1. LOOKING FOR PATTERNS BETWEEN VARIABLES WHY DO SCIENTISTS COLLECT DATA, GRAPH IT AND WRITE EQUATIONS TO EXPRESS RELATIONSHIPS BETWEEN VARIABLES ?

4. The Predictive Power of Patterns: For each of the following sets of numbers, predict the missing numbers and write an equation for the pattern. Y = X Y 0 0 1 5 2 10 3 15 4 20 5 ?

5. The Predictive Power of Patterns: For each of the following sets of numbers, predict the missing numbers and write an equation for the pattern. Y = 5X X Y 0 0 1 5 2 10 3 15 4 20 5 25

6. Representing Pattern with a Graph

7. The Predictive Power of Patterns: For each of the following sets of numbers, predict the missing numbers and write an equation for the pattern. Y = X Y 1 1 2 1/2 3 1/3 4 1/4 5 1/5 6 ?

8. The Predictive Power of Patterns: For each of the following sets of numbers, predict the missing numbers and write an equation for the pattern. Y = 1/X X Y 1 1 2 1/2 3 1/3 4 1/4 5 1/5 6 1/6

9. Graph for Y = 1/x

10. The Predictive Power of Patterns: For each of the following sets of numbers, predict the missing numbers and write an equation for the pattern. Y = X Y 1 3 2 6 3 11 4 18 5 27 6 ? 50 ?

11. The Predictive Power of Patterns: For each of the following sets of numbers, predict the missing numbers and write an equation for the pattern. Y = X 2 + 2 X Y 1 3 2 6 3 11 4 18 5 27 6 38 50 2502

12. Graph of y = x 2 + 2x

13. Regression Analysis Or, What the heck does that R 2 thing mean?

14. Basic Definitions Independent variable (x –axis) – a value you select or vary; Dependent variable (y-axis)- measured value that depends on choice of value of independent variable Constant – value is fixed during experiment so it will not impact dependent variable

15. Value of R can be used to judge the predictive power of a particular equation How well does the value of x predict the value of y?

16. Regression analysis represents correlation between two variable as number between -1 and 1 1 is a perfect positive correlation -1 is a perfect negative correlation 0 is no correlation Scientists typically like to see an R 2 value of 0.95 or higher to have a high degree of confidence in the relationship between two variables, however...

17. R is a measure of correlation, not causation In other words just because there is an apparent mathematical relationships between two variables does not always mean that x caused y. The relationship might be a coincidence.

18. source: tylervigen.com