Data Prep for Modeling
Data Summary: The Variables: Store, and Holiday Flag are Continuous,
but Should be Categorical
## Store Date Weekly_Sales Holiday_Flag
## Min. : 1 Length:6435 Min. : 209986 Min. :0.00000
## 1st Qu.:12 Class :character 1st Qu.: 553350 1st Qu.:0.00000
## Median :23 Mode :character Median : 960746 Median :0.00000
## Mean :23 Mean :1046965 Mean :0.06993
## 3rd Qu.:34 3rd Qu.:1420159 3rd Qu.:0.00000
## Max. :45 Max. :3818686 Max. :1.00000
## Temperature Fuel_Price CPI Unemployment
## Min. : -2.06 Min. :2.472 Min. :126.1 Min. : 3.879
## 1st Qu.: 47.46 1st Qu.:2.933 1st Qu.:131.7 1st Qu.: 6.891
## Median : 62.67 Median :3.445 Median :182.6 Median : 7.874
## Mean : 60.66 Mean :3.359 Mean :171.6 Mean : 7.999
## 3rd Qu.: 74.94 3rd Qu.:3.735 3rd Qu.:212.7 3rd Qu.: 8.622
## Max. :100.14 Max. :4.468 Max. :227.2 Max. :14.313
Data Summary now with Categorical Variables as Factors, and a Random
Variable for Splitting the Data
## Store Date Weekly_Sales Holiday_Flag
## 1 : 143 Length:6435 Min. : 209986 0:5985
## 2 : 143 Class :character 1st Qu.: 553350 1: 450
## 3 : 143 Mode :character Median : 960746
## 4 : 143 Mean :1046965
## 5 : 143 3rd Qu.:1420159
## 6 : 143 Max. :3818686
## (Other):5577
## Temperature Fuel_Price CPI Unemployment
## Min. : -2.06 Min. :2.472 Min. :126.1 Min. : 3.879
## 1st Qu.: 47.46 1st Qu.:2.933 1st Qu.:131.7 1st Qu.: 6.891
## Median : 62.67 Median :3.445 Median :182.6 Median : 7.874
## Mean : 60.66 Mean :3.359 Mean :171.6 Mean : 7.999
## 3rd Qu.: 74.94 3rd Qu.:3.735 3rd Qu.:212.7 3rd Qu.: 8.622
## Max. :100.14 Max. :4.468 Max. :227.2 Max. :14.313
##
## random
## Min. :0.0001523
## 1st Qu.:0.2453881
## Median :0.4969796
## Mean :0.5029555
## 3rd Qu.:0.7634041
## Max. :0.9999618
##
Linear model to predict sales
## Backward Elimination Method
## ---------------------------
##
## Candidate Terms:
##
## 1. Store
## 2. Holiday_Flag
## 3. Temperature
## 4. Fuel_Price
## 5. CPI
## 6. Unemployment
## 7. Store:Holiday_Flag
## 8. Store:Temperature
## 9. Store:Fuel_Price
## 10. Store:CPI
## 11. Store:Unemployment
## 12. Holiday_Flag:Temperature
## 13. Holiday_Flag:Fuel_Price
## 14. Holiday_Flag:CPI
## 15. Holiday_Flag:Unemployment
## 16. Temperature:Fuel_Price
## 17. Temperature:CPI
## 18. Temperature:Unemployment
## 19. Fuel_Price:CPI
## 20. Fuel_Price:Unemployment
## 21. CPI:Unemployment
##
##
## Step => 0
## Model => Weekly_Sales ~ Store + Holiday_Flag + Temperature + Fuel_Price + CPI + Unemployment + Store:Holiday_Flag + Store:Temperature + Store:Fuel_Price + Store:CPI + Store:Unemployment + Holiday_Flag:Temperature + Holiday_Flag:Fuel_Price + Holiday_Flag:CPI + Holiday_Flag:Unemployment + Temperature:Fuel_Price + Temperature:CPI + Temperature:Unemployment + Fuel_Price:CPI + Fuel_Price:Unemployment + CPI:Unemployment
