More Fun With Regression

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More Fun With Regression

• PO 777
• Prof. Steen

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. regress rephouse reppres ----------------------
--------------------------------------------------
------ rephouse Coef. Std. Err.
t Pgtt 95 Conf. Interval -------------
--------------------------------------------------
-------------- reppres 1.316001
.0249125 52.82 0.000 1.267142
1.36486 _cons -.0898492 .0111576
-8.05 0.000 -.1117316 -.0679668
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Multivariate Regression
yi a b1x1,i b2x2,i ei
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Pitfalls

• Omitting explanatory variables
• Including irrelevant explanatory variables
• Measurement error in explanatory variables
• Non-linear relationships
• Multicollinearity
• Outliers

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Irrelevant RHS variables

• True yi bxi ei
• Model yi b?x1i b?x2i ei

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Measurement Error in X

• True yi bxi ei
• X' X d
• E(d)0, var(di)sd2
• cov(X,d)0
• cov(e,d)0

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Multicollinearity

• . reg genpct lnrec lndis pctlast
• Source SS df MS
  Number of obs 818
• -------------------------------------------
  F( 3, 814) 85.10
• Model 37724.8101 3 12574.9367
  Prob gt F 0.0000
• Residual 120286.727 814 147.772391
  R-squared 0.2387
• -------------------------------------------
  Adj R-squared 0.2359
• Total 158011.537 817 193.404574
  Root MSE 12.156
• --------------------------------------------------
  ----------------------------
• genpct Coef. Std. Err. t
  Pgtt 95 Conf. Interval
• -------------------------------------------------
  ----------------------------
• lnrec -1.573258 6.443222 -0.24
  0.807 -14.22055 11.07403
• lndis 4.51684 6.419302 0.70
  0.482 -8.083495 17.11718
• pctlast -.0438444 .0094697 -4.63
  0.000 -.0624323 -.0252564
• _cons 13.71467 2.798213 4.90
  0.000 8.222105 19.20723
• --------------------------------------------------
  ----------------------------

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r.9995
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Diagnosing Multicollinearity

• Auxiliary R-squared r-squared for regression of
  each X on all other X's
• Tolerance 1-Auxiliary r-squared
• Variance inflation factor 1/Tolerance

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Treating Multicollinearity

• Drop variables with worst case of MC
• Create an index out of the co-linear variables
• Do nothing and explain the situation to the
  reader

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Non-Linear Relationships between X and Y
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Non-Linear Relationships between X and Y
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Non-Linear Relationships between X and Y
yi a b1x1,i b2x1,i2 ei
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Non-Linear Relationships between X and Y
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Non-Linear Relationships between X and Y
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Non-Linear Relationships between X and Y
X1new ln(X1 k)/k
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Non-Linear Relationships between X and Y
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Non-Linear RelationshipsLogarithmic
Transformation
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Non-Linear Relationships between X and Y
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Outliers!
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