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Scatterplots and Correlation

Scatterplots and Correlation. two quantitative variables. Type of Coffee and amount of Caffeine. Interested in the relationship between them. Form. Direction. Strength. Dots close to a line. Dots really spread out.

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Scatterplots and Correlation

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  1. Scatterplots and Correlation

  2. two quantitativevariables

  3. Type of Coffee and amount of Caffeine

  4. Interested in the relationship between them

  5. Form

  6. Direction

  7. Strength Dots close to a line Dots really spread out

  8. We want to examine whether the amount of rainfall per year increases or decreases corn bushel output. A sample of 10 observations was taken, and the amount of rainfall (in inches) was measured, as was the subsequent growth of corn.

  9. Step 1: Scatterplot

  10. Dependent Var? Independent Var? Form? Direction? Strength? Outliers? What does this tell us?

  11. Step 2: Correlation and R2

  12. Sign on r matches direction of the scatterplot data. r = +0.9 r = -0.8

  13. Correlation not dependent upon units of variables

  14. Ignores the distinction between X and Y variables.

  15. Only for straight-line relationships. Brain Functionality Age

  16. -1 -0.8 -0.5 0 0.5 0.8 1 Strong Mod Weak Mod Strong Measures direction and strength of the linear relationship Demo Game

  17. The correlation between corn yield and amount of rain is 0.995 Describe strength of the correlation. What does this imply?

  18. R2 The PERCENT of the dependent variable that is explained by the independent variable

  19. Given Correlation, finding R2

  20. Given R2 What is the correlation (careful of sign)

  21. Correlation is 0.995, what is R2 value?

  22. In our example, R2is 99.06% What does that mean?

  23. Step 3: Regression line

  24. Goal: go through “middle” of points minimize residuals

  25. Intercept Slope

  26. Intercept

  27. Slope

  28. What is the equation USED for?

  29. Prediction vs. Extrapolation

  30. Prediction

  31. What is the predicted corn yield if rain = 3 in? y = 50.83 + 9.63 x

  32. What is the predicted corn yield if rain = 3 in? y = 50.83 + 9.63 x y = 50.83 + 9.63 (3) = 79.72 bushels of corn

  33. Data close to line – more accurate predictions (i.e. r close to 1 or -1, R2 close to 100%)

  34. Extrapolation

  35. On the rain/corn data above, predict the corn yield for • 5 inches of rain • 7.2 inches of rain • 0 inches of rain • 100 inches of rain

  36. X = 5 Predict: 98.96 bushels of corn Prediction Safe

  37. X=7.2 Predict: 120.135 bushels of corn “prediction” Pretty safe

  38. X=0 Predict: 50.835 bushels of corn Extrapolation unsafe

  39. X=100 Predict: 1013.335 bushels of corn Extrapolation unsafe

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