## R2 => 0.934
##
## Initiating stepwise selection...
##
## Step => 1
## Removed => Fuel_Price:Unemployment
## Model => Weekly_Sales ~ Store + Holiday_Flag + Temperature + Fuel_Price + CPI + Unemployment + Store:Holiday_Flag + Store:Temperature + Store:Fuel_Price + Store:CPI + Store:Unemployment + Holiday_Flag:Temperature + Holiday_Flag:Fuel_Price + Holiday_Flag:CPI + Holiday_Flag:Unemployment + Temperature:Fuel_Price + Temperature:CPI + Temperature:Unemployment + Fuel_Price:CPI + CPI:Unemployment
## R2 => 0.93362
##
## Step => 2
## Removed => Holiday_Flag:Unemployment
## Model => Weekly_Sales ~ Store + Holiday_Flag + Temperature + Fuel_Price + CPI + Unemployment + Store:Holiday_Flag + Store:Temperature + Store:Fuel_Price + Store:CPI + Store:Unemployment + Holiday_Flag:Temperature + Holiday_Flag:Fuel_Price + Holiday_Flag:CPI + Temperature:Fuel_Price + Temperature:CPI + Temperature:Unemployment + Fuel_Price:CPI + CPI:Unemployment
## R2 => 0.93362
##
## Step => 3
## Removed => Unemployment
## Model => Weekly_Sales ~ Store + Holiday_Flag + Temperature + Fuel_Price + CPI + Store:Holiday_Flag + Store:Temperature + Store:Fuel_Price + Store:CPI + Store:Unemployment + Holiday_Flag:Temperature + Holiday_Flag:Fuel_Price + Holiday_Flag:CPI + Temperature:Fuel_Price + Temperature:CPI + Temperature:Unemployment + Fuel_Price:CPI + CPI:Unemployment
## R2 => 0.93362
##
## Step => 4
## Removed => CPI:Unemployment
## Model => Weekly_Sales ~ Store + Holiday_Flag + Temperature + Fuel_Price + CPI + Store:Holiday_Flag + Store:Temperature + Store:Fuel_Price + Store:CPI + Store:Unemployment + Holiday_Flag:Temperature + Holiday_Flag:Fuel_Price + Holiday_Flag:CPI + Temperature:Fuel_Price + Temperature:CPI + Temperature:Unemployment + Fuel_Price:CPI
## R2 => 0.93362
##
## Step => 5
## Removed => Holiday_Flag:CPI
## Model => Weekly_Sales ~ Store + Holiday_Flag + Temperature + Fuel_Price + CPI + Store:Holiday_Flag + Store:Temperature + Store:Fuel_Price + Store:CPI + Store:Unemployment + Holiday_Flag:Temperature + Holiday_Flag:Fuel_Price + Temperature:Fuel_Price + Temperature:CPI + Temperature:Unemployment + Fuel_Price:CPI
## R2 => 0.93362
##
## Step => 6
## Removed => Holiday_Flag:Fuel_Price
## Model => Weekly_Sales ~ Store + Holiday_Flag + Temperature + Fuel_Price + CPI + Store:Holiday_Flag + Store:Temperature + Store:Fuel_Price + Store:CPI + Store:Unemployment + Holiday_Flag:Temperature + Temperature:Fuel_Price + Temperature:CPI + Temperature:Unemployment + Fuel_Price:CPI
## R2 => 0.93361
##
##
## No more variables to be removed.
##
## Variables Removed:
##
## => Fuel_Price:Unemployment
## => Holiday_Flag:Unemployment
## => Unemployment
## => CPI:Unemployment
## => Holiday_Flag:CPI
## => Holiday_Flag:Fuel_Price
Interpretations of Three Predictors:
$Fuel Price: When fuel prices goes up, sales go down.
Holiday_Flag: Sales increase during the holidays.
CPI: As the CPI goes up, so do sales.
The R^2 of the model (calculated on the validation data) is
0.9252588
Appendix
Model without Interactions
##
## Call:
## lm(formula = Weekly_Sales ~ . - Date, data = trainlm)
##
## Residuals:
## Min 1Q Median 3Q Max
## -516606 -70588 -12204 38978 1839175
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 1177191.3 274586.6 4.287 1.85e-05 ***
