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. :0.0000653
## 1st Qu.:0.2527042
## Median :0.4945870
## Mean :0.4980825
## 3rd Qu.:0.7453083
## Max. :0.9999414
##
## 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] 0.288 0.788 0.409 0.883 0.94 ...
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 interactions, 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 => 0.93
##
## Initiating stepwise selection...
##
## Step => 1
## 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 + Holiday_Flag:Unemployment + Temperature:Fuel_Price + Temperature:CPI + Temperature:Unemployment + Fuel_Price:CPI + Fuel_Price:Unemployment + CPI:Unemployment
## R2 => 0.93027
##
## Step => 2
## 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 + Holiday_Flag:Unemployment + Temperature:Fuel_Price + Temperature:CPI + Temperature:Unemployment + Fuel_Price:CPI + Fuel_Price:Unemployment + CPI:Unemployment
## R2 => 0.93027
##
## Step => 3
## 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 + Holiday_Flag:Unemployment + Temperature:Fuel_Price + Temperature:CPI + Temperature:Unemployment + Fuel_Price:CPI + CPI:Unemployment
## R2 => 0.93027
##
## 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:Unemployment + Temperature:Fuel_Price + Temperature:CPI + Temperature:Unemployment + Fuel_Price:CPI
## R2 => 0.93026
##
## Step => 5
## Removed => Store:Fuel_Price
## Model => Weekly_Sales ~ Store + Holiday_Flag + Temperature + Fuel_Price + CPI + Store:Holiday_Flag + Store:Temperature + Store:CPI + Store:Unemployment + Holiday_Flag:Temperature + Holiday_Flag:Fuel_Price + Holiday_Flag:Unemployment + Temperature:Fuel_Price + Temperature:CPI + Temperature:Unemployment + Fuel_Price:CPI
## R2 => 0.92952
##
##
## No more variables to be removed.
##
## Variables Removed:
##
## => Unemployment
## => Holiday_Flag:CPI
## => Fuel_Price:Unemployment
## => CPI:Unemployment
## => Store:Fuel_Price
Interpretations of three predictors
Fuel Price: When fuel prices go up, sales go down
Holiday_Flag1: Sales increase during holidays
CPI: As CPI goes up, so do sales
The model, using the training data, has an r^2 .9311
The model, using the validation data, has an r^2 .925
Appendix
Model without interactions
##
## Call:
## lm(formula = Weekly_Sales ~ . - Date, data = trainlm)
##
## Residuals:
## Min 1Q Median 3Q Max
## -513804 -69546 -11882 39468 1823766
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 1357543.2 278781.6 4.870 1.16e-06 ***
## Store2 351630.2 22573.7 15.577 < 2e-16 ***
## Store3 -1180716.9 23170.7 -50.957 < 2e-16 ***
## Store4 716535.6 116599.9 6.145 8.68e-10 ***
## Store5 -1282576.3 24140.1 -53.131 < 2e-16 ***
## Store6 -42348.2 23255.9 -1.821 0.068679 .
## Store7 -946003.2 35215.5 -26.863 < 2e-16 ***
## Store8 -699172.6 23983.0 -29.153 < 2e-16 ***
## Store9 -1068955.1 23877.8 -44.768 < 2e-16 ***
## Store10 628887.4 112929.0 5.569 2.71e-08 ***
## Store11 -217449.3 23756.1 -9.153 < 2e-16 ***
## Store12 -160159.8 105614.7 -1.516 0.129475
## Store13 665390.8 114607.5 5.806 6.85e-09 ***
## Store14 541155.6 43009.0 12.582 < 2e-16 ***
## Store15 -711503.8 105846.8 -6.722 2.02e-11 ***
## Store16 -1033264.4 39281.3 -26.304 < 2e-16 ***
## Store17 -482891.3 115651.4 -4.175 3.03e-05 ***
## Store18 -236188.4 103207.7 -2.288 0.022156 *
## Store19 88916.7 105944.5 0.839 0.401359
## Store20 568352.9 25871.2 21.969 < 2e-16 ***
## Store21 -815160.0 22958.8 -35.505 < 2e-16 ***
## Store22 -323211.6 100196.3 -3.226 0.001265 **
## Store23 -29770.2 113150.0 -0.263 0.792482
## Store24 27496.8 104872.5 0.262 0.793185
## Store25 -847649.9 25399.5 -33.373 < 2e-16 ***
## Store26 -359445.5 105525.4 -3.406 0.000664 ***
## Store27 439229.1 101050.9 4.347 1.41e-05 ***
## Store28 139953.5 105779.4 1.323 0.185880
## Store29 -750276.3 101676.3 -7.379 1.89e-13 ***
## Store30 -1122743.3 22425.9 -50.065 < 2e-16 ***
## Store31 -158464.1 22737.4 -6.969 3.65e-12 ***
## Store32 -332244.3 35092.7 -9.468 < 2e-16 ***
## Store33 -1023329.2 112745.7 -9.076 < 2e-16 ***
## Store34 -312719.9 107897.4 -2.898 0.003770 **
## Store35 -415109.3 98516.6 -4.214 2.56e-05 ***
## Store36 -1180433.3 23588.0 -50.044 < 2e-16 ***
## Store37 -1035121.3 22767.4 -45.465 < 2e-16 ***
## Store38 -796167.5 105624.2 -7.538 5.75e-14 ***
## Store39 -86778.8 23088.3 -3.759 0.000173 ***
## Store40 -455869.6 113041.5 -4.033 5.60e-05 ***
## Store41 -279251.2 37950.0 -7.358 2.20e-13 ***
## Store42 -730734.7 113110.0 -6.460 1.16e-10 ***
## Store43 -857065.6 25926.2 -33.058 < 2e-16 ***
## Store44 -1056135.9 115347.2 -9.156 < 2e-16 ***
## Store45 -676430.4 43141.6 -15.679 < 2e-16 ***
## Holiday_Flag1 75352.5 9602.9 7.847 5.30e-15 ***
## Temperature -904.9 159.4 -5.677 1.46e-08 ***
## Fuel_Price -42007.4 8681.7 -4.839 1.35e-06 ***
## CPI 2692.5 1262.7 2.132 0.033030 *
## Unemployment -23933.5 5245.3 -4.563 5.18e-06 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 162300 on 4475 degrees of freedom
## Multiple R-squared: 0.9183, Adjusted R-squared: 0.9174
## F-statistic: 1027 on 49 and 4475 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
## -587129 -57713 -9239 31164 1669777
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -5.552e+06 2.067e+06 -2.686 0.007251 **
