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Chapter 4: Describing the relation between two variables Univariate data:

Chapter 4: Describing the relation between two variables Univariate data: Only one variable is measured per a subject. Example: height. Bivariate data: Two variables are measured per a subject. Example: height and weight. This chapter deals with bivariate data.

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Chapter 4: Describing the relation between two variables Univariate data:

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  1. Chapter 4: Describing the relation between two variables Univariate data: Only one variable is measured per a subject. Example: height. Bivariate data: Two variables are measured per a subject. Example: height and weight. This chapter deals with bivariate data.

  2. Section 4.1: Scatter diagrams and correlation • Scatter diagrams(plots) show the data. • Correlation is a statistic measuring linear relationship between x and y variables.

  3. Quantitative bivariate data are usually displayed in a scatter plot (also called scatter diagram).

  4. The “X” variable is called many names: • Explanatory variable • Predictor variable • Independent variable • Weeks of gestation is our x-variable here.

  5. The “Y” variable is also called many names: • Response variable • Dependent variable • Outcome variable • Birth weight is our y-variable here.

  6. When trying to determine which variable you should put on the x or y axes, think “cause and effect”. The “cause” variable should be on the x-axis. The “effect” variable should be on the y-axis.

  7. Sample correlation coefficent (Also called “linear” or “Pearson product moment” correlation coefficient) -1 <= r <= 1

  8. If the slope is negative, r<0. If positive slope, r>1 r=-1 or 1 means all points lie on straight line. Bottom row shows pattern, but it’s not linear.

  9. http://xkcd.com/552/

  10. Practice: n=? Mean(x)=? Mean(y)=? SD(x)=? SD(y)=?

  11. Practice: n=? Mean(x)=? Mean(y)=? SD(x)=? SD(y)=? n=3 Mean(x)= 6, Mean(y)=3 SD(x) = 2, SD(y)=3 r=0.5

  12. Correlation=? (A) 0 (B) 0.41 (C) 0.97 (D) 1

  13. A) -1.2 B) -1 C) -0.99 D) 100

  14. A) -1 B)-0.99 C) -0.5 D) -0.25

  15. http://thedoghousediaries.com/2723

  16. A) -1 B) +0.5 C) +1 D) 100

  17. A) -0.9 B) +0.02 C) +0.9 D) +1

  18. A) +0.02 B) +0.04 C) +0.96 D) +1

  19. A) -1 B) -0.71 C) +1 D) +1.5

  20. A) -0.71 B) -0.2 C) +0.92 D) 1

  21. A) -1 B) -0.06 C) +0.99 D) +1

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