Chapter 11--Regression and Correlation Methods

# To account for shifting of the ozone holes

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Unformatted text preview: egression Tests for Subset of Regression Coeﬃcients Prediction (Forecasting) Dummy Variables Both Qualitative and Quantitative Predictors Example: Depletion of the ozone layer allows the most damaging ultraviolet radiation-UVB (280-320nm)-to reach the earth’s surface. An important consequence is the degree to which oceanic phytoplankton production inhibited by exposure to UVB, both near the ocean surface (where the eﬀect should be slight) and below the surface (where the eﬀect could be considerable). To measure this relationship, the researchers sampled from the ocean column at various depths at n = 17 locations around Antarctica during the austral spring of 1990. To account for shifting of the ozone hole’s positioning, they constructed a measure of UVB exposure integrated over exposure time. Does the eﬀect of UVB exposure on the percentage inhibition diﬀer at the surface and in the deep? How much diﬀerence is there? 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 Both Qualitative and Quantitative Predictors Cont’d... Let y Percent Inhibition, x1 =UCB and x2 = 1 if Deep and x2 = 0 if Surface. The full model is, µy |x1 ,x2 = β0 + β1 x1 + β2 x2 + β3 x1 x2 . When x2 = 0, the model reduces to µy |x1 ,x2 = β0 + β1 x1 . When x2 = 1, then µy |x1 ,x2 = β0 + β1 x1 + β2 + β3 x1 which can be rewritten as µy |x1 ,x2 = (β0 + β2 ) + (β1 + β3 )x1 . 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 Coeﬃcie...
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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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