2. Fitting Linear Functions to Data Lesson 1.6

3. 2 Cricket Chirps & Temp. ► Your assignment was to count cricket chirps and check the temperature ► The data is saved and displayed on a spreadsheet displayed on a spreadsheet displayed on a spreadsheet ► Your science teacher wants to know if you can find a linear equation to more or less match the data

4. 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

5. 4 Fitting Functions to Data ► Consider the data given by this example ► Note the plot of the data points  Close to being in a straight line Temperature Viscosity (lbs*sec/in 2 ) 16028 17026 18024 19021 20016 21013 22011 2309

6. 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 program such as Excel ► Use your TI calculator

7. 6 You Try It ► From Exercise 2, pg 65 ► Enter data into data matrix of calculator  APPS, 6, Current, Clear contents WeightCalories 1002.7 1203.2 1504.0 1704.6 2005.4 2205.9

8. 7 Using Regression On Calculator ► Choose F5 for Calculations ► Choose calculation type (LinReg for this) ► Specify columns where x and y values will come from

9. 8 Using Regression On Calculator ► It is possible to store the Regression EQuation to one of the Y= functions

10. 9 Using Regression On Calculator ► When all options are set, press ENTER and the calculator comes up with an equation approximates your data Note both the original x-y values and the function which approximates the data

11. 10 Using the Function ► Resulting function: ► Use function to find Calories for 195 lbs. ► C(195) = 5.24 This 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 WeightCalories 1002.7 1203.2 1504.0 1704.6 2005.4 2205.9

12. 11 Interpolation ► Use given data ► Determine proportional “distances” WeightCalories 1002.7 1203.2 1504.0 1704.6 195?? 2005.4 2205.9 30 0.8 25 x Note : This answer is different from the extrapolation results

13. 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

14. 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

15. 14 Assignment ► Lesson 1.6 ► Page 48 ► Exercises 1, 3, 5, 7