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. :0.0001067
## 1st Qu.:0.2511800
## Median :0.5092787
## Mean :0.5030516
## 3rd Qu.:0.7480175
## Max. :0.9994411
##
## tibble [6,435 × 9] (S3: tbl_df/tbl/data.frame)
## $ Store : Factor w/ 45 levels "1","2","3","4",..: 1 1 1 1 1 1 1 1 1 1 ...
## $ Date : chr [1:6435] "05-02-2010" "12-02-2010" "19-02-2010" "26-02-2010" ...
## $ Weekly_Sales: num [1:6435] 1643691 1641957 1611968 1409728 1554807 ...
## $ Holiday_Flag: Factor w/ 2 levels "0","1": 1 2 1 1 1 1 1 1 1 1 ...
## $ Temperature : num [1:6435] 42.3 38.5 39.9 46.6 46.5 ...
## $ Fuel_Price : num [1:6435] 2.57 2.55 2.51 2.56 2.62 ...
## $ CPI : num [1:6435] 211 211 211 211 211 ...
## $ Unemployment: num [1:6435] 8.11 8.11 8.11 8.11 8.11 ...
## $ random : num [1:6435] 0.8636 0.0275 0.8042 0.9408 0.9015 ...
Data split 70/30 into training and validation datasets.
- The training data has 4525 observations
- The validation data has 1910 observations
Linear model to predict sales
- A linear model was created using all possible predictors, except for
Date, predicting sales. This model allowed for the understanding of the
individual effects of each predictor.
- Then a model with all possible interactions was created, again,
excluding Date
- A backward selection was employed using alpha = 0.01 in order to
obtain a more parsimonious model.
- The resulting model with interations, as well as the initial model
without, can be found in the Appendix
## 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 => 0.932
##
## Initiating stepwise selection...
##
## Step => 1
## Removed => Holiday_Flag:CPI
## 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:Unemployment + Temperature:Fuel_Price + Temperature:CPI + Temperature:Unemployment + Fuel_Price:CPI + Fuel_Price:Unemployment + CPI:Unemployment
## R2 => 0.9322
##
## 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 + Temperature:Fuel_Price + Temperature:CPI + Temperature:Unemployment + Fuel_Price:CPI + Fuel_Price:Unemployment + CPI:Unemployment
## R2 => 0.9322
##
## 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 + Temperature:Fuel_Price + Temperature:CPI + Temperature:Unemployment + Fuel_Price:CPI + Fuel_Price:Unemployment + CPI:Unemployment
## R2 => 0.9322
##
## Step => 4
## Removed => Fuel_Price: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 + Temperature:Fuel_Price + Temperature:CPI + Temperature:Unemployment + Fuel_Price:CPI + CPI:Unemployment
## R2 => 0.9322
##
## Step => 5
## 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 + CPI:Unemployment
## R2 => 0.93219
##
## Step => 6
## 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 + Temperature:Fuel_Price + Temperature:CPI + Temperature:Unemployment + Fuel_Price:CPI
## R2 => 0.93218
##
##
## No more variables to be removed.
##
## Variables Removed:
##
## => Holiday_Flag:CPI
## => Holiday_Flag:Unemployment
## => Unemployment
## => Fuel_Price:Unemployment
## => Holiday_Flag:Fuel_Price
## => CPI:Unemployment
Interpretations of three predictors
- Holiday_Flag 1: When there is a holiday, sales will increase.
- Fuel Price: When fuel prices go up, sales will decrease.
- CPI: As the CPI goes up, sales will increase.
