1.3 Mathematical Modeling

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# 1.3 Mathematical Modeling - PowerPoint PPT Presentation

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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## PowerPoint Slideshow about '1.3 Mathematical Modeling' - ruth-johnston

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Presentation Transcript
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.
• 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
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