Math Plane 

The following project will help the user become more familiar with spreadsheets, scatterplots, and graphing models on the TI nspire calculator.

Project

Using the given data:

1) Construct a spreadsheet (and save the document)

2) Create a scatterplot

3) Find the linear regression model

4) Graph a logarithmic model

5) Compare the predictive capabilities and limitations of each model.

Step by Step Instructions and Illustrations:

Enter values into spreadsheet:

"ctrl"  "doc"

4: Add Lists & Spreadsheet

(Or, highlight the green spreadsheet icon to select "Lists & Spreadsheet")

Enter the x values in column A

Enter the corresponding y values in column B

In the top cells, label/name column A ("input") and label/name column B ("output")

Then, save the spreadsheet

"doc"

1: file

4: save

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Create a scatterplot:

Press "ctrl"   "doc"

From the menu, select 5: add Data & Statistics

A bunch of dots will appear on the screen.

Select x-variables

Move cursor to the bottom of the graph; press down on the keypad/mouse; find the "input" term in the list; enter

(screen: the dots will rearrange.)

Select y-variables:

Move cursor to the left side; press down on the keypad/mouse; find the "output" term in the list; enter

the scatterplot is created!

Linear Regression Model:

To put a "best fit line" among the dots,

"menu"

4: analyze

6: regression

1: show linear (y=mx + b)

"enter"

The linear model appears with the equation!

Logarithmic Regression Model:

"menu"

4: analyze

6: regression

9: show logarithmic

Compare the predicative abilities of future inputs:

For example, test x = 15.

(go to the scratchpad and input the equations, substituting x with 15)

Note the different outputs. Which is a better indicator?

A linear model is easier to calculate.

A logarithmic model integrates the "taper" at the end.

Try other regression models, such as quadratic or exponential.

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Application:  consider a scatterplot representing airplane speed every second of take-off..  A linear model has limitations (because an airplane can't increase in speed forever!)

(0, 0)

(1, 130)

(2, 280)

(3, 320)

(4, 400)

(5, 390)

(6, 450)

(7, 480)

(8, 470)

(9, 490)

If you wanted to estimate the speed at 20 seconds, a logarithmic model might offer a better fit.

***NOTE: if you try to run a logarithmic model, you must adjust the first entry (0, 0) --- because, logx does not exist when x = 0..   (so, you may eliminate the entry OR enter (.01, 0) to get an estimate)

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Math Comic #224 - "X's and O's" (1-21-16)

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