Quadratic Regression Using the Nspire Graphing CalculatorName: ______

We will use the following data to do a regression equation on our graphing calculator:

A golf ball is hit down a straight fairway. The following table shows the height of the ball with respect to time. The ball is hit at an angle of 70 degrees with the horizontal with a speed of 40 meters/sec.

Time / 0 / .5 / 1 / 1.5 / 2 / 2.5 / 3 / 3.5 / 4 / 4.5
Height / 0 / 17.2 / 31.5 / 42.9 / 51.6 / 57.7 / 61.2 / 62.3 / 61.0 / 57.2

First, let’s graph the data by hand:

A) What should we label our x-axis and y-axis?

B) Plot the points.

C) What kind of function does this appear to be? Explain.

1)Using the NSpire Graphing Calculator to Enter and Graph Data.

Select 1: New Document

Press Enter.

Select 4: Add Lists & Spreadsheet

Press Enter.

2)Make sure that as you type in the headings of each column you are in the very top part of the columns. Press Enter after each heading is complete. Put the cursor in the first row of the spreadsheet to start entering the data.

Enter all the data from your table.

Please Note: You cannot see all the data in the screen shot.

3)Making a Scatter Plot of the Data on the NSpire Graphing Calculator

Insert a new page by pressing the Control Key (ctrl) and the Doc Key.

Select 5: Add Data & Statistics

Press Enter.

Notice the message at the bottom of the screen and the left part of the screen: “Click or Enter to add variable”.

Move the cursor to this message on the x-axis.
Press Enter.
Select time.
Press Enter. / Move the cursor to this message on the y-axis. The message may not appear right away until the cursor gets close to it.
Select height. / Press Enter.

4) What type of function does this appear to be?______

5) Finding a Regression Equation on the Calculator – showing on the graph

Press Menu.

Select 4: Analyze

Use the right arrow on the Touch Pad and select 6: Regression.

Use the right arrow on the Touch Pad and select

4: Show quadratic

Press Enter.

Write the quadratic function that is shown (round to the nearest tenth).

______

(NOTE: If you need to move the equation to see it, move the hand over it, then click and hold with the center button until the hand closes. Then you can drag the equation.)

6) Finding a Regression Equation on the Calculator using the Lists and Spreadsheets

Push “Ctrl” “left arrow” to get back to page 1.
Place the cursor in the first row of column c
Press Menu
Choose 4: Statistics
Choose 1: Stat Calculations
Choose 6: Quadratic Regression / A pop up menu will appear (see below)
Choose: time for x list
Height for y list
Everything else should be fine – click ok, or enter.

8. Record the equation from the data – remember f(x) = ax2 + bx + c

______

9. In the list of information, find the “R2” number. _____

If this number is really close to 1 (like 0.98, 1.03…) then your equation is a good fit for this data.

Is this equation a good fit for the data? Explain.

9. Using the equation you found above, determine what time the golf ball will hit the ground.

Quadratic Regression PRACTICE

1) At 1821 feet tall, the CN Tower in Toronto, Ontario, is the world’s tallest self-supporting structure.

Suppose you are standing in the observation deck on top of the tower and you toss a penny from there and watch it fall to the ground. The table below shows the penny’s distance from the ground as it is falling.

Time
(seconds) / Distance
(feet)
0 / 1821
2 / 1757
4 / 1565
6 / 1245
8 / 797
10 / 221

a) Graph the data on a scatter plot and sketch it here.

LABEL your axes with the correct variables.

b) What type of graph does it appear to be?

c) Write a regression equation for the data (round to the tenth). Record the R2 value.

d) Is this a good fit for the data? Explain.

e) How many seconds will it take for the penny to hit the ground? Explain how you found your answer.

2) After you take medicine, it takes time for the amount of drug in your blood to increase, then it gradually decreases again. The concentration (in milligrams per liter) of a medication in a person’s blood as time passes is given by this data:

Time
(Hours) / Concentration
(mg/l)
0 / 0
0.5 / 78.1
1 / 99.8
1.5 / 84.4
2 / 50.1
2.5 / 15.6

a) Graph the data on a scatter plot. What did you put on your x and y axes?

b) Write a regression equation for the data (round to the tenth). Record the R2 value.

c) Is this equation a good fit for the data? Why or why not?

d) How much medication is left after 2.25 hours?

e) What is the maximum concentration of the medicine? When does it occur? Does this answer make sense for the problem?

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