## Store2 1.390e+06 3.731e+06 0.372 0.709572
## Store3 -7.319e+05 2.495e+06 -0.293 0.769288
## Store4 2.277e+06 4.832e+06 0.471 0.637543
## Store5 -3.365e+05 3.015e+06 -0.112 0.911122
## Store6 -3.187e+05 3.202e+06 -0.100 0.920710
## Store7 -7.687e+06 4.412e+06 -1.742 0.081509 .
## Store8 -7.409e+05 2.607e+06 -0.284 0.776265
## Store9 -2.417e+06 2.943e+06 -0.821 0.411532
## Store10 1.530e+07 4.841e+06 3.161 0.001581 **
## Store11 3.802e+05 2.493e+06 0.153 0.878791
## Store12 6.552e+05 3.325e+06 0.197 0.843815
## Store13 1.635e+07 5.779e+06 2.830 0.004676 **
## Store14 1.287e+07 2.550e+06 5.048 4.65e-07 ***
## Store15 4.437e+06 2.167e+06 2.047 0.040698 *
## Store16 1.478e+06 3.789e+06 0.390 0.696566
## Store17 8.385e+05 2.607e+06 0.322 0.747771
## Store18 6.805e+06 4.054e+06 1.679 0.093295 .
## Store19 5.823e+06 2.181e+06 2.670 0.007609 **
## Store20 4.292e+06 2.388e+06 1.797 0.072386 .
## Store21 -5.944e+06 3.926e+06 -1.514 0.130123
## Store22 5.058e+06 3.706e+06 1.365 0.172374
## Store23 7.387e+06 5.375e+06 1.374 0.169378
## Store24 4.762e+06 2.117e+06 2.249 0.024554 *
## Store25 3.642e+06 2.359e+06 1.544 0.122680
## Store26 5.105e+06 5.208e+06 0.980 0.327070
## Store27 7.757e+06 2.077e+06 3.734 0.000191 ***
## Store28 5.090e+06 3.439e+06 1.480 0.138904
## Store29 1.996e+06 3.480e+06 0.573 0.566395
## Store30 1.817e+06 3.787e+06 0.480 0.631345
## Store31 -4.447e+06 3.928e+06 -1.132 0.257554
## Store32 -4.202e+06 4.346e+06 -0.967 0.333632
## Store33 2.755e+06 5.164e+06 0.534 0.593699
## Store34 3.041e+06 2.245e+06 1.354 0.175665
## Store35 4.901e+06 2.239e+06 2.188 0.028694 *
## Store36 3.601e+06 3.489e+06 1.032 0.302085
## Store37 9.487e+04 3.350e+06 0.028 0.977412
## Store38 2.959e+05 3.365e+06 0.088 0.929921
## Store39 -6.233e+06 3.382e+06 -1.843 0.065413 .
## Store40 5.915e+06 5.705e+06 1.037 0.299907
## Store41 -6.364e+05 5.167e+06 -0.123 0.901977
## Store42 3.138e+06 5.207e+06 0.603 0.546745
## Store43 2.658e+06 2.004e+06 1.326 0.184755
## Store44 3.456e+06 5.990e+06 0.577 0.564001
## Store45 1.855e+06 2.704e+06 0.686 0.492794
## Holiday_Flag1 4.297e+05 2.521e+05 1.704 0.088454 .
## Temperature 4.481e+04 1.894e+04 2.365 0.018050 *
## Fuel_Price -8.552e+04 6.073e+04 -1.408 0.159165
## CPI 3.160e+04 8.103e+03 3.900 9.78e-05 ***
## Store2:Holiday_Flag1 -5.246e+04 9.013e+04 -0.582 0.560556
## Store3:Holiday_Flag1 -9.513e+04 9.088e+04 -1.047 0.295295
## Store4:Holiday_Flag1 -8.738e+04 1.093e+05 -0.799 0.424157
## Store5:Holiday_Flag1 -1.324e+05 9.447e+04 -1.402 0.161074
## Store6:Holiday_Flag1 -5.329e+04 9.321e+04 -0.572 0.567508
## Store7:Holiday_Flag1 9.233e+03 9.443e+04 0.098 0.922121
## Store8:Holiday_Flag1 -1.035e+05 1.013e+05 -1.021 0.307234
## Store9:Holiday_Flag1 -1.581e+05 9.421e+04 -1.678 0.093417 .