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
## -521372 -69198 -10988 39000 1839948
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 1476404.3 269418.4 5.480 4.49e-08 ***
## Store2 376211.4 22812.9 16.491 < 2e-16 ***
## Store3 -1161932.4 23308.5 -49.850 < 2e-16 ***
## Store4 682057.0 112906.2 6.041 1.66e-09 ***
## Store5 -1263279.0 23680.1 -53.348 < 2e-16 ***
## Store6 -2067.0 23055.8 -0.090 0.928569
## Store7 -935684.8 34608.5 -27.036 < 2e-16 ***
## Store8 -681611.6 23464.4 -29.049 < 2e-16 ***
## Store9 -1046003.3 23673.2 -44.185 < 2e-16 ***
## Store10 570399.2 109778.8 5.196 2.13e-07 ***
## Store11 -210310.0 22875.7 -9.194 < 2e-16 ***
## Store12 -212997.5 103146.2 -2.065 0.038980 *
## Store13 599878.7 110993.2 5.405 6.83e-08 ***
## Store14 556189.8 42007.9 13.240 < 2e-16 ***
## Store15 -744702.5 102513.7 -7.264 4.40e-13 ***
## Store16 -1022803.6 38358.8 -26.664 < 2e-16 ***
## Store17 -507761.3 112031.7 -4.532 5.99e-06 ***
## Store18 -282429.2 100314.1 -2.815 0.004892 **
## Store19 71247.2 102760.3 0.693 0.488136
## Store20 546816.0 24883.9 21.975 < 2e-16 ***
## Store21 -795895.3 22590.4 -35.232 < 2e-16 ***
## Store22 -345210.7 97313.4 -3.547 0.000393 ***
## Store23 -88037.2 109424.0 -0.805 0.421122
## Store24 -24488.0 101770.5 -0.241 0.809861
## Store25 -835621.0 25087.8 -33.308 < 2e-16 ***
## Store26 -383034.7 102236.2 -3.747 0.000182 ***
## Store27 397733.3 98022.7 4.058 5.04e-05 ***
## Store28 104966.9 103355.7 1.016 0.309881
## Store29 -797758.2 98667.1 -8.085 7.92e-16 ***
## Store30 -1106669.4 22699.1 -48.754 < 2e-16 ***
## Store31 -160010.4 23116.7 -6.922 5.09e-12 ***
## Store32 -318823.6 34478.4 -9.247 < 2e-16 ***
## Store33 -1070457.9 109189.3 -9.804 < 2e-16 ***
## Store34 -357805.9 104847.8 -3.413 0.000649 ***
## Store35 -452792.2 95562.3 -4.738 2.22e-06 ***
## Store36 -1164983.6 23039.9 -50.564 < 2e-16 ***
## Store37 -1014412.2 22705.9 -44.676 < 2e-16 ***
## Store38 -836107.5 103118.7 -8.108 6.58e-16 ***
## Store39 -63503.9 22659.7 -2.803 0.005093 **
## Store40 -489429.0 109486.2 -4.470 8.01e-06 ***
## Store41 -242951.4 36937.9 -6.577 5.34e-11 ***
## Store42 -780236.5 109692.0 -7.113 1.32e-12 ***
## Store43 -837938.2 25301.2 -33.119 < 2e-16 ***
## Store44 -1100178.0 111588.5 -9.859 < 2e-16 ***
## Store45 -673125.8 42171.2 -15.962 < 2e-16 ***
## Holiday_Flag1 68726.9 9493.6 7.239 5.29e-13 ***
## Temperature -768.0 157.1 -4.889 1.05e-06 ***
## Fuel_Price -37785.4 8544.5 -4.422 1.00e-05 ***
## CPI 1971.2 1224.8 1.609 0.107590
## Unemployment -24648.8 5093.7 -4.839 1.35e-06 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 159700 on 4456 degrees of freedom
## Multiple R-squared: 0.9213, Adjusted R-squared: 0.9204
## F-statistic: 1064 on 49 and 4456 DF, p-value: < 2.2e-16
Model with interactions
##
## Call:
## lm(formula = paste(response, "~", paste(c(include, cterms), collapse = " + ")),
## data = l)
##
## Residuals:
## Min 1Q Median 3Q Max
## -615190 -55043 -9284 31776 1688212
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -7.784e+06 3.325e+06 -2.341 0.019278 *