## Store2 349131.3 22526.6 15.499 < 2e-16 ***
## Store3 -1180472.8 22420.2 -52.652 < 2e-16 ***
## Store4 792499.4 115073.4 6.887 6.51e-12 ***
## Store5 -1276994.1 23568.8 -54.182 < 2e-16 ***
## Store6 -25895.9 22947.3 -1.128 0.259174
## Store7 -929692.1 35415.9 -26.251 < 2e-16 ***
## Store8 -719753.7 23599.0 -30.499 < 2e-16 ***
## Store9 -1063586.0 23490.6 -45.277 < 2e-16 ***
## Store10 687061.8 111861.6 6.142 8.87e-10 ***
## Store11 -209743.1 22677.1 -9.249 < 2e-16 ***
## Store12 -103006.2 105050.9 -0.981 0.326876
## Store13 748790.2 113277.3 6.610 4.30e-11 ***
## Store14 575837.2 42916.5 13.418 < 2e-16 ***
## Store15 -637699.9 104790.1 -6.086 1.26e-09 ***
## Store16 -1011942.2 38704.5 -26.145 < 2e-16 ***
## Store17 -399356.7 114191.2 -3.497 0.000475 ***
## Store18 -169102.9 102261.7 -1.654 0.098275 .
## Store19 179678.2 104585.9 1.718 0.085868 .
## Store20 571909.4 24821.8 23.041 < 2e-16 ***
## Store21 -813082.2 22450.5 -36.217 < 2e-16 ***
## Store22 -232820.0 99138.3 -2.348 0.018897 *
## Store23 24568.0 111570.5 0.220 0.825724
## Store24 95009.8 103779.2 0.915 0.359980
## Store25 -844351.7 25158.9 -33.561 < 2e-16 ***
## Store26 -280650.7 104466.5 -2.687 0.007247 **
## Store27 479417.9 99839.1 4.802 1.62e-06 ***
## Store28 197073.8 105174.4 1.874 0.061027 .
## Store29 -695850.1 100608.1 -6.916 5.30e-12 ***
## Store30 -1122822.2 22464.4 -49.982 < 2e-16 ***
## Store31 -157793.3 22277.6 -7.083 1.64e-12 ***
## Store32 -316477.0 34860.9 -9.078 < 2e-16 ***
## Store33 -949428.7 111367.0 -8.525 < 2e-16 ***
## Store34 -240079.9 106954.4 -2.245 0.024838 *
## Store35 -373637.4 97860.2 -3.818 0.000136 ***
## Store36 -1179879.1 22408.0 -52.654 < 2e-16 ***
## Store37 -1032674.6 22827.4 -45.238 < 2e-16 ***
## Store38 -724615.4 105135.0 -6.892 6.28e-12 ***
## Store39 -92296.2 22966.7 -4.019 5.95e-05 ***
## Store40 -391232.2 111596.0 -3.506 0.000460 ***
## Store41 -247376.2 37849.6 -6.536 7.05e-11 ***
## Store42 -666458.1 111816.2 -5.960 2.72e-09 ***
## Store43 -848044.0 25856.9 -32.798 < 2e-16 ***
## Store44 -983625.2 113752.9 -8.647 < 2e-16 ***
## Store45 -645589.4 42826.7 -15.074 < 2e-16 ***
## Holiday_Flag1 70121.6 9729.7 7.207 6.70e-13 ***
## Temperature -975.5 161.6 -6.035 1.72e-09 ***
## Fuel_Price -44356.4 8691.6 -5.103 3.48e-07 ***
## CPI 3552.9 1245.2 2.853 0.004346 **
## Unemployment -22917.4 5151.6 -4.449 8.86e-06 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 160600 on 4375 degrees of freedom
## Multiple R-squared: 0.9208, Adjusted R-squared: 0.9199
## F-statistic: 1038 on 49 and 4375 DF, p-value: < 2.2e-16
Model with Interactions
##
## Call:
## lm(formula = Weekly_Sales ~ (. - Date)^2, data = trainlm)
##
## Residuals:
## Min 1Q Median 3Q Max
## -619109 -57035 -9405 32811 1615565
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -1.297e+07 8.019e+06 -1.618 0.105782
