29MultipleReg

# 29MultipleReg - Statistical Techniques I EXST7005 Multiple Regression Multiple Regression Multiple Regression s The objectives are the same Testing

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Statistical Techniques I EXST7005 Multiple Regression

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Multiple Regression The objectives are the same. Testing hypotheses about potential relationships (correlations), fitting and documenting relationships, and estimating parameters with confidence intervals. The big difference is that a multiple regression will correlate a dependent variable (Y) with several independent variables (X's). Multiple Regression
Multiple Regression (continued) The regressions equation is similar. The sample equation is Yi = b0 + b1x1i + b2x2i + b3x3i + ei The assumptions for the regression are the same as for Simple Linear Regresson The interpretation of the parameter estimates a the same (units are Y units per X units, and measure the change in Y for a 1 unit change in X).

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Multiple Regression (continued) Diagnostics are the same for simple linear regression and multiple regression. Residuals can still be examined for outliers, homogeniety, normality, curvature, etc. as with SLR The only difference is that, since we have several X's, we would usually plot the residuals on Yhat instead of a single X variable.
Multiple Regression (continued) There is only really one new issue here, and thi is in the way we estimate the parameters. If the independent (X) variables were totally and absolutely independent (covariance or correlation = 0), then it wouldn't make any difference if we fitted them one at a time or all together, they would have the same value.

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Multiple Regression (continued) However, in practice there will always be some correlation between the X variables. If two X variables were PERFECTLY correlated, they would both account for the SAME variation in Y, so which would get the variation? If two X variables are only partially correlated they would share part of the variation in Y, so how is it partitioned?
Multiple Regression (continued) To demonstrate this we will look at a simple example and develop a new notation called the Extra SS. For multiple regression there will be, as with simple linear regression, a SS for the "MODEL" This SS lumps together all SS for all variables. This is not usually very informative. We will wa to look at the variables individually.

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Multiple Regression (continued) To do this there are two other SS provided by SAS. In PROC REG these are not provided by default. To see them you must request them. This can be done by adding the options SS1 and/or SS2 to the model statement. In PROC GLM (which will do regressions nicely, but has fewer diagnostics than PROC REG), the TYPE 1 and TYPE 3 SS are provided by default. For regression TYPE 2 and TYPE 3 are the sam
Multiple Regression (continued) To do multiple regression in SAS we simple specify a model with the variables of interest. For example, a regression on Y with 3 variables

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## This note was uploaded on 12/29/2011 for the course EXST 7087 taught by Professor Wang,j during the Fall '08 term at LSU.

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29MultipleReg - Statistical Techniques I EXST7005 Multiple Regression Multiple Regression Multiple Regression s The objectives are the same Testing

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