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Casio CFX-9850 TechSkills 1_ Functions.pdf

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Quantitative Methods
QMS 202
Charles Barkley

Casio CFX-9850 TechSkills 1: Functions Casio CFX-9850 TechSkills 2: Regression In this TechSkills module, we take a given data set and fit an appropriate function to the data. The formal process of fitting a function to a given data set is called regression. Regression is a formal component of statistics. We start with fitting the simplest type of function, a linear function. Linear Regression Linear regression is the process of fitting a straight line to a data set. A linear function has the form y = ax + b. Hence, the task of linear regression is to determine values for a and b that create the straight line that best fits the given data. For example, we consider a data set from Sullivan and Sullivan, Precalculus enhanced with graphing utilities, Second Edition, page 112, Example 3. Plot 1 2 3 4 5 6 7 8 9 10 11 12 2 Fertilizer, X (lbs/100ft 0 0 5 5 10 10 15 15 20 20 25 25 Yield, Y (bushels) 4 6 10 7 12 10 15 17 18 21 23 22 Our first task is to enter the data set into the Casio. Fortunately, the Casio makes this a simple task. Turn the calculator on, and then press the key to display the MAIN MENU. Press to select the STAT menu. A spreadsheet is now displayed. Enter the fertilizer amounts in List 1 and the corresponding yields in List 2. Use the thumb pad to navigate from List 1 to List 2. To enter the fertilizer amounts in List 1, press , , , , ..., 25 . Then use the thumb pad to navigate to List 2. To enter the yields in List 2, press , , 10 , ,..., 22 . Note that a specific number is not actually placed into the list until you press the key. After the data set has been entered and checked for accuracy, we are ready to see a plot of the data. Press the key to access the GRPH menu. Press to select GPH1, statistical graph 1. A plot of the data set appears. Notice that it looks reasonable to fit a straight line through the displayed data points. A suite of regression types appears at the bottom of the screen. Press to select X, the CasioÕs symbol for linear regression. The screen then displays the LinearReg screen with the values for the linear form y = ax+b for the straight line of best fit. Here, to three decimal places, the linear equation of best fit is y = .717x + 4.786. Press to select COPY to copy the linear regression equation into the Graph Func editor. Press to store the regression equation as function Y1 in the Graph Func menu and return to the LinearReg screen; otherwise, press to return to the LinearReg screen. Press to select DRAW. The Casio then displays the linear regression line superimposed on the data. Of course there are other functional relationships besides linear. The Casio supports a handy suite of choices, including linear, quadratic, cubic, quartic, logarithmic, exponential, power, sinusoidal and logistic. Casio CFX-9850 TechSkills 1: Functions Non-Linear Regression To illustrate obtaining a function from data, we utilize a data set for the growth of the brewers' yeast, Saccharomyces cerevisiae, obtained by the biologist Tor Carlson in 1913. Here, time is measured in hours and population in biomass units. First enter the data set. Press to return to the spreadsheet. To clear the old data, press again to return to the main spreadsheet menu. Press to access more options. Press to select DEL-A (delete all), and then press to select YES. Use the thumb pad to move to another column with data and delete the entries by pressing the key, then press to select YES. After the old data are completely cleared, then enter the new data set. After the data are entered and checked, then we are ready for the regression. If GRPH is not displayed as the menu item, press the key to select more menu options until GRPH is the F1 menu item. Then press to select GRPH. Press to select GPH1. A plot of the data set appears. Use V-Window to adjust the viewing window; for example, Xmin: -1, max: 8, scale: 1, Ymin: 0, max
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