[PDF] TI-8283 Data Fitting Tutorial—An Overview

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TI-82,83 Data Fitting Tutorial - An Overview

What should this tutorial help you do with your TI-82,83 Calculator? After completing this tutorial, you will be able to: l Enter, graph and manipulate data relating two variablesm Find linear, exponential, and power regression functions for your data - that is, find the linear, exponential or power function that best fits the data ( in the sense of minimizing the sum of the squares of the vertical deviations of the func tion graphs from the data points).m Determine how well a regression function fits the data points by statist ical as well as graphical means.m You will do all this in an interactive context involving some interestin g real data on stomach and lung cancer.l

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DF_pg01

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An Illustrative Problem: Cancer Data

The best way to learn the data-fitting capabilities of the TI-82,83 is t hrough a real problem using real data.l The table below lists the number of deaths per year, per 100,000 women i n the U. S. from lung cancer and stomach cancer during this century.l Our task is to find the linear, exponential and power functions that bes t fit this data, and evaluate the "goodness of fit" for each of these functions.l

YearLung CancerStomach Cancer

1930228

19402.520.5

19505.114

196069

1970105.5

1980214.5

199030.53

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DFPG02

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TI-82, 83 Similarities and Differences as they relate to this tutorial The primary keys on the TI-82 and TI-83 are the same and are in the same positions on the keyboards. There are differences between the 2nd functions, alpha functi ons, menu items and menu item positions.l Differences between the 2nd functions and the alpha functions do not com e in to play in this tutorial.l Differences between menu items, the placement of menu items and the use of menu items will be noted. Different TI-83 keystrokes will be placed in [*] after the TI-82 keystrokes are given.l

All graphic displays are for the TI-82.l

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df_pg03.htm http://mtl.math.uiuc.edu/non-credit/fitting82/HtmlPages/df_pg03.htm [03-

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The Statistics Menu

The TI-82 keypad is shown to the right.l

In this tutorial, we will be making extensive

use of the Statistics menu shown below. [TI-83 screen shows '5:SetUpEditor' also]l

To get to the Statistics menu, press the STAT

key (outlined in red on the keypad).l

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Clearing Previous Data

To clear any previously stored data, press the

4 key while in the Statistics menu. This will

display ClrList on the Home Screen as shown to the right.l

To clear lists L

1 , L 2 and L 3 , complete the command to readl

ClrList L

1 ,L 2 ,L 3 as shown in the first line of the middle screen. Then press the ENTER key.

The TI-82,83 will respond with the

message DONE as shown in the middle screen.

The lists L

1 through L 6 are referenced using the 2nd key (upper left on the keypad, outlined in red in combination) with the appropriate key 1-6 also outlined in red. For example: L 4 = 2nd, 4 m

Exercise 1: Clear lists L

4 , L 5 and L 6 .l

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Exercise 1 Answer

Use the following keystrokes:

l

STAT 4 to get the upper screenl

2nd 4(L

4 ) , 2nd 5(L 5 ) , 2nd 6(L 6 ) to get the middle screenl

ENTER to get the bottom screenl

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To the Exercise1 page

df_pg24.htm http://mtl.math.uiuc.edu/non-credit/fitting82/HtmlPages/df_pg24.htm [03-05-2001 02:11:02] Making sure the TI-83's STAT EDIT lists and Regression information appear the same as the TI-82's List capabilities for the TI-83 are more extensive than those of the TI- 82.l
To insure that the STAT EDIT lists appear the same on the TI-83 as they do in the rest of this tutorial, do the following as a precautionary measure. Pressl

STAT, 5(SetUpEditor), ENTER The screen will

say SetUpEditor and DONE.

These keystrokes clear out any user-defined lists

which may have been in the STAT EDIT lists and put in the lists L 1 , L 2 , L 3 , L 4 , L 5 and L 6 To insure that information for LinReg, ExpReg and PwrReg which we will u se later are the same, perform the following keystrokes. Press l

2nd, 0(CATALOG), cursor down to DiagnosticOn

and then Press ENTER twice. The screen will say

DiagnosticOn and DONE.

These keystrokes cause the value of the correlation of coefficient, r, t o be shown.

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Entering Two-Variable Data

Return to the Statistics menu by pressing the STAT key. l Then press the 1 key to edit the lists. Any previous values should have been cleared from the lists. The resulting screen is shown at the right. l

Use the arrow keys to enter the years in L

1 and the lung death rate in L 2 . The resulting screen is shown at the right. [TI-83: the 1, 2, 3, etc. on L 1 , etc. will not appear as subscripts.] l Leave the remaining lists empty for now. We will need them later.l

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Displaying Two-Variable Data on a Scatter Plot

Press the 2nd key, then the Y= key (STAT PLOT) to get the STAT

PLOTS menu shown at the right.

l Make sure that all plots are OFF. To turn the plots off, press the 4 key, followed by the ENTER key. The TI-82,83 will respond with

DONE.l

Press the Y= key and clear any functions that may have been entered. This is accomplished using the ARROW keys and the

CLEAR key.l

At this point, everything that could have cluttered our data plot has been cleared or turned off. l (Continued on the next page ... )

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Displaying Two-Variable Data on a Scatter Plot

(Continued from the previous page) Return to the STAT PLOT menu by pressing 2nd, then Y=. l

Press the 1 key to change the options for Plot 1.

l Use the ARROW keys and the ENTER key to edit the screen so as to match the one shown at the upper right. [TI-83: Press 2nd 1(L 1 ) and

2nd 2(L

2 ) to assign L1 and L2 to Xlist and Ylist.] l Press ZOOM, cursor down to 9:ZoomStat and them press ENTER to display the data (or just press ZOOM 9) as shown in the screen to the right.l

