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010+Correlation

# 817 10 6 thus 0817 0873 and with 98 condence level we

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Unformatted text preview: x2 i 1 4 9 16 25 x2 i xi yi 1 2 6 8 20 xi yi = 37 Solution. Null hypothesis is H0 = {ρ = 0}, alternative hypothesis is Ha = {ρ = 0}. Rejection region is RR = ρ2 ≥ ˆ 1 1 = = 0.873 , 1 + (n − 2)/t2 2 1 + (5 − 2)/4.5412 α/ 6 A. Zhensykbaev Correlation Find test statistic ρ2 : ˆ SSxy = 7, SSxx = 10, SSyy = 6, ρ2 = ˆ 72 = 0.817. 10 · 6 Thus 0.817 < 0.873, and with 98% condence level we conclude that the data of sales revenue and advertising expenditure are independent. Due to independence for normally distributed samples we can apply t-statistic. Spearman's rank correlation coecient. If sample sizes are small and the t-test is not appropriable to decide is there any dependence between two variables we apply the Spearman's rank sum test. Let us given two samples of size n: {X1 , . . . , Xn } {Y1 , . . . , Yn }. First step is to rank the observations as in the Wilcoxon test. So let the rank of the observation Xi is equal to ui , rank Xi = ui , and the rank of the observation Yi is equal to vi , rank Yi = vi . Next, calculate the test statistic...
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