1. Linear Approximation Lesson 2.6

2. Midpoint Formula Common way to approximate between two values is to use the mid value or average Midpoint between two values in the x-y plane (x 1, y 1 ) (x 2, y 2 )

3. Visualizing Data with the Calculator Press the APPS button Choose 6 Data/Matrix and NEW Review slides from Lesson 1.2 Review slides from Lesson 1.2

4. Using Regression 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

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

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

7. 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

8. 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

9. Interpolation Use given data Determine proportional “distances” WeightCalories 1002.7 1203.2 1504.0 1704.6 195?? 2005.4 2205.9 30 0.8 15 x Note : This answer is different from the extrapolation results

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

11. 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

12. Assignment Lesson 2.6 Page 146 Exercises 1 – 31 odd