## Store2 -8.328e+06 5.495e+06 -1.516 0.129697
## Store3 1.889e+06 3.703e+06 0.510 0.609945
## Store4 -2.748e+06 7.500e+06 -0.366 0.714049
## Store5 1.826e+06 4.222e+06 0.433 0.665337
## Store6 -8.610e+06 4.279e+06 -2.012 0.044279 *
## Store7 -3.933e+06 4.659e+06 -0.844 0.398721
## Store8 6.520e+05 3.513e+06 0.186 0.852764
## Store9 1.436e+05 4.106e+06 0.035 0.972102
## Store10 2.073e+07 7.273e+06 2.851 0.004384 **
## Store11 -4.198e+06 3.793e+06 -1.107 0.268433
## Store12 4.777e+06 5.124e+06 0.932 0.351290
## Store13 6.280e+06 8.784e+06 0.715 0.474685
## Store14 1.385e+07 2.901e+06 4.774 1.87e-06 ***
## Store15 6.727e+06 3.828e+06 1.757 0.078958 .
## Store16 1.836e+06 4.658e+06 0.394 0.693477
## Store17 8.365e+06 5.463e+06 1.531 0.125780
## Store18 5.679e+06 5.624e+06 1.010 0.312665
## Store19 6.023e+06 3.839e+06 1.569 0.116757
## Store20 2.697e+06 2.808e+06 0.960 0.337027
## Store21 -5.632e+06 5.121e+06 -1.100 0.271564
## Store22 2.645e+06 5.310e+06 0.498 0.618372
## Store23 6.190e+06 7.004e+06 0.884 0.376866
## Store24 3.306e+06 4.038e+06 0.819 0.413033
## Store25 2.558e+06 2.831e+06 0.903 0.366390
## Store26 6.840e+06 7.164e+06 0.955 0.339768
## Store27 8.873e+06 3.697e+06 2.400 0.016430 *
## Store28 5.927e+06 5.169e+06 1.147 0.251579
## Store29 4.592e+06 4.541e+06 1.011 0.311922
## Store30 5.648e+06 5.094e+06 1.109 0.267627
## Store31 -1.307e+06 5.043e+06 -0.259 0.795475
## Store32 -5.998e+06 4.845e+06 -1.238 0.215800
## Store33 6.848e+06 6.524e+06 1.050 0.293871
## Store34 3.031e+06 4.106e+06 0.738 0.460485
## Store35 7.233e+06 3.455e+06 2.094 0.036341 *
## Store36 8.115e+06 5.566e+06 1.458 0.144954
## Store37 4.464e+06 5.582e+06 0.800 0.423964
## Store38 4.605e+06 5.362e+06 0.859 0.390537
## Store39 -5.297e+06 5.464e+06 -0.969 0.332398
## Store40 8.144e+06 7.023e+06 1.160 0.246230
## Store41 -1.281e+07 5.476e+06 -2.339 0.019399 *
## Store42 8.783e+06 6.771e+06 1.297 0.194609
## Store43 4.461e+06 3.196e+06 1.396 0.162900
## Store44 1.006e+07 8.961e+06 1.122 0.261818
## Store45 2.942e+06 2.931e+06 1.004 0.315504
## Holiday_Flag1 -8.335e+04 1.193e+06 -0.070 0.944286
## Temperature 6.239e+04 1.983e+04 3.146 0.001667 **
## Fuel_Price 1.715e+06 9.382e+05 1.828 0.067593 .
## CPI 6.924e+04 3.734e+04 1.854 0.063766 .
## Unemployment 1.793e+05 8.970e+05 0.200 0.841608
## Store2:Holiday_Flag1 5.534e+04 8.636e+04 0.641 0.521689
## Store3:Holiday_Flag1 -1.309e+05 8.421e+04 -1.554 0.120225
## Store4:Holiday_Flag1 1.466e+05 5.189e+05 0.283 0.777495
## Store5:Holiday_Flag1 -4.930e+04 1.042e+05 -0.473 0.636169
## Store6:Holiday_Flag1 -9.919e+04 9.195e+04 -1.079 0.280803
## Store7:Holiday_Flag1 5.371e+04 1.531e+05 0.351 0.725685
## Store8:Holiday_Flag1 -1.204e+05 9.942e+04 -1.211 0.225996
## Store9:Holiday_Flag1 -6.759e+04 1.363e+05 -0.496 0.620056
## Store10:Holiday_Flag1 -4.352e+04 5.073e+05 -0.086 0.931649
## Store11:Holiday_Flag1 -1.131e+05 8.650e+04 -1.307 0.191248
## Store12:Holiday_Flag1 1.584e+05 4.998e+05 0.317 0.751290
## Store13:Holiday_Flag1 -4.353e+04 5.090e+05 -0.086 0.931840
## Store14:Holiday_Flag1 6.613e+02 1.954e+05 0.003 0.997300
## Store15:Holiday_Flag1 9.934e+04 4.804e+05 0.207 0.836178
## Store16:Holiday_Flag1 -2.810e+04 1.644e+05 -0.171 0.864258