## Store2 -1.448e+06 5.378e+06 -0.269 0.787736
## Store3 -2.558e+06 4.118e+06 -0.621 0.534464
## Store4 5.445e+06 5.715e+06 0.953 0.340845
## Store5 -3.285e+06 4.029e+06 -0.815 0.414934
## Store6 -1.191e+07 4.419e+06 -2.696 0.007041 **
## Store7 -1.018e+07 4.602e+06 -2.212 0.027039 *
## Store8 -4.216e+06 3.574e+06 -1.180 0.238128
## Store9 -4.062e+06 4.254e+06 -0.955 0.339616
## Store10 7.908e+06 6.312e+06 1.253 0.210291
## Store11 -6.479e+06 3.842e+06 -1.686 0.091815 .
## Store12 -3.929e+06 5.591e+06 -0.703 0.482328
## Store13 1.581e+07 8.209e+06 1.926 0.054197 .
## Store14 6.594e+06 3.100e+06 2.127 0.033444 *
## Store15 1.590e+06 2.858e+06 0.556 0.577946
## Store16 -4.478e+06 4.489e+06 -0.998 0.318554
## Store17 6.649e+05 4.023e+06 0.165 0.868715
## Store18 2.648e+06 5.014e+06 0.528 0.597474
## Store19 1.599e+06 2.871e+06 0.557 0.577529
## Store20 -3.126e+06 2.893e+06 -1.080 0.280051
## Store21 -1.191e+07 5.327e+06 -2.236 0.025392 *
## Store22 -4.229e+06 4.685e+06 -0.903 0.366687
## Store23 2.675e+06 5.396e+06 0.496 0.620152
## Store24 2.231e+04 3.299e+06 0.007 0.994604
## Store25 -2.839e+06 2.964e+06 -0.958 0.338123
## Store26 -1.271e+06 5.727e+06 -0.222 0.824333
## Store27 5.106e+06 2.844e+06 1.795 0.072655 .
## Store28 7.170e+06 5.866e+06 1.222 0.221683
## Store29 -8.769e+05 4.399e+06 -0.199 0.842025
## Store30 1.348e+06 5.292e+06 0.255 0.798894
## Store31 -8.720e+06 5.212e+06 -1.673 0.094389 .
## Store32 -1.068e+07 4.663e+06 -2.291 0.022005 *
## Store33 1.244e+06 5.955e+06 0.209 0.834499
## Store34 4.783e+05 3.656e+06 0.131 0.895910
## Store35 3.396e+05 2.852e+06 0.119 0.905201
## Store36 3.393e+06 5.037e+06 0.674 0.500571
## Store37 -2.470e+05 5.027e+06 -0.049 0.960818
## Store38 -1.812e+05 4.992e+06 -0.036 0.971051
## Store39 -1.630e+07 4.821e+06 -3.380 0.000731 ***
## Store40 3.833e+06 5.619e+06 0.682 0.495170
## Store41 -1.991e+07 5.883e+06 -3.384 0.000721 ***
## Store42 5.233e+06 6.710e+06 0.780 0.435561
## Store43 -4.982e+05 3.074e+06 -0.162 0.871254
## Store44 4.248e+06 8.083e+06 0.526 0.599204
## Store45 -2.910e+06 3.130e+06 -0.930 0.352492
## Holiday_Flag1 -4.523e+04 7.370e+04 -0.614 0.539444
## Temperature 6.303e+04 1.915e+04 3.291 0.001006 **
## Fuel_Price 2.010e+06 6.676e+05 3.010 0.002626 **
## CPI 4.651e+04 1.445e+04 3.218 0.001301 **
## Store2:Holiday_Flag1 6.671e+04 8.679e+04 0.769 0.442150
## Store3:Holiday_Flag1 -5.017e+04 9.179e+04 -0.547 0.584692
## Store4:Holiday_Flag1 8.443e+04 8.676e+04 0.973 0.330538
## Store5:Holiday_Flag1 -5.642e+04 9.142e+04 -0.617 0.537183
## Store6:Holiday_Flag1 7.768e+04 8.856e+04 0.877 0.380469
## Store7:Holiday_Flag1 1.084e+05 8.905e+04 