## Store10:Holiday_Flag1 1.723e+04 8.807e+04 0.196 0.844895
## Store11:Holiday_Flag1 -1.497e+05 9.904e+04 -1.511 0.130801
## Store12:Holiday_Flag1 2.564e+05 1.610e+05 1.593 0.111217
## Store13:Holiday_Flag1 8.884e+03 9.284e+04 0.096 0.923769
## Store14:Holiday_Flag1 4.812e+04 8.870e+04 0.542 0.587509
## Store15:Holiday_Flag1 -8.486e+04 9.339e+04 -0.909 0.363561
## Store16:Holiday_Flag1 -1.058e+05 1.021e+05 -1.036 0.300240
## Store17:Holiday_Flag1 -7.390e+03 9.233e+04 -0.080 0.936209
## Store18:Holiday_Flag1 1.523e+05 1.084e+05 1.404 0.160372
## Store19:Holiday_Flag1 1.172e+05 8.891e+04 1.318 0.187440
## Store20:Holiday_Flag1 -4.434e+04 8.670e+04 -0.511 0.609055
## Store21:Holiday_Flag1 -8.342e+04 8.939e+04 -0.933 0.350770
## Store22:Holiday_Flag1 -3.481e+04 9.641e+04 -0.361 0.718101
## Store23:Holiday_Flag1 -1.684e+04 1.077e+05 -0.156 0.875741
## Store24:Holiday_Flag1 1.291e+05 9.380e+04 1.376 0.168860
## Store25:Holiday_Flag1 -3.212e+04 9.119e+04 -0.352 0.724660
## Store26:Holiday_Flag1 5.135e+04 9.684e+04 0.530 0.595933
## Store27:Holiday_Flag1 1.666e+05 8.991e+04 1.852 0.064032 .
## Store28:Holiday_Flag1 3.018e+05 1.614e+05 1.870 0.061600 .
## Store29:Holiday_Flag1 1.141e+05 1.107e+05 1.031 0.302754
## Store30:Holiday_Flag1 -1.109e+05 9.046e+04 -1.226 0.220313
## Store31:Holiday_Flag1 -7.891e+02 8.912e+04 -0.009 0.992935
## Store32:Holiday_Flag1 -5.212e+04 9.426e+04 -0.553 0.580318
## Store33:Holiday_Flag1 -8.074e+04 9.401e+04 -0.859 0.390489
## Store34:Holiday_Flag1 7.672e+04 1.009e+05 0.761 0.446987
## Store35:Holiday_Flag1 1.480e+05 9.095e+04 1.627 0.103734
## Store36:Holiday_Flag1 -1.072e+05 9.108e+04 -1.177 0.239091
## Store37:Holiday_Flag1 -1.292e+05 8.872e+04 -1.456 0.145477
## Store38:Holiday_Flag1 1.216e+05 1.582e+05 0.769 0.442167
## Store39:Holiday_Flag1 2.622e+04 8.911e+04 0.294 0.768597
## Store40:Holiday_Flag1 -1.154e+05 1.078e+05 -1.071 0.284396
## Store41:Holiday_Flag1 -4.886e+04 9.344e+04 -0.523 0.601045
## Store42:Holiday_Flag1 -2.231e+04 1.161e+05 -0.192 0.847651
## Store43:Holiday_Flag1 -1.721e+04 1.021e+05 -0.169 0.866141
## Store44:Holiday_Flag1 -1.229e+05 9.314e+04 -1.320 0.186883
## Store45:Holiday_Flag1 -3.279e+04 9.818e+04 -0.334 0.738392
## Store2:Temperature -1.095e+03 1.530e+03 -0.716 0.474184
## Store3:Temperature 1.198e+03 1.684e+03 0.711 0.476871
## Store4:Temperature -2.316e+04 7.919e+03 -2.925 0.003465 **
## Store5:Temperature 1.064e+03 1.711e+03 0.622 0.534237
## Store6:Temperature 8.358e+02 1.585e+03 0.527 0.597949
## Store7:Temperature -1.267e+03 2.290e+03 -0.553 0.580193
## Store8:Temperature -1.569e+03 1.611e+03 -0.974 0.330308
## Store9:Temperature 8.142e+02 1.599e+03 0.509 0.610613
## Store10:Temperature -2.741e+04 7.675e+03 -3.571 0.000359 ***
## Store11:Temperature -2.774e+03 1.817e+03 -1.527 0.126884
## Store12:Temperature -1.635e+04 7.191e+03 -2.274 0.023010 *
## Store13:Temperature -2.057e+04 7.731e+03 -2.661 0.007818 **
## Store14:Temperature -5.019e+03 2.911e+03 -1.724 0.084760 .
## Store15:Temperature -1.628e+04 7.176e+03 -2.268 0.023350 *
## Store16:Temperature -1.694e+03 2.543e+03 -0.666 0.505322
## Store17:Temperature -1.659e+04 7.766e+03 -2.137 0.032684 *
## Store18:Temperature -1.536e+04 7.046e+03 -2.181 0.029274 *
## Store19:Temperature -1.429e+04 7.175e+03 -1.992 0.046457 *
## Store20:Temperature -6.260e+03 1.679e+03 -3.729 0.000194 ***
## Store21:Temperature 1.114e+03 1.542e+03 0.722 0.470140
## Store22:Temperature -1.465e+04 6.814e+03 -2.150 0.031626 *
## Store23:Temperature -1.679e+04 7.620e+03 -2.204 0.027577 *
## Store24:Temperature -1.388e+04 7.101e+03 -1.955 0.050626 .
## Store25:Temperature -3.020e+02 1.626e+03 -0.186 0.852691
## Store26:Temperature -1.348e+04 7.169e+03 -1.880 0.060182 .
## Store27:Temperature -1.114e+04 6.867e+03 -1.623 0.104742
## Store28:Temperature -1.735e+04 7.202e+03 -2.409 0.016020 *
## Store29:Temperature -1.550e+04 6.916e+03 -2.241 0.025086 *
## Store30:Temperature 1.564e+03 1.493e+03 1.047 0.294966
## Store31:Temperature -6.441e+01 1.505e+03 -0.043 0.965864
## Store32:Temperature -1.443e+03 2.276e+03 -0.634 0.526144
## Store33:Temperature -1.642e+04 7.663e+03 -2.143 0.032200 *
## Store34:Temperature -1.640e+04 7.304e+03 -2.246 0.024784 *
## Store35:Temperature -1.216e+04 6.678e+03 -1.821 0.068641 .
## Store36:Temperature 2.243e+03 1.769e+03 1.268 0.204797
## Store37:Temperature 1.299e+03 1.774e+03 0.732 0.464136
## Store38:Temperature -1.341e+04 7.191e+03 -1.865 0.062245 .
## Store39:Temperature 1.253e+03 1.772e+03 0.707 0.479501
## Store40:Temperature -1.709e+04 7.616e+03 -2.244 0.024885 *
## Store41:Temperature -2.007e+03 2.471e+03 -0.812 0.416633
## Store42:Temperature -1.765e+04 7.691e+03 -2.295 0.021797 *
## Store43:Temperature 2.706e+03 1.768e+03 1.531 0.125943
## Store44:Temperature -1.703e+04 7.772e+03 -2.192 0.028469 *
## Store45:Temperature -5.881e+03 2.911e+03 -2.021 0.043393 *
## Store2:CPI -3.984e+03 1.373e+04 -0.290 0.771615
## Store3:CPI -1.884e+03 8.854e+03 -0.213 0.831505
## Store4:CPI 1.636e+04 3.310e+04 0.494 0.621138
## Store5:CPI -3.637e+03 1.054e+04 -0.345 0.730155
## Store6:CPI 5.566e+02 1.174e+04 0.047 0.962178
## Store7:CPI 2.905e+04 1.684e+04 1.725 0.084599 .
