Lecture13-2 - 1 Graphical Analysis of Residuals Plot...

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2 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
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3 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
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4 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 Residual Residuals Versus the Fitted Values (response is Y2) 10 9 8 7 6 5 3 2 1 0 -1 Fitted Value Residual Residuals Versus the Fitted Values (response is Y3)
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5 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
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6 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
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7 10 20 30 40 50 60 70 -20 -10 0 10 20 30 Fitted Value Residua l 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 Residual Residuals Versus the Fitted Values (response is ln(salar)
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8 1. High correlation between X variables 1. Leads to unstable coefficients for the X variables in model 1. Always exists in practice - matter of degree
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9 1. Examine Correlation Matrix Are correlations between pairs of X variables more than with Y variable? 2. Examine Variance Inflation Factor ( VIF ) If VIF j > 5, multicollinearity may be a concern If VIF j > 10, multicollinearity is severe These are only rough guidelines… 3. Eliminate one correlated X variable (usually the one with the highest VIF value)
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2 1 1 = - j j VIF r 10 Regress the j -th variable X j on all other X i ( i j ) variables to get coefficient of determination, r j 2 Minimum VIF = 1 Maximum VIF as r j 2 1
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11 You work in advertising for the New York Times .
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