1.217 0.223696
## Store8:Holiday_Flag1 -1.925e+04 8.862e+04 -0.217 0.828021
## Store9:Holiday_Flag1 -2.665e+04 9.494e+04 -0.281 0.778981
## Store10:Holiday_Flag1 1.501e+05 9.504e+04 1.580 0.114208
## Store11:Holiday_Flag1 -6.607e+04 8.845e+04 -0.747 0.455083
## Store12:Holiday_Flag1 -9.407e+04 9.757e+04 -0.964 0.335076
## Store13:Holiday_Flag1 1.202e+05 8.792e+04 1.367 0.171568
## Store14:Holiday_Flag1 -1.038e+05 8.906e+04 -1.165 0.243898
## Store15:Holiday_Flag1 6.733e+04 8.893e+04 0.757 0.449047
## Store16:Holiday_Flag1 9.098e+04 9.987e+04 0.911 0.362383
## Store17:Holiday_Flag1 9.902e+04 8.871e+04 1.116 0.264379
## Store18:Holiday_Flag1 3.855e+04 9.961e+04 0.387 0.698778
## Store19:Holiday_Flag1 9.483e+04 8.545e+04 1.110 0.267120
## Store20:Holiday_Flag1 -2.877e+03 9.331e+04 -0.031 0.975403
## Store21:Holiday_Flag1 1.694e+04 9.999e+04 0.169 0.865481
## Store22:Holiday_Flag1 -1.014e+05 1.131e+05 -0.897 0.369948
## Store23:Holiday_Flag1 1.925e+04 9.098e+04 0.212 0.832416
## Store24:Holiday_Flag1 1.175e+05 9.481e+04 1.239 0.215456
## Store25:Holiday_Flag1 -5.491e+04 8.977e+04 -0.612 0.540820
## Store26:Holiday_Flag1 8.527e+04 9.146e+04 0.932 0.351209
## Store27:Holiday_Flag1 1.122e+05 8.535e+04 1.314 0.188839
## Store28:Holiday_Flag1 8.557e+04 9.425e+04 0.908 0.363977
## Store29:Holiday_Flag1 4.579e+04 8.972e+04 0.510 0.609822
## Store30:Holiday_Flag1 -8.289e+04 9.419e+04 -0.880 0.378889
## Store31:Holiday_Flag1 -2.912e+04 1.046e+05 -0.278 0.780744
## Store32:Holiday_Flag1 -5.947e+04 9.111e+04 -0.653 0.513958
## Store33:Holiday_Flag1 -8.181e+04 8.706e+04 -0.940 0.347409
## Store34:Holiday_Flag1 -1.098e+04 8.848e+04 -0.124 0.901240
## Store35:Holiday_Flag1 1.012e+05 9.823e+04 1.030 0.302997
## Store36:Holiday_Flag1 -7.624e+04 9.741e+04 -0.783 0.433862
## Store37:Holiday_Flag1 -8.889e+04 9.135e+04 -0.973 0.330569
## Store38:Holiday_Flag1 -7.505e+04 8.697e+04 -0.863 0.388242
## Store39:Holiday_Flag1 9.906e+04 9.562e+04 1.036 0.300245
## Store40:Holiday_Flag1 2.409e+04 8.887e+04 0.271 0.786334
## Store41:Holiday_Flag1 7.114e+04 8.896e+04 0.800 0.423956
## Store42:Holiday_Flag1 -8.792e+04 9.093e+04 -0.967 0.333651
## Store43:Holiday_Flag1 -5.904e+04 8.690e+04 -0.679 0.496926
## Store44:Holiday_Flag1 -5.263e+04 9.130e+04 -0.577 0.564304
## Store45:Holiday_Flag1 -4.118e+04 9.853e+04 -0.418 0.675972
## Store2:Temperature 6.091e+02 1.650e+03 0.369 0.712000
## Store3:Temperature 2.536e+03 1.851e+03 1.370 0.170728
## Store4:Temperature -3.074e+04 8.124e+03 -3.783 0.000157 ***
## Store5:Temperature 1.515e+03 1.812e+03 0.836 0.403104
## Store6:Temperature 2.950e+03 1.702e+03 1.733 0.083095 .
