371chapter14f2011 - Chapter 14 Simple Linear Regression...

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Chapter 14 Simple Linear Regression 14.1 Preliminary Remarks We have only a short time to introduce the ideas of regression .Tog iveyousomeideahowla rge the topic of regression is, The Department of Statistics offers a one-semester course on it, Statistics 333. The topics we could cover fall into two broad categories: results; and checking assumptions. We will have time for results only and that is all that will be ontheFnalexam.IfIevergetaround to writing Chapter 15, it will address the issue of checking assumptions. 14.2 The Simple Linear Regression Model ±or each unit, or case, as they tend to be called in regression,wehavetwonumbers,denotedby X and Y .Thenumberofgrea terin teres ttousisdeno tedby Y and is called the response . Predictor is the common label for the X variable. Very roughly speaking, we want to study whether there is an association or relationship between X and Y ,withspecialinterestinthequestionofusing X to predict Y . It is very important to remember (and almost nobody does) thattheideaofexper imen ta land observational studies introduced in Chapter 9 applies here too, in a way that will be discussed below. We have data on n cases. When we think of them as random variables we use upper case letters and when we think of speciFc numerical values we use lower casele t ters . Thus ,wehavethe n pairs ( X 1 ,Y 1 ) , ( X 2 ,Y 2 ) , ( X 3 ,Y 3 ) ,... ( X n ,Y n ) , which take on speciFc numerical values ( x 1 ,y 1 ) , ( x 2 ,y 2 ) , ( x 3 ,y 3
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1. Experimental :Theresearcherde l ibera te lyse lec tstheva luesof X 1 ,X 2 ,X 3 ,...X n . 2. Observational :Theresearcherse lec tsun i ts(usua l lyassumedtobea trandom from a popu- lation or to be i.i.d. trials) and observes the values of two random variables per unit. Here are two very quick examples. 1. Experimental :Theresea rche risin te res tedinthey ie ld ,pe rac re ,o face rtain crop. Denote the yield by Y .There sea rche rbe l ieve stha tthey ie ldw i l lbea f fec tedbythe concentration of, say, a certain fertilizer that will be applied to the plant. The values of X 1 ,X 2 ,X
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371chapter14f2011 - Chapter 14 Simple Linear Regression...

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