## Store8:CPI -1.772e+02 9.072e+03 -0.020 0.984414
## Store9:CPI 4.960e+03 1.052e+04 0.471 0.637368
## Store10:CPI -7.895e+04 3.113e+04 -2.536 0.011254 *
## Store11:CPI -1.555e+03 8.773e+03 -0.177 0.859318
## Store12:CPI 1.182e+04 1.995e+04 0.593 0.553504
## Store13:CPI -8.652e+04 3.889e+04 -2.224 0.026177 *
## Store14:CPI -5.105e+04 7.972e+03 -6.404 1.68e-10 ***
## Store15:CPI -1.704e+04 9.455e+03 -1.803 0.071526 .
## Store16:CPI -7.981e+03 1.469e+04 -0.543 0.586898
## Store17:CPI 1.216e+04 1.336e+04 0.911 0.362525
## Store18:CPI -3.029e+04 2.131e+04 -1.422 0.155210
## Store19:CPI -2.164e+04 9.544e+03 -2.267 0.023416 *
## Store20:CPI -9.873e+03 8.240e+03 -1.198 0.230905
## Store21:CPI 1.784e+04 1.449e+04 1.231 0.218434
## Store22:CPI -1.726e+04 1.868e+04 -0.924 0.355321
## Store23:CPI -2.980e+04 3.306e+04 -0.901 0.367522
## Store24:CPI -1.833e+04 1.475e+04 -1.243 0.214011
## Store25:CPI -1.623e+04 8.209e+03 -1.977 0.048075 *
## Store26:CPI -1.723e+04 2.815e+04 -0.612 0.540529
## Store27:CPI -2.469e+04 9.454e+03 -2.612 0.009045 **
## Store28:CPI -1.706e+04 2.084e+04 -0.819 0.412923
## Store29:CPI -2.620e+03 1.835e+04 -0.143 0.886478
## Store30:CPI -1.173e+04 1.401e+04 -0.837 0.402527
## Store31:CPI 1.679e+04 1.447e+04 1.160 0.245990
## Store32:CPI 1.626e+04 1.656e+04 0.982 0.326170
## Store33:CPI -8.609e+03 3.387e+04 -0.254 0.799368
## Store34:CPI -5.108e+03 1.133e+04 -0.451 0.652107
## Store35:CPI -4.449e+04 9.285e+03 -4.792 1.71e-06 ***
## Store36:CPI -2.107e+04 1.321e+04 -1.596 0.110647
## Store37:CPI -4.330e+03 1.250e+04 -0.346 0.729101
## Store38:CPI 1.017e+04 2.022e+04 0.503 0.615018
## Store39:CPI 2.711e+04 1.264e+04 2.145 0.031989 *
## Store40:CPI -2.284e+04 3.525e+04 -0.648 0.517056
## Store41:CPI 8.858e+03 2.027e+04 0.437 0.662101
## Store42:CPI -6.583e+03 3.387e+04 -0.194 0.845895
## Store43:CPI -1.430e+04 7.218e+03 -1.982 0.047577 *
## Store44:CPI -1.094e+04 4.070e+04 -0.269 0.788163
## Store45:CPI -8.683e+03 8.400e+03 -1.034 0.301355
## Store1:Unemployment 1.237e+05 7.030e+04 1.759 0.078594 .
## Store2:Unemployment 1.110e+05 9.207e+04 1.205 0.228208
## Store3:Unemployment 1.078e+05 6.841e+04 1.576 0.115002
## Store4:Unemployment -9.468e+03 4.513e+04 -0.210 0.833838
## Store5:Unemployment 1.073e+05 1.028e+05 1.043 0.297040
## Store6:Unemployment 1.507e+05 8.846e+04 1.703 0.088579 .
## Store7:Unemployment 2.929e+05 1.210e+05 2.421 0.015538 *
## Store8:Unemployment 1.707e+05 9.007e+04 1.895 0.058124 .
## Store9:Unemployment 1.750e+05 9.134e+04 1.916 0.055476 .
## Store10:Unemployment -6.044e+04 7.134e+04 -0.847 0.396948
## Store11:Unemployment 1.178e+05 7.115e+04 1.656 0.097756 .
## Store12:Unemployment 7.588e+04 4.165e+04 1.822 0.068547 .
