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Unformatted text preview: Linear correlation 9 of 17 -4-2 2 4-15-5 5 10 r = -0.88 r^2 = 0.78 x y Hypothesis test for linear correlation. Definition 1.5 requirements (1) simple paired ( x,y ) random samples, (2) Pairs of ( x,y ) have a bivariate normal distribution 2 , (3) correlation is linear. null hypothesis = 0 (no linear correlation) alternative hypothesis 6 = 0 ( a linear correlation exists 3 ) Always make a scatter plot first to see if the relationship is linear. Linear correlation coefficient r and hypothesis test: cor.test(x, y) Calculates r from the sample and conducts the hypothesis test for H = 0. x vector of ordered x data. y vector of ordered y data. R Command Test statistic for linear correlation coefficient t = r- q 1- r 2 n- 2 (2) where df = n- 2. Note: n is number of pairs. Procedure for finding r 1. Define two ordered vectors ( x and y ) with the data....
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