chapter11.1 - CHAPTER11 SIMPLEREGRESSIONANDCORRELATION 1

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1 CHAPTER 11 SIMPLE REGRESSION AND CORRELATION
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In this chapter, we learn to estimate the curve of regression  of Y on X when the regression is considered to be linear. Linear curve of regression of Y on X Where  β  and   β 1  denote real numbers. x x Y 1 0 | β μ + =
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11.1 MODEL AND PARAMETER ESTIMATION From elementary algebra, y=b+mx, where b denotes the  y intercept and m denotes the slope of the line. In simple  linear regression model,  denotes the intercept and          the slope of the regression  line.   x x Y 1 0 | β μ + = 0 1
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In conducting a regression study, we shall be observing the variable  X  at  points  x 1  ,  x 2  ,  …….  x n  .  These  points  are assumed  to  be  measured  without  error.  When  they  are preselected by the experimenter, we say that the study is a controlled  study. When they are made at random, its termed as an  observational  study. In  both  cases,  we  shall  be  concerned  with  the  n  random variables    Y| x 1  ,  Y| x 2  ,…. .  Y| x n  .  Recall  that  the  random variable varies about its mean value. Let   xi Y i i x Y E | | μ - =
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Solving that equation , we get  In this expression, we have assumed that the random  difference  E i    has a mean zero. Since we are assuming a  linear regression, we have  It is customary to drop the conditional notation and  denote Y| x  by Y. Hence i i E x Y + + = 1 0 | β xi Y i i E x Y | | μ + = i E Y + + = 1 0
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This note was uploaded on 05/14/2010 for the course MATHEMATIC mathe taught by Professor Xyz during the Spring '10 term at Birla Institute of Technology & Science.

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chapter11.1 - CHAPTER11 SIMPLEREGRESSIONANDCORRELATION 1

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