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Business Forecasting ( Regression Model)
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Business Forecasting ( Regression Model)

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Duke Shu, a Willamette MBA interested in business forecasting, data mining, and strategic marketing, uploaded a series of his works to "cast a brick to attract a jade"--hoping to hear more ...

Duke Shu, a Willamette MBA interested in business forecasting, data mining, and strategic marketing, uploaded a series of his works to "cast a brick to attract a jade"--hoping to hear more constructive, brilliant feedback from industrial experts while networking with them.

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Business Forecasting ( Regression Model) Presentation Transcript

  • 1. Target Corporation Forecasting Exercise Author: Duke Shu http://www.linkedin.com/in/dukeshu
  • 2. Time Series Plots of Sales vs logSales Sales have an explicit growth trend over time. There is a strong seasonal variation with a high peak of Sales in Quarter 4 and a small peak (trough) in Quarter 2 of each year. Cycles are not obvious, but there might be a slight curve in the long-term suggesting possible exponential component. Irregular components do not give much noise. LogSales graph has less of variability.
  • 3. Time Series Plots of Interest Rates All the short-term interest rates unanimously comply with an “M” shape dynamics. Short-term rates seem to have more of irregular components. There is more explicit cyclical variation in Long-Term Rates compared to Short-Term rates. Most importantly, short-term rates and long-term rates have the same pattern and are correlated among themselves. This suggests that we can use a single interest rate from each group to analyze the affect of interest rates on sales. Attachment 1 includes the graphs of General Economic Indicators vs Interest rates. Consumer Price Index and GDP have been growing over time. Unemployment rate and Index of Consumer sentiment have a more cyclical pattern.
  • 4. Scatter Plots Based on the Scatter Plot and Basic Summary Statistics in Attachment 2, CPI- U, GDP, UnEmp andCPI-U 0.871 0.000 Time appear to beGDP 0.868 0.000 0.988 0.000 good predictors.UnEmp -0.694 -0.848 -0.883 Firstly, they are 0.000 0.000 0.000 statistically significantConSent 0.369 0.505 0.577 -0.822 0.027 0.002 0.000 0.000 with p-values around1MoLIBOR 0.110 0.521 -0.216 0.181 0.258 0.129 -0.628 0.000 0.701 0.000 0. Secondly, CPI-30YrMort -0.322 -0.474 -0.279 0.103 0.076 0.588 U, GDP and Time 0.055 0.002 0.100 0.550 0.658 0.000 have strong positiveTime 0.878 0.997 0.994 -0.868 0.542 -0.212 -0.485 0.000Correlations:Sales 0.000 CPI-U 0.000 GDP 0.000 UnEmp 0.001 ConSent 0.188 1MoLIBOR 0.001 30YrMort correlation with Sales, while UnEmp has relatively strong negative correlation with Sales.
  • 5. Model BSales = - 21916 - 27 CPI-U + 3.59 GDP + 999 UnEmp - 27.9 ConSent + 327 1MoLIBOR - 275 30YrMort Although R square is relatively high indicating that modelPredictor Coef SE Coef T P VIF explains almost 80% of variation in Sales, S is veryConstant -21916 17525 -1.25 0.221 large, which suggests a very inaccurate prediction. P-CPI-U -26.8 137.6 -0.19 0.847 68.4 values of individual coefficients are not significant. This isGDP 3.591 2.246 1.60 0.121 105.2UnEmp 999 1149 0.87 0.392 37.5 partially due to the strong multicollinearity in thisConSent -27.93 47.35 -0.59 0.560 5.6 model, which is indicated by very high values of VIF.1MoLIBOR 327.1 424.2 0.77 0.447 7.630YrMort -275.4 378.5 -0.73 0.473 1.7 The large positive regression coefficient for UnEmpS = 1025.80 R-Sq = 78.6% R-Sq(adj) = 74.2% contradicts to the common sense, scatter plot and negative correlation coefficient. Again, this is due to theAnalysis of Variance multicollenearity, which is correlation among predictors.Source DF SS MS F PRegression 6 112355704 18725951 17.80 0.000 Still, model itself is valid for predication purposeResidual Error 29 30515681 1052265 , because p-value of F test is around 0. However, it isTotal 35 142871385 unpersuasive to explain the model. Autocorrelation and Residual Time series plots show that there is a correlation/pattern between residuals, suggesting that a model might not be a perfect fit and time components should be included.