## Store7:Temperature -1.392e+03 2.489e+03 -0.559 0.575882
## Store8:Temperature 6.539e+02 1.698e+03 0.385 0.700184
## Store9:Temperature 1.905e+03 1.717e+03 1.109 0.267343
## Store10:Temperature -3.185e+04 7.957e+03 -4.002 6.38e-05 ***
## Store11:Temperature 1.665e+03 1.824e+03 0.913 0.361224
## Store12:Temperature -2.212e+04 7.578e+03 -2.919 0.003532 **
## Store13:Temperature -2.674e+04 8.020e+03 -3.334 0.000862 ***
## Store14:Temperature -9.149e+03 3.065e+03 -2.985 0.002851 **
## Store15:Temperature -2.268e+04 7.413e+03 -3.060 0.002228 **
## Store16:Temperature -2.687e+03 2.670e+03 -1.006 0.314285
## Store17:Temperature -2.467e+04 8.051e+03 -3.064 0.002197 **
## Store18:Temperature -2.132e+04 7.308e+03 -2.917 0.003547 **
## Store19:Temperature -2.246e+04 7.418e+03 -3.027 0.002484 **
## Store20:Temperature -3.053e+03 1.756e+03 -1.739 0.082125 .
## Store21:Temperature 2.839e+03 1.669e+03 1.701 0.089016 .
## Store22:Temperature -2.234e+04 7.042e+03 -3.172 0.001523 **
## Store23:Temperature -2.343e+04 7.807e+03 -3.001 0.002703 **
## Store24:Temperature -1.833e+04 7.379e+03 -2.483 0.013054 *
## Store25:Temperature -4.966e+02 1.799e+03 -0.276 0.782556
## Store26:Temperature -2.100e+04 7.396e+03 -2.840 0.004539 **
## Store27:Temperature -1.764e+04 7.083e+03 -2.490 0.012814 *
## Store28:Temperature -2.338e+04 7.594e+03 -3.078 0.002094 **
## Store29:Temperature -2.113e+04 7.199e+03 -2.935 0.003355 **
## Store30:Temperature 2.588e+03 1.632e+03 1.586 0.112702
## Store31:Temperature 1.633e+03 1.686e+03 0.969 0.332757
## Store32:Temperature -4.166e+03 2.452e+03 -1.699 0.089428 .
## Store33:Temperature -2.374e+04 7.913e+03 -3.000 0.002711 **
## Store34:Temperature -2.333e+04 7.577e+03 -3.079 0.002087 **
## Store35:Temperature -1.901e+04 6.932e+03 -2.743 0.006123 **
## Store36:Temperature 2.942e+03 1.903e+03 1.546 0.122134
## Store37:Temperature 2.013e+03 1.932e+03 1.042 0.297415
## Store38:Temperature -2.002e+04 7.568e+03 -2.646 0.008186 **
## Store39:Temperature 3.181e+03 1.861e+03 1.709 0.087498 .
## Store40:Temperature -2.461e+04 7.799e+03 -3.156 0.001612 **
## Store41:Temperature -3.147e+03 2.590e+03 -1.215 0.224490
## Store42:Temperature -2.498e+04 7.988e+03 -3.128 0.001773 **
## Store43:Temperature 2.965e+03 1.880e+03 1.577 0.114839
## Store44:Temperature -2.436e+04 8.029e+03 -3.034 0.002430 **
## Store45:Temperature -8.392e+03 3.108e+03 -2.700 0.006953 **
## Store2:Fuel_Price -2.071e+05 9.328e+04 -2.221 0.026422 *
## Store3:Fuel_Price -3.785e+04 1.054e+05 -0.359 0.719462
## Store4:Fuel_Price -9.605e+05 2.840e+05 -3.382 0.000727 ***
## Store5:Fuel_Price -9.066e+04 9.423e+04 -0.962 0.336033
