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Appendix 3
Method to Create a Cubic Regression Equation
This procedure is used to generate the coefficients for a cubic regression equation for a user-generated lean growth curve in the growth mode. These instructions apply to the Microsoft Excel® spreadsheet program. The use of this software program for this example should not be viewed as an expressed endorsement of the software by the authoring subcommittee or the National Research Council (see Note at the end of this Appendix). Other programs can be used, but the process of generating the coefficients will differ.
The Y statistic in the regression equation is the percentage of the overall mean of the carcass fat-free lean growth rate (or mean protein accretion rate) at a given body weight, with this overall mean expressed as 1.00. For example, if a value is 80 percent of the overall mean, the value at that point is 0.80.
Enter data so that the X variables (body weight) are in column A and the Y variables are in column B (or a column to the right of the X variables. NOTE: There must be at least 5 data points, and the mean of the Y variables should be 1.00.
Create a scatter plot of the data. First, highlight the data cells, then go to the tool bar and click on ChartWizard; the ChartWizard will guide you through the process if you follow the instructions in the dialog box at the bottom of the screen.
Click the mouse and drag a box on the screen. Then click in the following order: "Next, XY (scatter), Next, 1, Next, Next." Under "Add a Legend?", click "No" then click "Finish."
Double click on the chart that you have created; this will put you into chart edit mode.
Carefully click on one of the data points; this should highlight all data points. If not, click in another area and try again.
From the menu at the top of the screen, click on "Insert," and then select "Trendline."
A Trendline dialog box will appear with "Type" and "Options" as two tabs. On the "Type" page, single click on the "Polynomial" box; then under "Order,'' change to the number "3."
Now click on the "Options" tab in the dialog box and click the small boxes beside "Display Equation on Chart" and "Display R-Squared Value on Chart." Make sure that a check mark appears in those boxes. Click "OK."
The equation is now shown on the graph (see Appendix Figure 3-1). If it is covered by the trend line, click on the equation and drag it to a clean area.
The coefficients shown in the equation are entered in the model under user-generated lean growth curve. Note that, for Excel®, the coefficients are in reverse order as compared with the coefficients in the model. The R2 value indicates how well the data points fit the trend line (an R2 value of 1.0 is a perfect fit).
If the fit is poor, you might try a quadratic trend line. Repeat the procedure, except change the "3" to a "2" in item 6. If you select a quadratic equation, rather than a cubic equation, then enter a "0" in the fourth blank in the user-generated lean growth equation in the growth model.
Print and Save.
Note: Excel® is a registered trademark of the Microsoft Corporation in the United States and/or other countries. The Microsoft Excel Solver program was developed by Frontline Systems, Inc., P.O. Box 4288, Incline
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Appendix Figure 3-1. Graph of a cubic regression equation.
Village, NV 89450-4288. Portions of the Microsoft Excel Solver program code are copyright 1990, 1991, 1992, and 1995 by Frontline Systems, Inc. Portions are copyright 1989 by Optimal Methods, Inc. The Microsoft Excel Solver program uses Generalized Reduced Gradient (GRG2) nonlinear optimization code developed by Leon Lasdon, University of Texas at Austin, and Allan Waren, Cleveland State University. Linear and integer problems use the simplex method with bounds on the variables and the branch bound method, implemented by John Watson and Dan Fylstra, Frontline Systems, Inc. The Microsoft Excel Analysis Toolpak was developed by GreyMatter International, Inc., 173 Otis Street, P.O. Box 388, Cambridge, MA 02141. The Microsoft Excel® Spreadsheet Solution Templates were developed by Village Software, 186 Lincoln Street, Boston, MA 02111.
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Representative terms from entire chapter:
lean growth