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Lesson 9 - Ch9 Regression Stat113 Correlation Weve seen...

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Ch9: Regression Stat113
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Correlation We’ve seen that correlation measures the linear relationship between two variables In what direction? (pos. or neg.) How strong? (close to 1, or to -1) When two variables are strongly correlated, if we know an individuals value for one variable, this can help us to predict their value for the other variable
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Sample Situation Consider two variables with a strong, positive correlation Boats registered at a given marina in florida Manatee Kills at a given marina in florida Our individuals are marinas, and for each marina, for a ten year period, we have recorded the total number of motor boats that have ever been registered there, as well as the total number of manatees that have died there.
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Simplified Version Pearson Product-Moment Correlation No Selector   kills boats kills 1.000 0.912 boats 1.000 From DataDesk, we can view a data table by double clicking the variables, and a correlation table (Calc > Correlations > Pearson Product- Moment). Result: Correlation is Strong, Positive We might say: We can predict manatee deaths that have occurred in some other marina, whose manatee deaths we haven’t kept track of, in the following way: If the new marina has a value for Boats which is greater than the mean, by S standard deviations, then it’s value for Kills will be that many standard deviations above the mean of Kills .
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Contd… Suppose we get data for a new marina: Boats : 705 We want to predict Kills , so we must calculate the mean and standard deviation for both variables (Calc > Summaries > Reports) » 705 is about one standard deviation above the mean of Boats : (705 - 601.544)/103.832 ≈ 1 » 1 standard deviation (of Kills ) above the mean of Kills would be: 32.6111 + 12.8161 ≈ 45 » So using this model, we could expect there to have been about 45 Kills at this marina, for which we previously had no data.
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