## Store6:Fuel_Price -2.230e+05 8.963e+04 -2.488 0.012871 *
## Store7:Fuel_Price -2.603e+05 1.129e+05 -2.305 0.021217 *
## Store8:Fuel_Price -8.254e+04 9.043e+04 -0.913 0.361417
## Store9:Fuel_Price -4.605e+04 9.451e+04 -0.487 0.626064
## Store10:Fuel_Price -9.600e+05 2.873e+05 -3.342 0.000840 ***
## Store11:Fuel_Price -1.420e+05 1.040e+05 -1.365 0.172197
## Store12:Fuel_Price -1.000e+06 2.873e+05 -3.482 0.000503 ***
## Store13:Fuel_Price -7.374e+05 2.950e+05 -2.500 0.012466 *
## Store14:Fuel_Price -3.924e+05 1.290e+05 -3.042 0.002364 **
## Store15:Fuel_Price -8.661e+05 2.661e+05 -3.255 0.001142 **
## Store16:Fuel_Price -2.604e+05 1.226e+05 -2.125 0.033682 *
## Store17:Fuel_Price -8.718e+05 2.886e+05 -3.020 0.002540 **
## Store18:Fuel_Price -1.011e+06 2.663e+05 -3.795 0.000150 ***
## Store19:Fuel_Price -9.662e+05 2.668e+05 -3.621 0.000296 ***
## Store20:Fuel_Price -2.508e+05 8.957e+04 -2.800 0.005131 **
## Store21:Fuel_Price -1.804e+05 9.327e+04 -1.935 0.053096 .
## Store22:Fuel_Price -9.301e+05 2.561e+05 -3.632 0.000284 ***
## Store23:Fuel_Price -8.518e+05 2.660e+05 -3.202 0.001373 **
## Store24:Fuel_Price -9.360e+05 2.670e+05 -3.505 0.000461 ***
## Store25:Fuel_Price -1.827e+05 9.094e+04 -2.009 0.044625 *
## Store26:Fuel_Price -8.890e+05 2.669e+05 -3.331 0.000873 ***
## Store27:Fuel_Price -8.268e+05 2.536e+05 -3.260 0.001121 **
## Store28:Fuel_Price -8.502e+05 2.949e+05 -2.883 0.003956 **
## Store29:Fuel_Price -8.727e+05 2.658e+05 -3.283 0.001037 **
## Store30:Fuel_Price -8.087e+04 9.322e+04 -0.868 0.385694
## Store31:Fuel_Price -1.175e+05 9.256e+04 -1.269 0.204449
## Store32:Fuel_Price -2.521e+05 1.136e+05 -2.219 0.026509 *
## Store33:Fuel_Price -9.182e+05 2.826e+05 -3.250 0.001165 **
## Store34:Fuel_Price -9.563e+05 2.841e+05 -3.366 0.000769 ***
## Store35:Fuel_Price -8.924e+05 2.541e+05 -3.512 0.000450 ***
## Store36:Fuel_Price -7.547e+04 9.626e+04 -0.784 0.433080
## Store37:Fuel_Price -6.470e+04 9.692e+04 -0.668 0.504409
## Store38:Fuel_Price -9.114e+05 2.842e+05 -3.207 0.001352 **
## Store39:Fuel_Price -3.272e+05 9.745e+04 -3.358 0.000792 ***
## Store40:Fuel_Price -9.443e+05 2.644e+05 -3.572 0.000359 ***
## Store41:Fuel_Price -2.231e+05 1.141e+05 -1.956 0.050515 .
## Store42:Fuel_Price -8.749e+05 2.866e+05 -3.053 0.002283 **
## Store43:Fuel_Price -1.342e+05 1.018e+05 -1.319 0.187136
## Store44:Fuel_Price -8.809e+05 2.894e+05 -3.044 0.002352 **
## Store45:Fuel_Price -3.530e+05 1.281e+05 -2.755 0.005888 **
## Store2:CPI 8.877e+03 2.127e+04 0.417 0.676491
## Store3:CPI 4.932e+03 1.633e+04 0.302 0.762701
## Store4:CPI -2.426e+03 3.966e+04 -0.061 0.951230
## Store5:CPI 8.168e+03 1.569e+04 