## Store13:Unemployment -1.594e+05 7.912e+04 -2.015 0.044006 *
## Store14:Unemployment -1.292e+05 1.330e+05 -0.972 0.331263
## Store15:Unemployment 3.623e+04 8.476e+04 0.428 0.669034
## Store16:Unemployment 6.610e+04 1.268e+05 0.521 0.602073
## Store17:Unemployment 5.289e+04 7.337e+04 0.721 0.470984
## Store18:Unemployment 1.516e+04 1.110e+05 0.137 0.891376
## Store19:Unemployment 2.623e+04 8.743e+04 0.300 0.764220
## Store20:Unemployment -3.593e+04 8.298e+04 -0.433 0.665076
## Store21:Unemployment 2.831e+05 9.785e+04 2.893 0.003837 **
## Store22:Unemployment -2.967e+02 1.111e+05 -0.003 0.997870
## Store23:Unemployment -5.880e+04 1.424e+05 -0.413 0.679605
## Store24:Unemployment 8.775e+04 1.099e+05 0.799 0.424523
## Store25:Unemployment -4.563e+03 7.617e+04 -0.060 0.952233
## Store26:Unemployment -1.673e+04 1.584e+05 -0.106 0.915896
## Store27:Unemployment -1.406e+05 1.012e+05 -1.389 0.164769
## Store28:Unemployment 4.933e+04 4.199e+04 1.175 0.240137
## Store29:Unemployment 7.309e+04 7.693e+04 0.950 0.342162
## Store30:Unemployment 5.703e+04 9.269e+04 0.615 0.538403
## Store31:Unemployment 2.122e+05 9.782e+04 2.169 0.030146 *
## Store32:Unemployment 2.458e+05 1.213e+05 2.027 0.042775 *
## Store33:Unemployment 6.520e+04 6.763e+04 0.964 0.335101
## Store34:Unemployment 5.675e+04 4.105e+04 1.383 0.166880
## Store35:Unemployment 4.210e+05 8.992e+04 4.682 2.93e-06 ***
## Store36:Unemployment 7.127e+04 7.510e+04 0.949 0.342652
## Store37:Unemployment 8.717e+04 7.387e+04 1.180 0.238059
## Store38:Unemployment 5.625e+04 4.155e+04 1.354 0.175924
## Store39:Unemployment 1.525e+05 7.540e+04 2.022 0.043201 *
## Store40:Unemployment -3.171e+04 1.536e+05 -0.206 0.836470
## Store41:Unemployment 6.928e+03 1.637e+05 0.042 0.966238
## Store42:Unemployment 3.416e+04 7.547e+04 0.453 0.650808
## Store43:Unemployment 3.884e+04 4.529e+04 0.857 0.391234
## Store44:Unemployment 2.175e+04 7.938e+04 0.274 0.784105
## Store45:Unemployment 9.742e+04 1.397e+05 0.698 0.485472
## Holiday_Flag1:Temperature 1.481e+03 5.939e+02 2.494 0.012675 *
## Holiday_Flag1:Fuel_Price -3.641e+04 3.376e+04 -1.079 0.280819
## Holiday_Flag1:Unemployment -3.897e+04 2.189e+04 -1.780 0.075111 .
## Temperature:Fuel_Price 1.509e+03 6.036e+02 2.500 0.012467 *
## Temperature:CPI -2.142e+02 8.638e+01 -2.480 0.013187 *
## Temperature:Unemployment -7.086e+02 3.563e+02 -1.989 0.046797 *
## Fuel_Price:CPI -3.532e+02 2.973e+02 -1.188 0.234868
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 153900 on 4292 degrees of freedom
## Multiple R-squared: 0.9295, Adjusted R-squared: 0.9257
## F-statistic: 244 on 232 and 4292 DF, p-value: < 2.2e-16