## Store17:Holiday_Flag1 1.580e+05 5.135e+05 0.308 0.758292
## Store18:Holiday_Flag1 8.286e+04 4.687e+05 0.177 0.859678
## Store19:Holiday_Flag1 -3.885e+04 4.795e+05 -0.081 0.935428
## Store20:Holiday_Flag1 -1.372e+05 1.009e+05 -1.360 0.174020
## Store21:Holiday_Flag1 -1.245e+05 8.388e+04 -1.485 0.137697
## Store22:Holiday_Flag1 -1.504e+04 4.515e+05 -0.033 0.973434
## Store23:Holiday_Flag1 3.423e+04 4.961e+05 0.069 0.945002
## Store24:Holiday_Flag1 1.262e+05 4.791e+05 0.263 0.792240
## Store25:Holiday_Flag1 -1.163e+05 1.000e+05 -1.162 0.245110
## Store26:Holiday_Flag1 8.200e+04 4.776e+05 0.172 0.863675
## Store27:Holiday_Flag1 9.083e+04 4.597e+05 0.198 0.843386
## Store28:Holiday_Flag1 7.475e+04 5.032e+05 0.149 0.881930
## Store29:Holiday_Flag1 6.015e+04 4.665e+05 0.129 0.897409
## Store30:Holiday_Flag1 -1.623e+05 9.371e+04 -1.732 0.083401 .
## Store31:Holiday_Flag1 1.852e+04 8.637e+04 0.214 0.830223
## Store32:Holiday_Flag1 -1.165e+04 1.543e+05 -0.076 0.939786
## Store33:Holiday_Flag1 -6.878e+04 5.102e+05 -0.135 0.892783
## Store34:Holiday_Flag1 1.236e+04 4.924e+05 0.025 0.979978
## Store35:Holiday_Flag1 1.050e+05 4.515e+05 0.233 0.816089
## Store36:Holiday_Flag1 -1.684e+05 8.684e+04 -1.939 0.052579 .
## Store37:Holiday_Flag1 -1.662e+05 8.402e+04 -1.978 0.048014 *
## Store38:Holiday_Flag1 -3.352e+04 5.018e+05 -0.067 0.946750
## Store39:Holiday_Flag1 2.266e+05 1.041e+05 2.178 0.029495 *
## Store40:Holiday_Flag1 1.056e+04 4.958e+05 0.021 0.983004
## Store41:Holiday_Flag1 -9.792e+04 1.614e+05 -0.606 0.544223
## Store42:Holiday_Flag1 -5.177e+04 5.088e+05 -0.102 0.918955
## Store43:Holiday_Flag1 -1.224e+05 1.044e+05 -1.172 0.241175
## Store44:Holiday_Flag1 -2.095e+04 5.141e+05 -0.041 0.967505
## Store45:Holiday_Flag1 -3.631e+04 1.948e+05 -0.186 0.852127
## Store2:Temperature 6.468e+02 1.517e+03 0.426 0.669905
## Store3:Temperature 1.718e+03 1.739e+03 0.988 0.323384
## Store4:Temperature -3.095e+04 8.398e+03 -3.686 0.000231 ***
## Store5:Temperature 1.723e+03 1.747e+03 0.986 0.324135
## Store6:Temperature 1.776e+03 1.731e+03 1.026 0.304810
## Store7:Temperature -3.996e+03 2.490e+03 -1.605 0.108652
## Store8:Temperature 1.483e+03 1.620e+03 0.915 0.360038
## Store9:Temperature 2.058e+03 1.655e+03 1.243 0.213806
## Store10:Temperature -3.810e+04 8.242e+03 -4.622 3.91e-06 ***
## Store11:Temperature -2.565e+02 1.725e+03 -0.149 0.881796
## Store12:Temperature -2.844e+04 7.884e+03 -3.607 0.000314 ***
## Store13:Temperature -3.059e+04 8.305e+03 -3.683 0.000233 ***
## Store14:Temperature -9.522e+03 3.120e+03 -3.052 0.002286 **
## Store15:Temperature -2.535e+04 7.693e+03 -3.295 0.000993 ***
## Store16:Temperature -4.345e+03 2.661e+03 -1.633 0.102627
## Store17:Temperature -2.714e+04 8.340e+03 -3.254 0.001148 **
## Store18:Temperature -2.503e+04 7.587e+03 -3.300 0.000977 ***
## Store19:Temperature -2.705e+04 7.691e+03 -3.517 0.000441 ***
## Store20:Temperature -6.118e+03 1.663e+03 -3.679 0.000237 ***
## Store21:Temperature 8.856e+02 1.571e+03 0.564 0.572894
## Store22:Temperature -2.703e+04 7.289e+03 -3.709 0.000211 ***
## Store23:Temperature -2.439e+04 8.040e+03 -3.034 0.002431 **
## Store24:Temperature -2.356e+04 7.640e+03 -3.083 0.002062 **
## Store25:Temperature -1.257e+03 1.672e+03 -0.751 0.452437
## Store26:Temperature -2.308e+04 7.725e+03 -2.988 0.002825 **
## Store27:Temperature -1.972e+04 7.349e+03 -2.683 0.007323 **
## Store28:Temperature -2.998e+04 7.890e+03 -3.800 0.000147 ***
## Store29:Temperature -2.535e+04 7.480e+03 -3.389 0.000709 ***
## Store30:Temperature 1.786e+03 1.520e+03 1.175 0.240136
## Store31:Temperature 6.114e+01 1.535e+03 0.040 0.968230
## Store32:Temperature -4.279e+03 2.441e+03 -1.753 0.079738 .
