07b_ExtraSS

# 07b_ExtraSS - Statistical Techniques II EXST7015 Extra SS...

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Statistical Techniques II EXST7015 Extra SS 07b_Extra Sum of Squares 1

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Multiple regression involves two or more independent variables (X i ), but still only a single dependent variable (Y i ). There is an analysis for multiple dependent variables, it is called multivariate regression. The sample equation is; Y i = b 0 + b 1 x 1i + b 2 x 2i + b 3 x 3i + e i Multiple regression 07b_Extra Sum of Squares 2
Multiple regression (continued) The objectives in multiple regression are generally the same as SLR. Testing hypotheses about potential relationships (using correlations), fitting and documenting relationships, and estimating parameters with confidence intervals. 07b_Extra Sum of Squares 3

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Multiple regression (continued) The good news, most of what we know about simple linear regressions applies to multiple regression. The regressions equation is similar. The assumptions for the regression are the same as for Simple Linear Regression The interpretation of the parameter estimates are the same (units are Y units per X units, and measure the change in Y for a 1 unit change in X). 07b_Extra Sum of Squares 4
Multiple regression (continued) The diagnostics used in simple linear regression are mostly the same for multiple regression. Residuals can still be examined for outliers, homogeneity, normality, curvature, influence, 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. 07b_Extra Sum of Squares 5

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Multiple regression (continued) So what is different? Obviously, the calculations are more complicated. Algebraic equations basically do not exist. Matrix algebra must be used. Also, we now have several independent variables, X 1 , X 2 , X 3 , etc. We will need some mechanism to evaluate these individually. To this end, we will discuss a new type of Sum of Squares not needed for simple linear regression. 07b_Extra Sum of Squares 6
Multiple regression (continued) The use of several independent variables also creates some new problems. If the independent variable are highly correlated we have a problem called multicollinearity. We will need some diagnostics to evaluate this problem. Outside of the new diagnostics needed to deal with several independent variables, SLR and Multiple regression are very similar. 07b_Extra Sum of Squares 7

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Multiple regression (continued) To do multiple reg. in SAS we specify a model with the variables of interest. For example, a regression on Y with 3 variables X1, X2 and X3 would be specified as PROC REG; MODEL Y = X1 X2 X3; To get the SS1 and SS2 we add the options /ss1 ss2; 07b_Extra Sum of Squares 8
When a variable is added to a model, it usually accounts for some variation. In rare circumstances the variable will

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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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07b_ExtraSS - Statistical Techniques II EXST7015 Extra SS...

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