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