1. Fitting Linear Functions to Data
Lesson 1.6

2. 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

3. 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

4. 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

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

6. 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

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

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 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

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

11. 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

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
Exercises 1, 3, 5, 7