CLOates
16 Dec. 2009
MATH 1513-College Alg.

Some LateTest 5 Help

Since there have been several questions about regressions on the TI-84 calculator  and about one of the “fit a quadratic to three data points” problems, here are excerpts from some of my e-mailed responses to questions about these items.

EXPONENTIAL  REGRESSION  ON TI-84

Here's an outline of the exponential regression, done on a TI-84 calculator.

 

1.  Go to the "y=" screen and turn on statistical plot 1, using the up-arrow key and then the left arrow key to reach the "Plot1" item in the top left corner of the screen.  Press enter to make  "Plot1" appear as white letters on a black background.  (That means it's selected.)  Also, clear any function that's stored in Y1.

 

2.  Press the STAT key, then select EDIT from the top-row screen menu.  You'll see data lists L1 and L2.

 

3.  Clear the L1 and L2 lists by using up-arrow to go to the top of the column and then pressing CLEAR and ENTER for each column.

 

4.  Key the x data into column L1 and the y data into column L2.

 

5.  Press the ZOOM key and select 9:ZoomStat to see a plot of the data you keyed in.

 

6.  Press the STAT key, then select CALC from the top-row screen menu.  

 

7.  Select item 0: ExpReg from the menu that appears.  That will put "ExpReg" on a line on the main screen.

 

8.  The ExpReg function assumes the x data is in L1 and the y data is in L2, but we still need to tell it where to put the resulting exponential regression function, let's put it in Y1, as follows (step 9 )

 

9.  Press the VARS key, and  select Y-VARS from the top-line screen menu, then press ENTER twice to select the function variable, Y1 and put it after "ExpReg  " on the main screen.

 

10.  Press ENTER again to perform the regression, display the results, and put the resulting regressed function into Y1.  The equation is of the form y=a*b^x and the coefficients a and b are displayed on separate lines.  Note the r and r-squared values (correlation coefficient and coefficient of determination) for future reference.

 

11.  Press the GRAPH key to see both the plot of the data and the exponential function that ExpReg has fit to the data.

 

12.  Take a deep breath and relax.  It's over!

 

 

QUADRATIC  EQUATION  FIT  TO  THREE  DATA  POINTS

This is like the one we did in class the other night.  Given the three data points, y = 43, 62, and 86,  for x = 0, 7, and 31, we can state these three equations from the f(x) =  ax^2 + bx + c "prototype":

 

a(0)^2 + b(0) + c  =  43

 

a(7)^2 + b(7) + c  =  62

 

a(31)^2 + b(31) + c  =  86  .

 

Let's re-write these in the form we'd usually see them, as follows:

 

                       c  =  43

 49a    + 7b   + c  =  62

961a   + 31b  + c  =  86 .

 

In matrix form, this looks like this:

 

0       0      1      43

49     7      1      62

961   31     1      86    .

 

Now we can edit this into the TI-84  MATRIX facility and use the rref( ) function to get the following:

 

1     0     0    -0.05529+

0     1     0     3.10138+

0     0     1    43.

 

So  a ~= -.055 (to 3 DPs)

      b ~= 3.1

and c~=  43.

 

The quadratic function that fits the three points is f(x) = -0.055 x^2  +  3.1 x   +  43 .

 

Clearer?  Clear as mud?  Let me know.

 

I hope this helps!

 

Prof. Oates