  • 6. Model CSales = - 28533 + 70.7 CPI-U + 1.96 GDP + 862 UnEmp + 14.5 ConSent + 84 1MoLIBOR - 66 30YrMort + 225 Q2 + 227 Q3 + 2201 Q4 Model C compared to Model B has better quality indicators (R square is about 98%, S is significantly smaller although still high). GDP, UnEmp and seasonal variation indicator Q4 are now statistically significant, but have a high VIF. Adequacy indicators (independence, mean zero, constant variance, normal distribution) look better than in Model B). However multicolineary problem is still salient, because several VIF are too high. The autocorrelation in Model improved largely, because most of the bars are under ULC or LLC except for one.
  • 7.  Model D logSales = 3.47 + 0.0557 Q2 + 0.0547 Q3 + 0.395 Q4 + 0.0297 CPI-U+ 0.00395 ConSent - 0.0318 MoodysAaa Observation: Model D compared to Model C gets improved in terms of the quality and adequacy of the residuals. T-tests and F-test show that coefficients are significant. VIF for each of predicator is now in acceptable limits, which indicates that no significant multicollinearity exists among predictors. This is due to the Log transformation of y, which reduces the variation in Sales.
  • 8. Model ElogSales = 3.58 + 0.0307 CPI-U + 0.0517 Q2 + 0.0477 Q3 + 0.386 Q4 + 0.0230 1MoLIBOR - 0.0307 30YrMort K1 (original-scale MSE) 59052.7 compare to previous MSE 1052265 or 132855 K2 (original-scale std. dev. Residual) 243.008 compare to 1025 or 365. all indicates a significant improvement in Model E The model indicates a decrease in long-term interest will increase sales while increase in short- term interest will increase sales. Because consumers see less interest in savings in long- term, they start to spend more.
  • 9. Prediction of four quarters of 2002 The prediction of 2002 Q1 and Q4 are both beyond the boundary of prediction, because both LfitS and FitS are substantially larger than previously average ones.
  • 10. Model FlogSales = 3.81 + 0.0303 CPI-U + 0.0462 Q2 + 0.0560 Q3 + 0.393 Q + 0.0325 1MoLIBOR - 0.0582 30YrMort1 Model F compared to Model E improves slightly in terms of quality(S=0.030 compared to 0.038 R-Sq=99.4% compared to 99.2%) and adequacy. Residuals are more independent, normal, mean zero, constant variance. This improvement may be caused by a slight increase in multicolinearity among predicators due to the lag of mortgage rate.
  • 11. Attachment 1: General Economic Indicators vs Interest rates Time Series Plot of CPI-U, 1MoLIBOR, 30YrMort Time Series Plot of GDP, 1MoLIBOR, 30YrMort 200 Variable Variable C PI-U 9000 GDP 1MoLIBOR 1MoLIBOR 30YrMort 8000 30YrMort 150 7000 6000 5000 DataData 100 4000 3000 50 2000 1000 0 0 4 8 12 16 20 24 28 32 36 40 4 8 12 16 20 24 28 32 36 40 Index Index Time Series Plot of UnEmp, 1MoLIBOR, 30YrMort Time Series Plot of ConSent, 1MoLIBOR, 30YrMort 10 Variable 120 Variable UnEmp C onSent 9 1MoLIBOR 1MoLIBOR 30YrMort 100 30YrMort 8 7 80 6 DataData 60 5 40 4 3 20 2 0 1 4 8 12 16 20 24 28 32 36 40 4 8 12 16 20 24 28 32 36 40 Index Index
  • 12. Attachment 2: Basic summary statistics Descriptive Statistics: Sales, CPI-U, GDP, UnEmp, ConSent, 1MoLIBOR, ... Variable N N* Mean SE Mean StDev Minimum Q1 Median Q3 Sales 36 4 5276 337 2020 2459 3678 5052 6643 CPI-U 40 0 162.12 1.83 11.56 143.10 152.38 161.70 172.75 GDP 36 4 8204 132 792 6989 7492 8174 9005 UnEmp 36 4 5.166 0.154 0.924 3.970 4.333 5.115 5.660 ConSent 36 4 96.82 1.44 8.67 77.40 90.78 94.60 105.68 1MoLIBOR 40 0 4.759 0.233 1.473 1.501 3.385 5.432 5.731 30YrMort 40 0 7.498 0.105 0.666 6.077 7.023 7.402 7.942 Time 40 0 20.50 1.85 11.69 1.00 10.25 20.50 30.75