0.521 0.602692
## Store6:CPI 4.634e+04 1.744e+04 2.658 0.007900 **
## Store7:CPI 3.906e+04 1.829e+04 2.135 0.032796 *
## Store8:CPI 1.374e+04 1.397e+04 0.983 0.325546
## Store9:CPI 1.104e+04 1.686e+04 0.655 0.512471
## Store10:CPI -2.362e+04 4.331e+04 -0.545 0.585527
## Store11:CPI 2.474e+04 1.525e+04 1.622 0.104848
## Store12:CPI 5.125e+04 3.876e+04 1.322 0.186223
## Store13:CPI -8.550e+04 5.820e+04 -1.469 0.141863
## Store14:CPI -2.760e+04 1.193e+04 -2.313 0.020775 *
## Store15:CPI 3.607e+03 1.719e+04 0.210 0.833793
## Store16:CPI 1.565e+04 1.714e+04 0.913 0.361512
## Store17:CPI 1.775e+04 2.506e+04 0.709 0.478673
## Store18:CPI 1.061e+04 2.825e+04 0.376 0.707179
## Store19:CPI 1.686e+04 1.737e+04 0.971 0.331540
## Store20:CPI 1.940e+04 1.127e+04 1.720 0.085431 .
## Store21:CPI 4.210e+04 2.109e+04 1.996 0.046010 *
## Store22:CPI 4.437e+04 2.585e+04 1.716 0.086171 .
## Store23:CPI 4.115e+03 3.262e+04 0.126 0.899627
## Store24:CPI 2.231e+04 2.594e+04 0.860 0.389811
## Store25:CPI 8.676e+03 1.161e+04 0.747 0.454814
## Store26:CPI 2.600e+04 3.000e+04 0.867 0.386252
## Store27:CPI -1.371e+04 1.814e+04 -0.756 0.449854
## Store28:CPI -2.996e+04 4.186e+04 -0.716 0.474166
## Store29:CPI 1.914e+04 2.504e+04 0.764 0.444716
## Store30:CPI -1.030e+04 2.091e+04 -0.493 0.622225
## Store31:CPI 3.304e+04 2.068e+04 1.598 0.110200
## Store32:CPI 4.374e+04 1.846e+04 2.370 0.017844 *
## Store33:CPI 6.294e+03 4.053e+04 0.155 0.876607
## Store34:CPI 1.852e+04 2.205e+04 0.840 0.400908
## Store35:CPI -8.191e+03 1.569e+04 -0.522 0.601735
## Store36:CPI -2.109e+04 2.039e+04 -1.034 0.301105
## Store37:CPI -4.073e+03 2.026e+04 -0.201 0.840704
## Store38:CPI 1.750e+04 3.394e+04 0.516 0.606200
## Store39:CPI 6.986e+04 1.958e+04 3.568 0.000363 ***
## Store40:CPI -1.074e+03 3.384e+04 -0.032 0.974676
## Store41:CPI 8.242e+04 2.343e+04 3.518 0.000439 ***
## Store42:CPI -1.838e+04 4.611e+04 -0.399 0.690195
## Store43:CPI -1.541e+03 1.254e+04 -0.123 0.902229
## Store44:CPI -1.392e+04 5.724e+04 -0.243 0.807923
## Store45:CPI 8.262e+03 1.180e+04 0.700 0.483908
## Store1:Unemployment -3.149e+04 8.247e+04 -0.382 0.702636
## Store2:Unemployment 3.734e+04 1.167e+05 0.320 0.749022
## Store3:Unemployment 5.481e+03 9.687e+04 0.057 0.954877
## Store4:Unemployment -4.543e+04 4.324e+04 -1.051 0.293526
## Store5:Unemployment 2.637e+04 1.141e+05 0.231 0.817292
## Store6:Unemployment 3.138e+05 1.058e+05 2.967 0.003025 **
## Store7:Unemployment 2.668e+05 1.150e+05 2.321 0.020346 *
## Store8:Unemployment 7.698e+04 9.761e+04 0.789 0.430370
## Store9:Unemployment 5.699e+04 1.074e+05 0.531 0.595712
## Store10:Unemployment 1.114e+04 7.527e+04 0.148 0.882346
## Store11:Unemployment 1.346e+05 8.920e+04 1.509 0.131273
## Store12:Unemployment 8.689e+04 4.672e+04 1.860 0.063007 .
