Chapter 11--Regression and Correlation Methods

The term linear refers to the way the coecients enter

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Unformatted text preview: nts Prediction (Forecasting) Dummy Variables Both Qualitative and Quantitative Predictors Cont’d ... How are the parameters β2 and β3 interpreted? How is the hypothesis H0 : β2 = β3 = 0 interpreted? What about the hypothesis H0 : β3 = 0? How do we test the above two hypothesis? In summary, we include a dummy variables for the qualitative variables and, in addition, we include interaction between all the dummy variables and the quantitative variables. The term Regression Model refers to the case when there are only quantitative predictor variables. When there are only qualitative predictors, the model is called ANOVA Model. A Linear Models refers to the situation where both quantitative and qualitative predictors are involved. The term linear refers to the way the coefficients enter the model. 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 Example: Ozone Layer The scatter plot, 60 Inhibition of Phytoplankton Production 50 q q Suface Deep 30 q q 20 Percent Inihibition 40 q q q q 10 q q q q q 0 q q q q q q 0.00 0.01 0.02 0.03 0.04 UVB Exposure R 2 = 0.729 and sε = 8.521. 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 Example: Ozone Layer Cont’d... The ANOVA Table, Source Regression Residual Total SS 2537.170 943.8 3480.971 df 3 13 16 MS 845.728 72.6 F 11.649 Sig. 0.001 Inference on the individual partial slopes. Variable (Constant) UVB Depth UBV×Depth ˆ βj 2.967 258.936 -1.467 980.039 SE 9.726 309.612 10.538 581.539 t 0.305 0.836 -0.139 2.568 95% CI for βUVB×Depth is (155.774, 1804.305). Chapter 11: Regression and Correlation Methods Stat 491: Biostatistics p-value 0.765 0.418 0.891 0.023...
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This note was uploaded on 02/03/2014 for the course STAT 491 taught by Professor Solomonharrar during the Fall '12 term at Montana.

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