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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 .

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1 3 mathematical modeling
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
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
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
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
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
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
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
Find “Best Fit” Linear Function

  • Press STAT and highlight CALC

  • Highlight 4:LinReg

  • Press ENTER


Find slope and y int of line
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
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
Input into Y= Automatically

  • Highlight 1:Y1 and press ENTER

  • Press ENTER again


Graph best fit line
Graph Best Fit Line

  • Press GRAPH


Use model to predict
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
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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