This preview shows page 1. Sign up to view the full content.
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 radiationUVB (280320nm)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...
View
Full
Document
This note was uploaded on 02/03/2014 for the course STAT 491 taught by Professor Solomonharrar during the Fall '12 term at Montana.
 Fall '12
 SolomonHarrar
 Statistics, Biostatistics, Correlation

Click to edit the document details