a ZoomStat window. The number of people who know the rumor each day is shown below.Ī scatter plot provides a better way to illustrate the data.
Then scroll down to LinReg (ax+b) and press ENTER. Then enter the x-values of the dataset in column L1 and the y-values in column L2: Step 2: Find the Line of Best Fit Next, we will find the line of best fit. On subsequent days, each student who knew the rumor used the randInt command to select a student to tell. Step 1: Enter the Data First, we will enter the data values. On the second day, the initial student then randomly selected a student to tell by using the randInt command. The simulation of the spread of a rumor was created by randomly selecting one student to know the rumor on Day 1. An equation that models the data will be found by using the logistic regression feature on the TI-83. Scatter plot of those values will be created.
Data from the experiment will be entered into a table of values and aĪ scatter plot is a graphical display of data plotted as points on a coordinate plane to show the relationship between two quantities. In this lesson you will use the TI-83 to model the data created in Lesson 5.1.
Module 5 - Logistic Growth - Lesson 2 Module 5 - Logistic Growth
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