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1.3 Mathematical ModelingPowerPoint Presentation

1.3 Mathematical Modeling

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1.3 Mathematical Modeling

- A real world problem described using mathematics
- Recognize real-world problem
- Collect data
- Plot data
- Construct model
- Explain and predict

Linear Regression

- The process of finding a function that best fits the data points is called curve fitting.
- Curve fitting using linear functions is called linear regression.

Linear Regression on the TI-83

- The first step is to enter the data into the calculator.
- Hit STAT and highlight 1:EDIT on the menu list.
- Press ENTER

Entering data into the lists

- If data is in list, move cursor to highlight list name, press CLEAR followed by ENTER
- Enter the x values in L1 and the y values in L2.

Engage the Stat Plot

- Press 2nd followed by Y=.
- Press ENTER.
- Move cursor to highlight On and press ENTER.
- Move cursor to highlight scatterplot, and press ENTER.
- Make sure the Xlist is L1 and the Ylist is L2.

Adjusting the Window

- Standard viewing rectangle is [10,10] xscl=1 and [10,10] yscl=1
- Press WINDOW and enter new dimensions
- New window [0,30] xscl=3 and [0,20] yscl=2

Graph data

- To view data points, press GRAPH
- Data points can be “fitted” by a straight line
- Each x tick mark represents 3 years
- Each y tick mark represents 2 million households

Find “Best Fit” Linear Function

- Press STAT and highlight CALC
- Highlight 4:LinReg
- Press ENTER

Find Slope and Y Int of Line

- Press ENTER a second time
- Recall y=mx+bwhere m=slope and b=yint
- Note a=slope

Entering “Best Fit” line in Grapher

- Press STAT, arrow over to CALC, and highlight 4:LinReg
- Press VARS, arrow over to Y-VARS and highlight 1:Function
- Press ENTER

Input into Y= Automatically

- Highlight 1:Y1 and press ENTER
- Press ENTER again

Graph Best Fit Line

- Press GRAPH

Use Model to Predict

- Use table feature to find prediction
- Press 2nd then WINDOW (TBLSET)
- Arrow down to change Independent to ASK

Use Table to Find Prediction

- Press 2ndGRAPH (TABLE)
- Enter 33 since 2003 is 33 years after 1970
- Press ENTER
- Interpret answer
- Approx. 16.644 million apt households in 2003.

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