1. Georgetown-Coastal Carolina Partnership Workshop 2016
05-Analyzing Functions
Georgetown-Coastal Carolina Partnership Workshop 2016

2. When to Sell?

3. Introduction to Modeling Workshop

4. Scatter Plots and Correlation
A scatter plot (or scatter diagram) is used to show the relationship between two variables
Correlation analysis is used to measure strength of the association (linear relationship) between two variables
Only concerned with strength of the relationship
No causal effect is implied

5. Correlation v. Causation
Ice cream and Polio

6. Scatter Plot Examples Linear relationships Curvilinear relationships y

7. Sketch a strong linear correlation and a weak linear correlation.

8. Scatter Plot Examples Strong relationships Weak relationships y y x x

9. Sketch two variables that have no relationship.

10. Scatter Plot Examples
(continued)
No relationship y x y x

11. Correlation Coefficient, r
Between -1 and +1 inclusive.
Measures the strength and direction of linear correlations.
Closer to 1 or -1 shows a strong linear relationship.

12. Coefficient of Determination, R2
Between 0 (poor fit) and 1 (excellent fit)
Ratio of explained variance over total variance.
Give the percent of variance in y that is explained by x.

13. TI-84 Regression Steps Press STAT
Edit Lists Enter Data Default L1 (x) & L2 (y)
STAT > Calc
Choose type of regression
Tell Xlist (L1) Ylist (L2)
Should give R2 and r [2nd 0 (catalog) , Turn Diagnostics On]
If not

14. Linear Regression Activity
Age Game

15. Warm-Up
Reflection on yesterday

16. Remember Non-Linear Correlationsy x y x

17. Parent Function Exploration
Explore in pairs other function types that can be used to model data.

18. Function Patterns Pairs
Try to find a pattern in both the domain and range of the listed functions.

19. Function Patterns Add-Add  Linear Add-Second Difference  Quadratic
Multiply-Multiply  Power
Add-Multiply Exponential
Multiply-Add Logarithmic

20. Thunderstorm Data
Can you find a function pattern in the data below? (remember this is real data)

21. Thunderstorms Activity
Work in groups of 3 to model this real-life data with a linear regression model.
Answer the questions individually, but ask your teammates for help if needed.

22. Toothpick Functions
In your groups, determine a mathematical model that gives the total number of toothpicks required to construct a square of any size that is subdivided into 1x1 squares of toothpicks. The 1x1 and 2x2 are shown below.

23. Gasoline Problem
The gasoline gauge on a van initially read 1/8 full. When 15 gallons were added to the tank, the gauge read 3/4 full. How many more gallons are needed to fill the tank?

24. Planet Regression

25. Car Wreck Exploration
The data below show the speed a mid-size car was traveling, s, and the resulting length in feet, l, of tire skid marks when they slam on brakes.