1. Bivariate EDA

2. Quantitative Bivariate EDASlide #2 Bivariate EDA –Graphically –Numerically –Model Describe the relationship between pairs of variables

3. 1.What is the name of this plot? 2.What type of variable is latitude? 3.Which variable is considered the response variable? 4.What is the approximate percentage females at a latitude of 55? at 45? at 35? Quantitative Bivariate EDASlide #3 Figure 1. Plot of the percent female kingfishers observed at different latitudes during the Christmas Bird Count, 1992.

4. Quantitative Bivariate EDASlide #4 Variables & Axes Response (dependent) variable –variability is being explained or values predicted –y-axis Explanatory (independent, predictor) variable –used to explain variability or to make predictions –x-axis

5. Quantitative Bivariate EDASlide #5 Bivariate EDA -- Description Association/Direction – what words are used? Positive Negative None What four things are described in a bivariate EDA for quantitative data?

6. Quantitative Bivariate EDASlide #6 What Type of Association? 708090100110120130 70 80 90 100 110 120 130 X Y + - +- Negative

7. Quantitative Bivariate EDASlide #7 What Type of Association? 708090100110120130 70 80 90 100 110 120 130 X Y + - +- Positive

8. Quantitative Bivariate EDASlide #8 What Type of Association? 708090100110120130 70 80 90 100 110 120 130 X Y + - +- None

9. Quantitative Bivariate EDASlide #9 Items to Describe in a Bivariate EDA Association/Direction Form – what two forms will we consider? Linear Non-linear

10. Quantitative Bivariate EDASlide #10 Items to Describe in a Bivariate EDA Association/Direction Form Outliers 708090100110120130 70 80 90 100 110 120 130 X Y

11. Quantitative Bivariate EDASlide #11 Items to Describe in a Bivariate EDA Association/Direction Form Outliers Strength -- how closely the points cluster to the form

12. Strength? Quantitative Bivariate EDASlide #12 708090100110120130 70 80 90 100 110 120 130 X Y

13. Which is More Strong? Quantitative Bivariate EDASlide #13

14. Quantitative Bivariate EDASlide #14 Correlation Coefficient 1. Standardize both X and Y 2. Product paired standardized values 3. Sum products 4. Divide by n-1 1n  s yy y i          s xx x i          r       n 1i      *

15. Quantitative Bivariate EDASlide #15 A measure of association/direction Correlation Coefficient

16. Quantitative Bivariate EDASlide #16 r for positive Association? 708090100110120130 70 80 90 100 110 120 130 X Y + - + - 1. Standardize both X and Y

17. Quantitative Bivariate EDASlide #17 r for positive Association? 708090100110120130 70 80 90 100 110 120 130 X Y + - + - 2. Product paired standardized values + + - -

18. Quantitative Bivariate EDASlide #18 r for positive Association? 708090100110120130 70 80 90 100 110 120 130 X Y + - + - 3. Sum products + + - - Positive

19. Quantitative Bivariate EDASlide #19 r for positive Association? 708090100110120130 70 80 90 100 110 120 130 X Y + - + - 4. Divide by n-1 + + - - Positive

20. Quantitative Bivariate EDASlide #20 r for Positive Association? 708090100110120130 70 80 90 100 110 120 130 X Y + - + - + + - - Thus, r is Positive

21. Quantitative Bivariate EDASlide #21 r for Negative Association? 708090100110120130 70 80 90 100 110 120 130 X Y + - +- + + - - Thus, r is Negative

22. Quantitative Bivariate EDASlide #22 A measure of association and strength Correlation Coefficient +1 0 WeakestStrongest

23. Quantitative Bivariate EDASlide #23 A measure of association and strength of a linear relationship with no outliers Moral … PLOT YOUR DATA!! Correlation Coefficient r = 0.817

24. Quantitative Bivariate EDASlide #24 Correlation Review Variables must be quantitative Form must be linear without outliers -- i.e., PLOT -1 < r < 1 No distinction between which variable is on x and which is on y (though, response variable should always be y) r does not depend on units of x and y Correlation is not causation We won’t compute r - must interpret and identify strength

25. Perform a bivariate EDA from Figure 1. Quantitative Bivariate EDASlide #25 Figure 1. Plot of the percent female kingfishers observed at different latitudes during the Christmas Bird Count, 1992. r = -0.673

26. Perform a bivariate EDA from Figure 2. Quantitative Bivariate EDASlide #26 Figure 2. Plot of the maximum temperature versus herbage yield for grassland headfires in west Texas. r=0.798

27. Perform a bivariate EDA from Figure 3. Quantitative Bivariate EDASlide #27 Figure 3. Plot of the number of pupae per gallery and the density of attacks for the beetle Ips cembrae r=-0.612

28. Quantitative Bivariate EDASlide #28 Examine handout – plot() – cor() Quantitative Bivariate EDA in R