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Quantitative Methods
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QMS 202
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Charles Barkley
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Lecture

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Quantitative Methods

QMS 202

Charles Barkley

Winter

Description

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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