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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
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 .
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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