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Fitting Linear Functions to Data: Cricket Chirps & Temp.

Learn to fit linear equations to real data, analyze using regression, avoid extrapolation pitfalls, and understand correlation coefficients. Complete exercises to master the concepts.

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Fitting Linear Functions to Data: Cricket Chirps & Temp.

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  1. Fitting Linear Functions to Data Lesson 1.6

  2. Cricket Chirps & Temp. • Your assignment was tocount cricket chirpsand check the temperature • The data is saved and displayed on a spreadsheet • Your science teacher wantsto know if you can find alinear equation to more orless match the data

  3. Problems with Data • Real data recorded • Experiment results • Periodic transactions • Problems • Data not always recorded accurately • Actual data may not exactly fit theoretical relationships • In any case … • Possible to use linear (and other) functions to analyze and model the data

  4. Fitting Functions to Data • Consider the data given by this example • Note the plot ofthe data points • Close to beingin a straight line

  5. Finding a Line to Approximate the Data • Draw a line “by eye” • Note slope, y-intercept • Statistical process (least squares method) • Use a computer programsuch as Excel • Use your TI calculator

  6. You Try It • From Exercise 2, pg 65 • Enter data into data matrix ofcalculator • APPS, 6, Current, Clear contents

  7. Using Regression On Calculator • Choose F5 for Calculations • Choose calculationtype (LinReg for this) • Specify columns where x and y values will come from

  8. Using Regression On Calculator • It is possible to store the Regression EQuation to one of the Y= functions

  9. Using Regression On Calculator • When all options areset, press ENTER andthe calculator comesup with an equation approximates your data Note both the original x-y values and the function which approximates the data

  10. Using the Function • Resulting function: • Use function to find Caloriesfor 195 lbs. • C(195) = 5.24This is called extrapolation • Note: It is dangerous to extrapolate beyond the existing data • Consider C(1500) or C(-100) in the context of the problem • The function gives a value but it is not valid

  11. Interpolation • Use given data • Determine proportional“distances” x 25 0.8 30 Note : This answer is different from the extrapolation results

  12. Interpolation vs. Extrapolation • Which is right? • Interpolation • Between values with ratios • Extrapolation • Uses modeling functions • Remember do NOT go beyond limits of known data

  13. Correlation Coefficient • A statistical measure of how well a modeling function fits the data • -1 ≤ corr ≤ +1 • |corr| close to 1  high correlation • |corr| close to 0  low correlation • Note: high correlation does NOT imply cause and effect relationship

  14. Assignment • Lesson 1.6 • Page 48 • Exercises1, 3, 5, 7

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