## Store33:Temperature -2.720e+04 8.215e+03 -3.311 0.000938 ***
## Store34:Temperature -2.752e+04 7.889e+03 -3.489 0.000491 ***
## Store35:Temperature -2.131e+04 7.197e+03 -2.961 0.003082 **
## Store36:Temperature 1.686e+03 1.822e+03 0.925 0.355056
## Store37:Temperature 9.967e+02 1.820e+03 0.548 0.583967
## Store38:Temperature -2.613e+04 7.902e+03 -3.306 0.000954 ***
## Store39:Temperature 3.202e+03 1.850e+03 1.731 0.083584 .
## Store40:Temperature -2.543e+04 8.037e+03 -3.164 0.001568 **
## Store41:Temperature -4.342e+03 2.623e+03 -1.656 0.097895 .
## Store42:Temperature -2.873e+04 8.268e+03 -3.475 0.000516 ***
## Store43:Temperature 7.914e+02 1.791e+03 0.442 0.658549
## Store44:Temperature -2.705e+04 8.356e+03 -3.237 0.001218 **
## Store45:Temperature -9.762e+03 3.117e+03 -3.131 0.001751 **
## Store2:Fuel_Price -2.454e+05 9.050e+04 -2.711 0.006726 **
## Store3:Fuel_Price 4.240e+04 9.617e+04 0.441 0.659322
## Store4:Fuel_Price -1.013e+06 3.627e+05 -2.794 0.005235 **
## Store5:Fuel_Price 3.207e+03 9.324e+04 0.034 0.972568
## Store6:Fuel_Price -1.901e+05 8.695e+04 -2.186 0.028850 *
## Store7:Fuel_Price -1.226e+05 1.184e+05 -1.035 0.300635
## Store8:Fuel_Price 1.706e+04 8.939e+04 0.191 0.848646
## Store9:Fuel_Price 3.270e+04 9.404e+04 0.348 0.728071
## Store10:Fuel_Price -7.926e+05 3.415e+05 -2.321 0.020343 *
## Store11:Fuel_Price -1.443e+05 9.995e+04 -1.444 0.148873
## Store12:Fuel_Price -7.544e+05 3.163e+05 -2.386 0.017098 *
## Store13:Fuel_Price -8.571e+05 3.649e+05 -2.349 0.018871 *
## Store14:Fuel_Price -2.274e+05 1.367e+05 -1.664 0.096114 .
## Store15:Fuel_Price -7.315e+05 3.232e+05 -2.263 0.023663 *
## Store16:Fuel_Price -1.565e+05 1.400e+05 -1.118 0.263828
## Store17:Fuel_Price -6.151e+05 3.643e+05 -1.688 0.091415 .
## Store18:Fuel_Price -8.393e+05 3.148e+05 -2.666 0.007712 **
## Store19:Fuel_Price -8.191e+05 3.230e+05 -2.536 0.011255 *
## Store20:Fuel_Price -2.399e+05 9.632e+04 -2.491 0.012780 *
## Store21:Fuel_Price -7.778e+04 8.815e+04 -0.882 0.377669
## Store22:Fuel_Price -7.768e+05 3.079e+05 -2.523 0.011666 *
## Store23:Fuel_Price -7.856e+05 3.598e+05 -2.183 0.029077 *
## Store24:Fuel_Price -8.323e+05 3.220e+05 -2.585 0.009778 **
## Store25:Fuel_Price -1.046e+05 9.299e+04 -1.125 0.260512
## Store26:Fuel_Price -7.323e+05 3.256e+05 -2.249 0.024561 *
## Store27:Fuel_Price -7.214e+05 3.077e+05 -2.344 0.019123 *
## Store28:Fuel_Price -8.012e+05 3.175e+05 -2.524 0.011651 *
## Store29:Fuel_Price -7.336e+05 3.037e+05 -2.415 0.015760 *
## Store30:Fuel_Price 4.340e+03 8.777e+04 0.049 0.960571
## Store31:Fuel_Price 1.033e+04 8.920e+04 0.116 0.907830
## Store32:Fuel_Price -1.115e+05 1.153e+05 -0.967 0.333533
## Store33:Fuel_Price -7.653e+05 3.396e+05 -2.254 0.024262 *
## Store34:Fuel_Price -8.705e+05 