NOTE: ZoomStat automatically sizes the GRAPH

window to display the data in the lists chosen.m Exercise 2: Enter the stomach cancer data into list L 3 , and display a plot of the data. Don't forget to change the Ylist in the Plot 1 menu (above) to L3.l

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Exercise 2 Answer

Use the following keystrokes:

l

2nd Y=(STATPLOT) 1m

Use the arrow keys and ENTER to match the upper

screenm

ZOOM 9 to match the lower screen

m

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Back

To the Exercise2 page

df_pg25.htm http://mtl.math.uiuc.edu/non-credit/fitting82/HtmlPages/df_pg25.htm [03-05-2001 02:11:17] Finding the Linear Regression Line for the Lung Cancer Data Return to the Statistics Menu (by pressing the STAT key), and highlight CALC by using the right ARROW key. Press the 5 key to show LinReg(ax+b) on the Home Screen. [TI-83: STAT, CALC, 4] l

Complete to get LinReg(ax+b) L

1 ,L 2 as shown on the upper screen at the right and then press ENTER to get the screen shown at the right.l The values of a and b are the coefficients of the regression line y = a x + b for the lung cancer data. The value of r is the correlation coefficient - more about its meaning later!l Exercise 3: Find the linear regression line for the stomach cancer data. l

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Exercise 3 Answer

Use the following keystrokes:

l

STAT CALC 5 2nd 1(L

1 ) 2nd 3(L 3

ENTERm

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df_pg26.htm http://mtl.math.uiuc.edu/non-credit/fitting82/HtmlPages/df_pg26.htm [03-

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Displaying the Linear Regression Line for Stomach Cancer with the Stomach Cancer Data Let's see how well the regression line for stomach cancer from exercise 3 fits the stomach cancer data by plotting both on a single graph. l STAT Plot 1 should already be set up to display the stomach cancer data which is in L 3 because of exercise

2. You might wish to see, however, that STAT Plot 1

shows the Xlist as L1 and the Ylist as L3. You may also wish to rerun LinReg L 1 ,L 3 to make sure the linear regression equation for the stomach cancer data is your current function. m Press the Y= key. All the functions should be cleared. (If not, clear them now.) The blinking cursor should be at Y 1 . (If not, move it there.) m Press the VARS key, followed by the 5 key (Statistics). m

Use the RIGHT ARROW key to select EQ, then press

the 7 key (RegEQ) [TI-83: press the 1 key]. This will copy the most recent regression data into an equation for Y 1 ( right screen). m Press ZOOM 9 (9:ZoomStat) keys to display the data and the graph of the linear regression equation (lower right screen). m Exercise 4: Display the linear regression line with the data for the lung cancer da ta (list L 2 ).l

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Exercise 4 Answer

Use the following keystrokes:

l

2nd Y= 1m

Use the arrow keys and ENTER to match the upper

screenm

STAT CALC 5 2nd 1(L

1 ) , 2nd 2(L 2 ) ENTER to get the linear regression equationm Y= CLEAR VARS 5 EQ 7 [TI-83: 1] to copy the linear regression equation into Y 1 m ZOOM 9 to get the plot of the data and linear regression linem

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df_pg27.htm http://mtl.math.uiuc.edu/non-credit/fitting82/HtmlPages/df_pg27.htm [03-

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Brief comments on the "Goodness of Fit"

of the Linear Regression Line The stomach cancer data is again shown to the right with its linear regression line. l The correlation coefficient (r) for this data was calculated along wit h the linear regression data to be: r =-0.9565401904l In general, the closer the absolute value of r is to 1, the better the f it. l In this case, the correlation coefficient does not rule out the possibil ity of a linear fit, but a look at the graph makes me think that we can get a better fit with some other type of regression.l

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Finding the Exponential Regression Curve for the Lung Cancer Data Let's have the TI-82,83 determine the exponential function y = a•b x that best fits the lung cancer data. l Press the STAT key again, highlight CALC, and use the

DOWN ARROW to highlight A: ExpReg. [TI-83: down

ARROW to highlight 0: ExpReg]m

Press the ENTER key once to show ExpReg on the Home Screen, complete

ExpReg to show ExpReg L

1 ,L 2 as shown in the upper screen and then press ENTER a second time to display the data for the exponential function tha t best fits the lung cancer data as shown in the bottom screen. m

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Displaying the Exponential Regression Curve for Lung Cancer with the Lung Cancer Data Make sure the TI-82,83 is set up to display the lung cancer data (list L2). (Review the "Displaying Two-Variable Data" pages if necessary.) l Enter the exponential function in the Functions menu.l

Press the Y= key. Clear out any functions in Y

1 and leave the blinking cursor there.m Press the VARS key, followed by the 5 key (Statistics).m Use the RIGHT ARROW key to select EQ, the press the 7 key (RegEQ) [TI-83: 1 key]. This will copy the most recent regression data (which should be the exponential regression data) into an equation for Y1 (upper right).m Press the ZOOM, 9 keys to display the data and the exponential regressio n curve (lower right).l

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Brief comments on the "Goodness of Fit"

of the Exponential Regression Curve The lung cancer data is again shown to the right with its exponential regression curve. l

This curve obviously fits the data quite well.l

The correlation coefficient (r) for this curve was calculated along wi th the exponential regression data: l r = 0.9905617187 which is very close to 1. Exercise 5: Determine the exponential function that best fits the stomach cancer da ta, and display it along with the data. l

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df_pg28.htm

Exercise 5 Answer

l

Use the following keystrokes:

m

2nd Y= 1

m

Use the arrow keys and ENTER to match the upper

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