10-5 Nonlinear Regression 567 Nonlinear Regression Access tech supplements, videos, and data sets at www.TriolaStats.com TECH CENTER Statdisk Statdisk can find the quadratic model using the Multiple Regression function. The following procedure features data from Table 10-7. 1. Enter the population data from Table 10-7 in column 1 of the Sample Editor. 2. Enter the corresponding coded year values (1, 2, 3 . . . , 12) in column 2. 3. Enter the squares of the coded year values (1, 4, 9, . . . , 144) in column 3. 4. Click Analysis in the top menu. 5. Select Multiple Regression from the dropdown menu. 6. Select columns 1, 2, 3 and select column 1 as the dependent variable. 7. Click Evaluate. Statdisk provides the coefficients for the regression equation and value for R2. StatCrunch StatCrunch can find the model for a quadratic function (polynomial of order 2). 1. Click Stat in the top menu. 2. Select Regression from the dropdown menu, then select Polynomial from the submenu. 3. Select the column to be used for the x variable and y variable. 4. For a quadratic function select 2 under Poly. order. 5. Click Compute! Minitab 1. Click Stat in the top menu. 2. Select Regression from the dropdown menu and select Fitted Line Plot from the submenu. 3. Select the column to be used for the Response y variable and the column to be used for the Predictor x variable. 4. Choose the desired type of regression model: Linear, Quadratic or Cubic. 5. Click OK. TI-83, 83 84 Plus Calculator 8 us Ca cu ato 1. Turn on the Stat Diagnostics feature by pressing the G button, scrolling down to Stat Diagnostics, highlighting ON, and pressing [. 2. Press K, then select CALC in the top menu. 3. Select the desired model from the list of available options, then press [. 4. Enter the desired data list names for x and y variables (for TI-83 calculators, enter the list names separated by ,). 5. Select Calculate and press [. TIP: For TI-83 Plus calculators, turn Stat Diagnostics ON by pressingF 0for the Catalog menu. Scroll down toDiagnosticON and press [twice. R The basic syntax for creating a nonlinear least square test in R is provided below. R command: nls(formula, data, start) Where - formula is a nonlinear model formula including variables and parameters. - data is an optional data frame used to evaluate the variables in the formula. - start is a named list or named numeric vector of starting estimates. A complete list of R statistical commands is available at TriolaStats.com Excel The XLSTAT add-in cannot be used to create nonlinear regression models, so Excel itself must be used. 1. Select the range of cells containing paired data. 2. Click the Insert tab in the Ribbon and select Scatter in the Charts section. 3. Right-click on any data point on the scatterplot and select Add Trendline . . . 4. Selected desired model and check Display Equation on chart and Display R-squared value on chart. Statistical Literacy and Critical Thinking 1.Identifying a Model and R2 Samples of different square circuit boards are obtained. The sides of the squares are measured in cm (centimeters) and the areas are measured in cm2. Let x represent the side of a square, and let y represent its area. What formula best describes the relationship between x and y? Which of the five models describes this relationship? What should be the value of R2? 10-5 Basic Skills and Concepts
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