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Chapter 10

Chapter 10. 10-1. Bivariate Data. (x,y) data pairs Plotted with Scatter plots x = explanatory variable; y = response. Bivariate Normal Distribution – for a fixed value of x, y values should be normally distributed, or at least symmetric and mound shaped. Linear Relationship.

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Chapter 10

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  1. Chapter 10 10-1

  2. Bivariate Data (x,y) data pairs Plotted with Scatter plots x = explanatory variable; y = response Bivariate Normal Distribution – for a fixed value of x, y values should be normally distributed, or at least symmetric and mound shaped.

  3. Linear Relationship Scatter plot can show if there is a linear relationship between x and y. Positive correlation – if low x gives low y, high x gives high y Slope would be…. Negative correlation – if low x gives high y, high x gives low y Slope would be….

  4. Pearson Product-moment correlation Coefficient = r AKA sample correlation coefficient Number that indicates “strength” of the linear relationship between x and y -1 ≤ r ≤ 1 r = ±1  perfect linear correlation r = 0  no linear correlation If it is a population correlation coefficient, use the Greek letter ρ (rho)

  5. Bivariate data (x,y) Tables will be extremely helpful when you have to do this by hand! You can make lists to calculate the data values (i.e. with your cauclator) then put the numbers into the formulas.

  6. Generalizations r = 1 r = 0 r = -1

  7. Generalizations -1 < r < 0 0 < r < 1

  8. Example Let x be the average number of employees in a group health insurance plan, and let y be the average administrative cost as a percentage of claims. A) Make a scatter diagram and draw the line you think best fits the data B) Is the correlation low, moderate or strong? Positive or negative? C) Calculate r.

  9. Resources http://www.evl.uic.edu/cavern/multiperspective/Continuum/Training/scatter6.gif http://www.netmba.com/images/statistics/plot/scatter/scatterplot.gif http://fmrc.pulmcc.washington.edu/IMAGES/SPEX1.JPG http://cnx.org/content/m10950/latest/r2.gif http://www.itl.nist.gov/div898/handbook/eda/section3/gif/scatplo2.gif http://richardbowles.tripod.com/maths/correlation/scatter3.gif

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