Information on Using the Regression Feature of the TI-83 calculator

 

DIAGNOSTICS ON  -  this should only be done ONCE, before you do your first regression

            2nd – 0  (for CATALOG)

            Type D – and arrow down to DiagnosticsOn – and press ENTER

 

Entering Data

            STAT – 1:Edit     

 

           If the lists L1 and L2 have values, these must be cleared out.  To empty them, arrow up to the VERY top of list L1, i.e.highlight L1, and press CLEAR, similarly L2, etc.

 

          Then enter data x values into L1 and y values in L2

 

Viewing a Scatter Plot

            2nd – STAT PLOT  (the Y= key or above the 2nd key)

            1:   ENTER,   On  ENTER  ¯ENTER   ¯L1  ¯L2  

-  (this defines Plot 1 as a scatter plot L1 & L2)

           Make sure that in Y=, all the functions are cleared out (or turned off)

           ZOOM-9:ZoomStat  will show a Scatter plot of the data

 

Getting the Regression Equation

            STAT    ®  CALC  ¯¯¯ to 0:ExpReg  ENTER  ?ENTER

            Record the equation indicated for the values of a and b, and record r

 

Graphing the Regression Equation

            In Y=, enter the regression equation.  You may type it in by hand and  graph.  It should graph

the function over the scatterplot points.

 

**Note:  A shortcut to typing the function into Y1 is in the Y= screen, at the Y1= location,

paste in the function by pressing the following sequence of keys:  

VARS   5:Statistics  ®®EQ 1: RegEq  ?ENTER

 

***To turn off ALL Plots ***  -  2nd – STAT PLOT -  4:PlotsOff  -   ENTER

 

Types of Regression Equations on the TI-83

QuadReg  - 

ExpReg - 

CubicReg  - 

PwrReg - 

QuartReg  - 

Logistic - 

LnReg  - 

SinReg  - 

 

 

 

 

 

 

Example:  Online Shopping

 

The commercialization of the Internet is marked by massive increases in advertising and online

shopping.  The accompanying table illustrates this trend.  Sales are in millions of dollars.

Year

1996

1997

1998

1999

Online Sales of Recorded Music Enrollment

18

47

110

240

a)  Find the exponential function to model this data.

Let t = 0 represent 1995.  Enter the years into list L1, and the sales into list L2.   Define,

using STAT PLOT, Plot 1, as a scatter plot on L1 and L2.  Press Zoom:9 to see the  scatter plot. 

STAT-CALC-0 – ExpReg ENTER, gives f(x) = 7.966*2.368x.  Enter this function into Y1,

and graph.  Neat!! Huh!!

 

Also, let’s rename this function into the y = Aekx  form.   To do this, realize that 2.368 = ek,   so

k = ln 2.368 » 0.862.  Thus the function could be renamed as f(x) = 7.966e.0.862x

 

b)  Use the function to predict the online sales in 2002 … so find f(7) = 7.966e.0.862(7) =3,326.

 

 

Another Example

**Remember to clear out the functions in Y= between problems**

 

Example:  U.S. Population Model

The following data obtained from the U.S. Census Bureau represent the population of the United

States.  An ecologist is interested in finding a function that describes the population of the U.S.

Year

1900

1910

1920

1930

1940

Population

76,212,168

92,228,496

106,021,537

123,202,624

132,164,569

 

1950

1960

1970

1980

1990

151,325,798

179,323,175

203,302,031

226,542,203

248,709,873

 

a)  Let t = 0 represent 1900.  Enter the years into L1 and population into L2.  Define, using STAT

PLOT, Plot 1, as a scatter plot on L1 and L2.  Press Zoom:9 to see the  scatter plot.

 

b)  STAT ®CALC  ¯¯ -B:Logistic ENTER, (wait patiently …, it’s VERY slow!!) gives

f(x) = 695129657/(1+7.9105 e-0.0166223kx)    Enter this function into Y1, and graph over the points

on the scatter plot.

 

b)  Use the function to predict the population of the U.S. in 2001, this years census. (I got 280,744,859).   

 

c)  If this model continues, when will the population of the U.S. reach 300 million? 

Let Y2=300000000.  Extend the WINDOW so that Ymax is over 300,000,000, and Xmas is 120. 

Graph … and find the intersection point – t = 107.9 … so approximately in 2007.