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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
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.