Chapter 11--Regression and Correlation Methods

Chapter 11-Regression and Correlation Methods

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Unformatted text preview: he expected response for a given value of x is µ y |x = β 0 + β 1 x . β0 is the intercept and β1 is the slope of the regression line. 2 The unknown quantities β0 , β1 and σε are parameters to be estimated from the data. 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 16 Model for Simple Linear Regression Cont’d... q 14 q q q µy x = 8.4 + 0.5x 12 q q q q q q q q 10 q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q 8 YIELD OF POTATOES (tons per acre) q q q q q q q q q q q q q q q q q q q q q q q q q q q 0 2 4 6 8 FERTILIZER (cwt. per acre) Chapter 11: Regression and Correlation Methods Stat 491: Biostatistics 10 12 Introduction Least Square Estimates of the Parameters Inference about the Parameters Prediction Assessing Adequacy of Fit Correlation Multiple Regression Model for Simple Linear Regression Cont’d... Essentially, for the n individual data points (xi , yi ) we are assuming, yi = β0 + β1 xi + εi where εi ’s are independently normally distributed with mean 0 2 and variance σε . In addition to the independence, normality and homogeneity of variance assumptions, we have Linearity assumption as well. 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 Interpreting the Parameters β1 is the change in the expected response associated with a unit change in x . β0 is the expected value of y when x = 0. This interpretation of β0 may not always make sense. 2 σε is the variance around the regression line or the mean square prediction error. For example, 95% of the random variations lie within ±2σε . 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 Least Square Method Let the estimated regression line be denoted by, ˆ ˆ µ y |x = β 0 + β 1 x . ˆ ˆ ˆ...
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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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