lec2 - II.MultipleRegression...

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II. Multiple Regression
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Recall that for regression analysis:   The data must be from a probability sample.  The univariate distributions need not be normal,  but the usual warnings about pronounced  skewness & outliers apply.  The key evidence about the distributions &  outliers is provided not by the univariate graphs  but by the  y/x   bivariate scatterplots .
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 Even so, bivariate scatterplots &  correlations do not necessarily predict  whether explanatory variables will test  significant in a multiple regression  model.  That’s because a multiple regression  model expresses the  joint, linear  effects  of a set of explanatory  variables on an outcome variable.
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  On matters of causality in multiple  regression, see Agresti/Finlay  (chap. 10); King et al.; McClendon;  and Berk.  To reiterate, when might  regression analysis be useful even  when causal order isn’t clear?
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Let’s turn our attention now to multiple  regression, in which the outcome  variable  y  is a function of  k  explanatory  variables.  For every one-unit increase in  x,     y  increases/decreases by … units on  average, holding the other explanatory  variables fixed.
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  Hence slope (i.e. regression) coefficients  in multiple regression are commonly called  ‘partial coefficients.’  They indicate the independent effect of a  given explanatory variable  on  y , holding  the other explanatory variables constant.
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 Some other ways of saying ‘holding the  other variables constant’:  holding the other variables fixed  adjusting for the other variables  net of the other variables
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Statistical controls mimic experimental  controls.  The experimental method, however, is  unparalleled in its ability to isolate the  effects of explanatory ‘treatment’ variables  on an outcome variable, holding other  variables constant.
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 What’s the effect of the daily amount of  Cuban coffee persons drink on their levels  of displayed anger, holding constant  income, education, gender, race-ethnicity,  body weight, health, mental health, diet,  exercise, & so on? A Multiple Regression Example
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. reg science read write math Source        SS              df          MS         Number of obs   =    200                       F(  3,   196) =   65.32 Model       9752.65806    3      3250.88602          Prob > F =   0.0000 Residual   9754.84194   196     49.7696017        R-squared =  0.4999                       Adj R-squared =  0.4923 Total         19507.50     199     98.0276382 Root MSE =  7.0548 science       Coef.   Std. Err.       t P>t       [95% Conf.
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This note was uploaded on 07/11/2011 for the course SYA 6306 taught by Professor Tardanico during the Spring '09 term at FIU.

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lec2 - II.MultipleRegression...

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