Chapter 11--Regression and Correlation Methods

# xk and one dependent variable the linear regression

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Unformatted text preview: ferences in Multiple Regression Tests for Subset of Regression Coeﬃcients Prediction (Forecasting) Dummy Variables The Multiple Linear Regression We have k independent variables (x1 , x2 , . . . , xk ) and one dependent variable. The linear regression model is given by, y = β0 + β1 x1 + β2 x2 + · · · + βk xk + ε. The expected value of y for given values of x1 , x2 , . . . , xk is: µy |x1 ,x2 ,...,xk = β0 + β1 x1 + β2 x2 + · · · + βk xk . β0 is the y intercept and is interpreted as, when applicable, the expected value of y when each x is 0. β1 , β2 , . . . , βp are known as partial slopes or partial regression coeﬃcients. Their interpretation depends on what the respective x s are. 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 The Data and Notation The data looks like, Expt/Samp. Unit 1 2 . . . x1 x11 x21 . . . x2 x12 x22 . . . ··· ··· ··· . . . xk x1k x2k . . . y y1 y2 . . . n xn1 xn2 ··· xnk yn Scatter plot of all the data together is not possible except in some very special cases. 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 The Linear Regression Model For each observation on the i th sampling (experimental) units yi = β0 + β1 xi 1 + β2 xi 2 + · · · + βk xik + εi for i = 1, 2, 3, . . . , n. Assumptions: 1 2 3 4 Linearity: The Mathematical form of the relationship is correct. Homogeneity of Variance (constant variance): The variance of 2 εi is σε and it is the same for all i . Independence: The εi s are independent. Normality: εi is normally distributed. 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) Dum...
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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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