3.287e+05 -2.648 0.008124 **
## Store35:Fuel_Price -6.134e+05 3.034e+05 -2.021 0.043304 *
## Store36:Fuel_Price 1.783e+04 9.776e+04 0.182 0.855302
## Store37:Fuel_Price 2.452e+04 1.012e+05 0.242 0.808661
## Store38:Fuel_Price -7.613e+05 3.194e+05 -2.384 0.017188 *
## Store39:Fuel_Price -9.643e+04 9.896e+04 -0.974 0.329892
## Store40:Fuel_Price -7.601e+05 3.578e+05 -2.125 0.033672 *
## Store41:Fuel_Price -7.637e+04 1.316e+05 -0.580 0.561615
## Store42:Fuel_Price -7.224e+05 3.415e+05 -2.115 0.034474 *
## Store43:Fuel_Price -2.673e+04 1.098e+05 -0.243 0.807717
## Store44:Fuel_Price -6.824e+05 3.629e+05 -1.880 0.060129 .
## Store45:Fuel_Price -2.602e+05 1.355e+05 -1.921 0.054800 .
## Store2:CPI 3.783e+04 2.185e+04 1.732 0.083407 .
## Store3:CPI -1.268e+04 1.466e+04 -0.865 0.387214
## Store4:CPI 8.215e+04 4.409e+04 1.863 0.062510 .
## Store5:CPI -1.252e+04 1.667e+04 -0.751 0.452773
## Store6:CPI 3.540e+04 1.697e+04 2.085 0.037109 *
## Store7:CPI 1.412e+04 1.919e+04 0.736 0.461824
## Store8:CPI -6.105e+03 1.426e+04 -0.428 0.668683
## Store9:CPI -5.818e+03 1.664e+04 -0.350 0.726650
## Store10:CPI -9.419e+04 4.627e+04 -2.035 0.041869 *
## Store11:CPI 1.688e+04 1.504e+04 1.122 0.261918
## Store12:CPI 4.620e+03 4.309e+04 0.107 0.914632
## Store13:CPI 9.521e+03 5.800e+04 0.164 0.869626
## Store14:CPI -5.506e+04 1.151e+04 -4.783 1.79e-06 ***
## Store15:CPI -1.270e+04 1.669e+04 -0.761 0.446571
## Store16:CPI -9.117e+03 1.740e+04 -0.524 0.600317
## Store17:CPI -2.351e+04 2.525e+04 -0.931 0.351879
## Store18:CPI 2.308e+03 3.055e+04 0.076 0.939784
## Store19:CPI 1.538e+03 1.697e+04 0.091 0.927803
## Store20:CPI 3.017e+03 1.098e+04 0.275 0.783480
## Store21:CPI 1.753e+04 2.020e+04 0.868 0.385584
## Store22:CPI 1.530e+04 2.616e+04 0.585 0.558736
## Store23:CPI -5.872e+02 3.404e+04 -0.017 0.986236
## Store24:CPI 2.726e+04 2.590e+04 1.052 0.292753
## Store25:CPI -1.066e+04 1.092e+04 -0.976 0.329209
## Store26:CPI -8.150e+03 3.437e+04 -0.237 0.812608
## Store27:CPI -1.868e+04 1.796e+04 -1.040 0.298507
## Store28:CPI 2.443e+02 4.353e+04 0.006 0.995523
## Store29:CPI -7.547e+01 2.525e+04 -0.003 0.997616
## Store30:CPI -2.710e+04 2.001e+04 -1.354 0.175808
## Store31:CPI 3.316e+03 1.994e+04 0.166 0.867957
## Store32:CPI 2.305e+04 1.947e+04 1.184 0.236534
## Store33:CPI -1.545e+04 4.126e+04 -0.375 0.708046
## Store34:CPI 1.929e+04 2.433e+04 0.793 0.427885
## Store35:CPI -5.044e+04 1.617e+04 -3.119 0.001830 **
## Store36:CPI -3.967e+04 2.286e+04 -1.735 0.082818 .
## Store37:CPI -2.258e+04 2.299e+04 -0.982 0.326100
## Store38:CPI 3.381e+03 4.454e+04 0.076 0.939495
## Store39:CPI 2.340e+04 2.237e+04 1.046 0.295532
## Store40:CPI -1.713e+04 3.399e+04 -0.504 0.614249
## Store41:CPI 5.358e+04 2.133e+04 2.513 0.012025 *
## Store42:CPI -2.582e+04 4.246e+04 -0.608 0.543125
## Store43:CPI -2.041e+04 1.503e+04 -1.357 0.174729
## Store44:CPI -3.975e+04 5.879e+04 -0.676 0.499073
## Store45:CPI -9.500e+03 1.152e+04 -0.824 0.409749
## Store2:Unemployment 1.670e+05 1.355e+05 1.232 0.218021
## Store3:Unemployment -7.474e+04 1.111e+05 -0.673 0.501239
## Store4:Unemployment -1.038e+05 3.977e+05 -0.261 0.794154
## Store5:Unemployment -6.994e+04 1.369e+05 -0.511 0.609375
## Store6:Unemployment 2.157e+05 1.245e+05 1.732 0.083264 .
