# 17 - BUAD 310 Applied Business Statistics 1 Outline for Today Residual analysis Transformations Indicator variables Interactions C statistic Model

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Outline for Today Residual analysis Transformations Indicator variables Interactions C statistic Model building 2
Residual Analysis 1. Graphical Analysis of Residuals Plot residuals vs. fitted values Residuals = errors Difference between actual Y & predicted Y 2. Purposes Examine functional form (linear vs. non-linear model) Evaluate violations of assumptions 3

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An Example Regression Analysis: Y1 versus X Predictor Coef T P Constant 3.000 2.67 0.026 X 0.5001 4.24 0.002 S = 1.237 R-Sq = 66.7% R-Sq(adj) = 62.9% F P 17.99 0.002 Regression Analysis: Y2 versus X Predictor Coef T P Constant 3.001 2.67 0.026 X 0.5000 4.24 0.002 S = 1.237 R-Sq = 66.6% R-Sq(adj) = 62.9% F P 17.97 0.002 Regression Analysis: Y3 versus X Predictor Coef T P Constant 3.002 2.67 0.026 X 0.4997 4.24 0.002 S = 1.236 R-Sq = 66.6% R-Sq(adj) = 62.9% F P 17.97 0.002 4
Residual Plots 10 9 8 7 6 5 2 1 0 -1 -2 Fitted Value Residual Residuals Versus the Fitted Values (response is Y1) 10 9 8 7 6 5 1 0 -1 -2 Fitted Value Residuals Versus the Fitted Values (response is Y2) 10 9 8 7 6 5 3 2 1 0 -1 Fitted Value Residuals Versus the Fitted Values (response is Y3) 5

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Potential Transformations y y y ln y or x 2 ln x ln y or 1/x If scattterplots look like this, try suggested transformations… e ln y Overall residual plot looks like  this   try  ln   y 6
Transformations in Minitab Calc --> Calculator --> enter column In dialog box, select function if necessary Natural logarithm Exponential Square root Other Insert column to be transformed Also: Stat --> Regression --> Fitted Line Plot Can fit linear, quadratic or cubic and get plot Limited diagnostics; no other x-variables 7

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Residual Analysis: Salary Data 10 20 30 40 50 60 70 -20 -10 0 10 20 30 Fitted Value Residual Residuals Versus the Fitted Values (response is Salary () 3.0 3.5 4.0 4.5 -0.4 -0.3 -0.2 -0.1 0.0 0.1 0.2 0.3 Fitted Value Residuals Versus the Fitted Values (response is ln(salar) 8
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## This note was uploaded on 11/30/2010 for the course BUAD 310 at USC.

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17 - BUAD 310 Applied Business Statistics 1 Outline for Today Residual analysis Transformations Indicator variables Interactions C statistic Model

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