1. 1.4 Data in 2 Variables Definitions

2. 5.3 Data in 2 Variables: Visualizing Trends When data is collected over long period of time, it may show trends Trends allow you to make predictions about future events Trends can be over time, or over change in some other variable (e.g. mass) One effective way to visualize: scatterplot –Shows joint distribution of 2 variables

3. Scatterplots Independent variable Variable whose values are arbitrarily chosen Dependent variable Variable whose values depend on independent variable

4. Scatterplots can help determine if there is a relationship in the data –Is there a pattern in the data? there is a relationship As x increases, y increases there is no relationship As x increases, y stays pretty much the same

5. We can show the relationship using a line of best fit

6. If the data is nonlinear, we use a curve of best fit

7. Correlation Measure of the strength of the apparent relationship between two variables Look at upward/downward/horizontal trend –Positive/Negative/No correlation Look at how closely the points fit the curve of best fit –Strong/Moderate/Weak correlation Note: trend and fit are unrelated

8. Classifying Linear Relationships Strong positive correlation Positive slope Tightly clustered to line of best fit

9. Classifying Linear Relationships Strong negative correlation Negative slope Tightly clustered to line of best fit

10. Classifying Linear Relationships No correlation 0 slope Randomly scattered

11. Classifying Linear Relationships Moderate positive correlation

12. Classifying Linear Relationships Weak positive correlation

13. Classifying Linear Relationships Weak negative correlation

14. Warning!!! Correlation does not necessarily mean causation Just because there is a relationship between A and B does not mean A causes B –More on this next day

15. Using trends for predictions Use the equation of the line of best fit Extrapolation –Estimation of a value outside known data set Interpolation –Estimation of a value between two known values

16. y = mx + b Extrapolation Interpolation

17. Go to “Go For the Gold!”

18. Go for the Gold! Line of Best Fit: Men Mensdistance = 0.016 Year – 24.04 Sum of squares = 0.8308 Slope is 0.016: change in distance over time (in years) –Every year, the distance should increase by 1.6 cm Y-intercept is –24.04 –In year zero, they jumped backwards!? –meaningless

19. Go for the Gold! Line of Best Fit: Women Womensdistance = 0.021 Year –35 Sum of squares = 0.7447 Slope is 0.021; y-int is -35 –Every year, the winning women’s distance should increase by 2.1 cm. –Y-intercept is meaningless for this case In 2008, winning men’s distance should be 8.85 m and the women’s distance should be 7.17 m (actual distances 8.34 m and 7.04 m) In 2012?