## Store7:Unemployment 1.332e+05 1.671e+05 0.797 0.425439
## Store8:Unemployment -2.099e+04 1.168e+05 -0.180 0.857330
## Store9:Unemployment -1.985e+04 1.243e+05 -0.160 0.873106
## Store10:Unemployment -2.302e+05 4.055e+05 -0.568 0.570346
## Store11:Unemployment 1.089e+05 1.124e+05 0.970 0.332274
## Store12:Unemployment -6.285e+04 3.999e+05 -0.157 0.875105
## Store13:Unemployment -1.416e+05 4.027e+05 -0.352 0.725065
## Store14:Unemployment -1.635e+05 2.219e+05 -0.737 0.461272
## Store15:Unemployment -9.647e+04 3.901e+05 -0.247 0.804692
## Store16:Unemployment 1.218e+04 2.029e+05 0.060 0.952117
## Store17:Unemployment -1.397e+05 4.022e+05 -0.347 0.728420
## Store18:Unemployment -1.162e+05 3.855e+05 -0.302 0.763047
## Store19:Unemployment -9.519e+04 3.886e+05 -0.245 0.806495
## Store20:Unemployment -2.027e+05 1.214e+05 -1.670 0.094964 .
## Store21:Unemployment 1.637e+05 1.306e+05 1.253 0.210211
## Store22:Unemployment 8.452e+03 3.720e+05 0.023 0.981873
## Store23:Unemployment -1.501e+05 3.997e+05 -0.375 0.707350
## Store24:Unemployment -2.141e+05 3.866e+05 -0.554 0.579698
## Store25:Unemployment -8.607e+04 1.221e+05 -0.705 0.480789
## Store26:Unemployment -1.557e+05 4.301e+05 -0.362 0.717460
## Store27:Unemployment -1.661e+05 3.757e+05 -0.442 0.658551
## Store28:Unemployment -6.300e+04 3.996e+05 -0.158 0.874755
## Store29:Unemployment -6.005e+04 3.775e+05 -0.159 0.873596
## Store30:Unemployment -1.374e+05 1.317e+05 -1.043 0.296910
## Store31:Unemployment 5.242e+04 1.273e+05 0.412 0.680515
## Store32:Unemployment 2.386e+05 1.797e+05 1.328 0.184399
## Store33:Unemployment -8.437e+04 4.023e+05 -0.210 0.833910
## Store34:Unemployment -4.403e+04 3.965e+05 -0.111 0.911587
## Store35:Unemployment 4.017e+05 3.813e+05 1.054 0.292111
## Store36:Unemployment -1.188e+05 1.211e+05 -0.981 0.326593
## Store37:Unemployment -9.959e+04 1.232e+05 -0.809 0.418766
## Store38:Unemployment -9.447e+04 3.999e+05 -0.236 0.813269
## Store39:Unemployment 3.292e+04 1.221e+05 0.270 0.787518
## Store40:Unemployment -1.850e+05 4.008e+05 -0.462 0.644342
## Store41:Unemployment 4.368e+05 2.074e+05 2.106 0.035289 *
## Store42:Unemployment -1.268e+05 4.039e+05 -0.314 0.753615
## Store43:Unemployment -1.096e+05 9.932e+04 -1.103 0.270055
## Store44:Unemployment -1.337e+05 4.028e+05 -0.332 0.739941
## Store45:Unemployment -1.088e+04 2.268e+05 -0.048 0.961750
## Holiday_Flag1:Temperature 1.975e+03 6.107e+02 3.234 0.001229 **
## Holiday_Flag1:Fuel_Price -2.908e+04 4.905e+04 -0.593 0.553231
## Holiday_Flag1:CPI 1.028e+03 5.636e+03 0.182 0.855348
## Holiday_Flag1:Unemployment -3.337e+03 2.313e+04 -0.144 0.885310
## Temperature:Fuel_Price 2.998e+03 6.919e+02 4.333 1.50e-05 ***
## Temperature:CPI -3.318e+02 9.243e+01 -3.590 0.000334 ***
## Temperature:Unemployment -3.576e+02 3.624e+02 -0.987 0.323821
## Fuel_Price:CPI -8.976e+03 3.887e+03 -2.310 0.020965 *
## Fuel_Price:Unemployment -1.202e+03 2.263e+04 -0.053 0.957635
## CPI:Unemployment -5.326e+02 4.266e+03 -0.125 0.900654
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 151000 on 4145 degrees of freedom
## Multiple R-squared: 0.9336, Adjusted R-squared: 0.9292
## F-statistic: 209 on 279 and 4145 DF, p-value: < 2.2e-16