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STATS SHEET - CORRELATION AND REGRESSION b0= y-bar b1 x-bar...

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CORRELATION AND REGRESSION b 0 = y-bar - b 1 • x-bar b 1 = rs y R 2 = percent of variability in y that is explained by x s x SAMPLING DISTRIBUTION MODEL FOR A PROPORTION SD(p-hat) = √pq/n N(p, √pq/n) SAMPLING DISTRIBUTION MODEL FOR A MEAN SD(y-bar) = σ / √n N(μ, σ/√n) SE(p-hat)= √(p-hat • q-hat/ n) ONE PROPORTION Z-INTERVAL: A confidence interval for the true value of a proportion (p). The confidence interval is p-hat +/- z* SE(p-hat) where z* is a critical value from the Normal model corresponding to the specified CI. Choosing sample size: e.g. within 3% with 95% confidence ME= z* √(p-hat • q-hat/ n) n=(z*/ME) 2 p-hat • q-hat 0.03= 1.96 √(p-hat • q-hat/ n) 0.03= 1.96√((.05)(.05) / n) √n= 1.96√(.05)(.05) n=32.67 2 = 1067.1 0.03 Need at least 1068 respondents to have ME=3% with a 95% confidence level ONE PROPORTION Z-TEST z= (p-hat – p 0 ) / SD(p-hat) SD(p-hat)= √(p 0 •q 0 ) / n SAMPLING DISTRIBUTION MODEL FOR A DIFF BETWEEN 2 INDEPENDENT PROPORTIONS SD(p-hat 1 – p-hat 2 ) = √p 1 q 1 /n 1 + p 2 q 2 /n 2 ~N(p-hat 1 – p-hat 2 , SD)
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