Formulas for Exam 1 - Two independent samples Test Statistic for testing 0:or :210210HH 211110212222112121nnsnsnsnnsyytpp Confidence interval for21: 211,221211,22111 to 11nnstyynnstyypnkpnk For most situations, use a value of 2 for1,2 nkt. - Analysis of Variance: k groups, n observations per group nstLSDnkSSsMSMSnkndfsnSSSSpnkWithinprepErrorWithinirepErrorWithin211111,222 Replace 1,2 nkt by the value 2 for most situations. For large values of k replace 1,2 nkt by the value 3. A difference in sample means is statistically significant if the absolute value of the difference is greater than the value of LSD. 1- Least Squares Regression repErrorLinearLinearLinearLinearLinearLineariLineariiiMSMSFtdfSSMSdfCnmSSCmbYYbCYCm1 ˆˆˆˆ :equation predictionˆ :estimateintercept ˆ :estimate slopelinear 2121112111 The linear term is statistically significant if is greater than 2 or 3. Lineart repErrorQuadraticQuadraticQuadraticQuadraticQuadraticQuadraticiQuadraticiiiMSMSFtdfSSMSdfCnmSSCmCmbYCYCm1 ˆˆˆˆˆ :equation predictionˆ :estimate slope quadratic222222112222 The quadratic term is statistically significant if is greater than 2 or 3. Quadratict Coefficient of Determination: TotalModelSSSSR 2 Simple linear model:LinearModelSSSS Model with linear and quadratic terms: QuadraticLinearModelSSSSSS
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