## Store13:Unemployment -1.418e+05 9.384e+04 -1.511 0.130808
## Store14:Unemployment 6.247e+04 1.541e+05 0.405 0.685295
## Store15:Unemployment 8.233e+04 1.121e+05 0.735 0.462546
## Store16:Unemployment 1.623e+05 1.660e+05 0.978 0.328348
## Store17:Unemployment 1.327e+04 6.899e+04 0.192 0.847442
## Store18:Unemployment -4.998e+04 1.178e+05 -0.424 0.671315
## Store19:Unemployment 2.206e+03 1.141e+05 0.019 0.984582
## Store20:Unemployment 4.267e+04 8.561e+04 0.498 0.618171
## Store21:Unemployment 2.861e+05 1.159e+05 2.469 0.013572 *
## Store22:Unemployment 1.768e+05 1.152e+05 1.534 0.125036
## Store23:Unemployment 2.048e+04 1.383e+05 0.148 0.882292
## Store24:Unemployment 5.111e+04 1.332e+05 0.384 0.701160
## Store25:Unemployment 7.060e+04 8.932e+04 0.791 0.429275
## Store26:Unemployment 1.089e+05 1.805e+05 0.603 0.546356
## Store27:Unemployment 3.373e+04 1.227e+05 0.275 0.783431
## Store28:Unemployment 2.664e+04 4.565e+04 0.584 0.559499
## Store29:Unemployment 9.706e+04 8.004e+04 1.213 0.225322
## Store30:Unemployment -5.095e+04 1.156e+05 -0.441 0.659316
## Store31:Unemployment 1.921e+05 1.109e+05 1.732 0.083310 .
## Store32:Unemployment 3.027e+05 1.203e+05 2.517 0.011882 *
## Store33:Unemployment 6.491e+04 6.532e+04 0.994 0.320391
## Store34:Unemployment 6.117e+04 4.620e+04 1.324 0.185566
## Store35:Unemployment 4.276e+05 1.112e+05 3.846 0.000122 ***
## Store36:Unemployment -2.844e+04 9.612e+04 -0.296 0.767310
## Store37:Unemployment -7.433e+03 9.779e+04 -0.076 0.939415
## Store38:Unemployment 4.916e+04 4.306e+04 1.142 0.253602
## Store39:Unemployment 2.312e+05 9.064e+04 2.551 0.010789 *
## Store40:Unemployment -8.040e+04 1.497e+05 -0.537 0.591229
## Store41:Unemployment 6.053e+05 1.817e+05 3.330 0.000875 ***
## Store42:Unemployment -4.567e+03 7.737e+04 -0.059 0.952936
## Store43:Unemployment -1.297e+03 5.405e+04 -0.024 0.980858
## Store44:Unemployment 1.381e+03 9.126e+04 0.015 0.987925
## Store45:Unemployment 2.254e+05 1.653e+05 1.363 0.172843
## Holiday_Flag1:Temperature 1.785e+03 5.201e+02 3.432 0.000605 ***
## Temperature:Fuel_Price 2.149e+03 6.852e+02 3.136 0.001724 **
## Temperature:CPI -3.087e+02 8.862e+01 -3.484 0.000499 ***
## Temperature:Unemployment -8.473e+02 3.676e+02 -2.305 0.021232 *
## Fuel_Price:CPI -9.662e+03 3.075e+03 -3.142 0.001692 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 152100 on 4231 degrees of freedom
## Multiple R-squared: 0.9322, Adjusted R-squared: 0.9278
## F-statistic: 212.2 on 274 and 4231 DF, p-value: < 2.2e-16