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Unformatted text preview: 1 Chapter 3 Supplement Again, at the review, I deliberately did NOT cover some things for the sake of time. I needed to turn an 8 hour review into a 4 hour review. That being the case, I will elaborate on a few more things you should know from each chapter in my supplements. r , the correlation coefficient As I said that the review, r measures how strong the linear relationship between x and y , i.e. between 2 quantitative variables. Shown below are various values or r . r = 1 perfect () linear rel. r = .50 moderate () linear rel. r = 0 no linear relationship r = +.85 strong (+) linear rel. r = +1 perfect (+) linear rel. A few notes about r : r has no units and is bounded between 1 and +1. The closer the points are to a line, the closer r will be to 1 or +1. The closer r is to 1 or +1 the strong the relationship is between x and y . [Whats considered strong depends on the field of study.] r must have the same sign as the slope. If the slope is positive, r must be positive. If the slope is negative, r must be negative. On the exam, youll either be given r , or r 2 . If you are given r 2 , to find r take the square root of r 2 , i.e. = r (sign of the slope) 2 r . Correlation does NOT imply causation! Just because x and y are correlated (related), it does NOT imply that changes in x cause changes in y . 2 r is NOT affected by the units of x and y . Suppose we wanted to predict a students weight ( y , in lbs.) based on his/her height ( x , in inches). If, for example, we converted lbs. to kilograms and inches to centimeters, the correlation will NOT change. Switching what we call x = the explanatory variable and y = the response will NOT change r . Note : Changing the units of x and/or y , or changing what we call x and y will change the slope and the y-intercept of the regression line. [but not r ] On the exam, your professor may give you several scatter plots and have you determine the approximate values of r . You can get practice guessing r at the following site. http://www.stat.uiuc.edu/courses/stat100//java/GCApplet/GCAppletFrame.html Shown below is a screen shot from the website. We can see that Plots A, C and D have downward slopes, so we know the correlations must be negative. Since Plot As points are the most spread out, it implies that it is the one with the weakest negative correlation, i.e. closest to 0. So, the correlation for Plot A is 0.44. We can see that Plot C is slightly tighter than Plot D, so its correlation will be slighter closer to 1. So, the correlation for Plot C is 0.82 and the correlation for Plot D is 0.81. By process of elimination, the correlation for Plot B must be +0.24. This should make sense....
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This note was uploaded on 04/04/2012 for the course STA 2023 taught by Professor Ripol during the Spring '08 term at University of Florida.
- Spring '08