Quadratic Regression Lab
(For Graphing Calculator)
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Stephany Faulkner, Indian River High School, Chesapeake, VA.
Grade Level:
Algebra 2 - TI-81/-82/-83 Proficiency needed

Standards:
All/T.8 and All/T.19

Objective:
To use real temperature data from the Chesapeake Bay, to begin to see some natural mathematical Phenomena, and to begin to interpret the data mathematically.

Procedure:
Divide your class into equal groups, trying to keep the groups no larger than five. Have the students follow the initial entering of temperature data into the calculator (preferably the TI-82/83).

Enter as follows:

STAT -> EDIT

Now several columns appear, labeled L1 , L 2 , L3 ,. Etc.

The months will be entered in the L1 column as the numbers 1-12. The temperature will be entered into the L2 column.

After all data is entered correctly, preview the format/range of the graph as follows.

WINDOW -> FORMAT

Make sure everything is highlighted to the left.

WINDOW

Xmin = 0
Xmax = 14 These are the months --make sure the domain is slightly larger than the data
Xscl = 1 How to scale your X values-- for now go by ones
Ymin = 0
Ymax = 30 These are the temperatures--make sure the range again is slightly larger than the data
Yscl = 5 Just so that the graph will fit onto the screen

To Create the scatterplot onto the graphing calculator:

2nd Y=

A new menu appears and this puts one into the Stat Plot part of the calculator.

ENTER

Make sure ON is highlighted
Type: first box is highlighted
Xlist -- L1 (This is where you put your X values)
Ylist ---L 2 (This is where you put your Y values)
Mark: The first box should be highlighted as this is the largest mark and the easiest to read

Now
GRAPH

The data has been graphed as a scatterplot. It looks very much like a naturally occurring parabola. You can now have each group graph their own data. There are five years given. If you need more groups just give the same data to more than one group. Make sure each group has a large piece of graph paper to graph there points onto as well as into the calculator. After each has produced a scatterplot on their calculator, have them graph their scatterplot onto the large graph paper. Put the large pieces of graph paper onto a chalk board in order of years. Now students will be able to see that the temperatures are fairly periodic. Pick out one year's graph and lets go through the steps to develop a quadratic regression curve. Each group can be doing the quadratic regression curve with their own data. Here are the steps for finding the quadratic regression curve:

STAT CALC #6 QUADREG

At this point Quadreg should appear on the screen with a flashing cursor

ENTER

y = AX + BX + C
a =
b= Values for these variables should now appear
c=

In order to graph the curve of best fit:

Y= VARS 5/STATISTICS EQ 7/REGEQ

This puts your values into Y= to allow one to plot the "curve of best fit".

GRAPH

The scatterplot should appear first; then curve of best fit should appear on the screen.

It should look like this.

EXTENSIONS:

  1. Does the curve fit well?
  2. By looking at the graphs all together on the board, could you put a yardstick across the July temperatures and would it be level? If not a class discussion on Global warming could occur.
  3. Have students look at the table function in the calculator, and look at the X and Y values for symmetry.
  4. A day could be spent looking a residuals.
  5. Convert all the temperatures to Fahrenheit.
  6. Make a comparison of temperatures to different parts of the bay.

Chesapeake Bay Temperature DATA
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