Linear  Regression

 

The following example illustrates step-wise the use of the TI-83 to do a scatter-plot and a linear regression.

 

Part 1:  (Scatter- plot)  Scatter plot the following data:

x

6.5

11

13.2

15

18

23.1

24.4

26.6

30.5

34.3

37.6

41.5

y

0.51

0.68

0.73

0.79

0.88

0.99

1.01

1.08

1.13

1.26

1.28

1.32

 

1. Press:

     MODE      uu   u    ENTER           (sets FUNC graphing mode)

2. Press:

    STAT     5                                                    (selects 5:SetUpEditor)

3. Press:

    ENTER                                                       (stores lists in columns)

4. Press:

    STAT    1                                                     (selects 1:Edit)

 

If  elements are stored in  press:

t      CLEAR      ENTER      4      t      CLEAR      ENTER     

   

                                                                         (clears both lists)

then press:  3                 (moves cursor back to first row in )

 

5. Press:

     6      ·      5      ENTER                                       (stores 6.5 in )

 

Repeat to enter each of the twelve x-coordinates in the data-table.

 

6  Press:    4                 (moves cursor to the first row in )

7. Press:      ·      5 1      ENTER            (stores .51  in )

 

Repeat to enter each of the twelve y-coordinates in the data-table.

 

8. Press:      y =        (if necessary, clear any previous function by pressing  CLEAR )

 

9. Press:     t      ENTER       4        (turns off Plot 1, Plot 2, and Plot 3)

10. Press:      u      3      ENTER      ( to deselect function if necessary)

11. Press:     2nd       STAT      PLOT        1         ENTER       (turns on Plot 1)

12. Press:     u      ENTER                  (to select scatter plot)

 

 

 

13.  Press:     u      2nd                     ( to specify xlist: for Plot 1)

14.  Press:     u      2nd                     ( to specify ylist: for Plot 1)

15.  Press:     u      4      ENTER         (to select  +  as mark)

16.  Press:      ZOOM      9                      (to select  9:ZoomStat)

 

(Scatter) Plot 1 is displayed.

 

Part 2 (Linear regression)

 

To obtain a linear regression  to the data:

 

1.  Press:     STAT       4      4              ( to select 4:LinReg(ax + b) from STAT CALC)

2.  Press:     2nd           ,       2nd             ,

3.  Press:     VARS      4      1               (displays VARS Y-VARS FUNCTION)

4.  Press:     1                                           ( selects  1: )

 

Observe that  , ,   and     are pasted to the home screen as arguments of

LinReg(ax + b).

 

5.  Press:      ENTER                             (executes LinReg(ax + b) )

 

Values for  ‘a’   and   ‘b’    are displayed   on the home screen and the linear regression equation is stored in  .  To observe the scatter plot and the regression line Press:

                                                 GRAPH

 

Exercise: The following table lists data that show the life expectancy of women for various years.

Year (t)

1950 (t=0)       

1960 (t=10)

1970 (t = 20)

1980 (t = 30)

1990 (t = 40)

Life Expectancy in

Years

70.9

73.2

74.8

77.5

78.6

 

(a)   Find a linear function that fits the data.

 

 

 

 

(b) Use the model to predict the life expectancy in the year 2000.