ABCDEFGHIJKLMNOPQRSTUVWXYZ
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Multicollinearity- Auxilliary Regression and Correlation Matrix
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YearCEYdln(CE)ln(YD)
Crude Oil Prices
Interest Rate
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1970646.73643.86.58.2007823721.81.166
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1971699.93812.66.68.246066652.24-0.712
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1972768.239966.68.293049142.48-0.156
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1973849.642446.78.35326153.291.414
SUMMARY OUTPUT
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1974930.24197.16.88.3421490911.58-1.043
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19751030.64300.36.98.36644006711.53-3.543Regression Statistics
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19761147.74437.57.08.39784643412.8-0.657
Multiple R
0.9942142301
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19771274.04577.37.18.42886458413.92-1.19R Square0.9884619354
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19781422.34786.17.38.47347116314.020.113
Adjusted R Square
0.9871799283
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19791585.44879.47.48.4927775431.611.704
Standard Error
0.08117326438
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19801750.74914.57.58.49994529836.832.298
Observations
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19811933.95034.37.68.52402976935.934.704
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19822071.25145.47.68.54585839132.974.449ANOVA
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19832281.65322.87.78.5797547629.554.691dfSSMSF
Significance F
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19842492.35688.17.88.64613155228.785.848
Regression
315.241116115.080372037771.02683580
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19852712.85859.37.98.67578542227.564.331Residual270.17790566890.006589098849
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19862886.36081.88.08.71305598414.433.768Total3015.41902178
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19873076.36216.28.08.73491406718.442.819
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19883330.06508.68.18.78087965814.923.287
Coefficients
Standard Error
t StatP-value
Lower 95%
Upper 95%
Lower 95.0%
Upper 95.0%
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19893576.86699.48.28.80977324918.234.318
Intercept
-13.571486740.5434957319-24.970732880-14.68664787-12.45632561-14.68664787-12.45632561
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19903809.06830.88.28.82919707623.733.595ln(YD)2.4430872620.0636157400138.4038173802.3125585452.5736159782.3125585452.573615978
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19913943.56880.28.38.836403201.803
Interest Rate
0.011202003990.0096174091541.1647631720.2543031976-0.0085312895970.03093529759-0.0085312895970.03093529759
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19924197.67167.18.38.87725638919.321.007
Crude Oil Prices
0.0077272709420.001948841193.965059330.0004853926390.0037285791180.011725962770.0037285791180.01172596277
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19934452.07285.58.48.8936413516.970.625
Of the three explanatory variables, interest rate is the only one that is not-significant
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19944721.074858.58.92065629715.822.206
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19954962.677348.58.95338147217.023.333
Multicollinearity Testing
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19965244.67979.78.68.98465609620.673.083ln(YD)
Interest Rate
Crude Oil Prices
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19975536.88271.88.69.02060741919.093.12ln(YD)1
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19985877.38757.58.79.07766575512.723.584
Interest Rate
0.53091417471
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19996283.89053.18.79.11086251917.973.245
Crude Oil Prices
0.31617303080.60606879091
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20006767.29501.28.89.15917338528.53.576
None of the correlations are above .8, so I'm not overly concerned about multicollinearity at this point
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Auxilliary Regression
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SUMMARY OUTPUT
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Regression Statistics
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Multiple R
0.7037216797
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R Square0.4952242025
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Adjusted R Square
0.4591687884
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Standard Error
1.595055883
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Observations
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ANOVA
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dfSSMSF
Significance F
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Regression
269.8896998334.9448499213.735085690.00006972352419
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Residual2871.237691522.544203269
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Total30141.1273914
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Coefficients
Standard Error
t StatP-value
Lower 95%
Upper 95%
Lower 95.0%
Upper 95.0%
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Intercept
-25.678706449.51347065-2.6991943720.01165078172-45.16616766-6.191245215-45.16616766-6.191245215
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ln(YD)2.9741145091.1165661842.6636258120.012673955470.68693236295.2612966560.68693236295.261296656
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Crude Oil Prices
0.11045045840.032106061013.4401746890.0018411569850.044684173790.17621674310.044684173790.1762167431
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I ran an auxilliary regression using the variable I was concerned about, Interest Rate, as a dependent variable
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With an R2 of about 50% compared to about 99% in the baseline, multicollinearity does not appear to be a cause for concren in this model
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