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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

Fertilizer, X (lbs/100ft2)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.

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