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Chapter 11--Regression and Correlation Methods

# Let y be the yield in bushels for four varieties a b

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Unformatted text preview: f glucose associated with exercise. How is the hypothesis H0 : β1 = 0 interpreted? Lesson: Two sample t -test can be treated as a regression problem. Chapter 11: Regression and Correlation Methods Stat 491: Biostatistics Introduction Least Square Estimates of the Parameters Inference about the Parameters Prediction Assessing Adequacy of Fit Correlation Multiple Regression Introduction Inferences in Multiple Regression Tests for Subset of Regression Coeﬃcients Prediction (Forecasting) Dummy Variables One Qualitative Variables with More Than Two Categories If there are t categories then we use t − 1 dummy variables. Let y be the yield in bushels for four varieties (A, B, C and D) of corns. We will use three dummy variables, say x1 , x2 and x3 . y Variety x1 x2 x3 y Variety x1 x2 x3 934 1 000 987 3 010 1041 1 000 951 3 010 1028 1 000 976 3 010 840 3 010 953 1 000 880 2 100 992 4 001 963 2 1 0 0 1143 4 001 924 2 1 0 0 1140 4 001 946 2 1 0 0 1191 4 001 Chapter 11: Regression and Correlation Methods Stat 491: Biostatistics Introduction Least Square Estimates of the Parameters Inference about the Parameters Prediction Assessing Adequacy of Fit Correlation Multiple Regression Introduction Inferences in Multiple Regression Tests for Subset of Regression Coeﬃcients Prediction (Forecasting) Dummy Variables More Than Two Categories Cont’d... The full linear model is, µy |x1 ,x2 ,x3 = β0 + β1 x1 + β2 x2 + β3 x3 . For a yield from variety A, the model reduces µy |x1 ,x2 ,x3 = β0 . For a yields in varieties B, C and D, the model reduces, respectively, to µy |x1 ,x2 ,x3 = β0 + β1 , µy |x1 ,x2 ,x3 = β0 + β2 and µy |x1 ,x2 ,x3 = β0 + β3 . How are the parameters β1 , β2 and β3 interpreted? How do we interpret the hypothesis H0 : β1 = β2 = β3 = 0? How do we test this hypothesis? Lesson: One-way ANOVA problem can be treated as a regression problem. Chapter 11: Regression and Correlation Methods Stat 491: Biostatistics Introduction Least Square Estimates of the Parameters Inference about the Parameters Prediction Assessing Adequacy of Fit Correlation Multiple Regression Introduction Inferences in Multiple R...
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