Fitting Linear Functions to Data Lesson 1.6

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

Problems with Data Real data recorded Problems In any case … 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

Fitting Functions to Data Temperature Viscosity (lbs*sec/in2) 160 28 170 26 180 24 190 21 200 16 210 13 220 11 230 9 Consider the data given by this example Note the plot of the data points Close to being in a straight line

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

You Try It From Exercise 2, pg 65 Weight Calories 100 2.7 120 3.2 150 4.0 170 4.6 200 5.4 220 5.9 From Exercise 2, pg 65 Enter data into data matrix of calculator APPS, 6, Current, Clear contents

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

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

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

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 Weight Calories 100 2.7 120 3.2 150 4.0 170 4.6 200 5.4 220 5.9

Note : This answer is different from the extrapolation results Interpolation Use given data Determine proportional “distances” Weight Calories 100 2.7 120 3.2 150 4.0 170 4.6 195 ?? 200 5.4 220 5.9 x 25 0.8 30 Note : This answer is different from the extrapolation results

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

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

Assignment Lesson 1.6 Page 48 Exercises 1, 3, 5, 7