Assignment 7
John Berlam, Jack Dobrowski
2024-03-25
1. Summary of Walmart Data
Stores were initially categorized by number rather than by StoreID
## 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. :14.3132. Splitting data into training and validation 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. :0.0000049
## 1st Qu.:0.2553981
## Median :0.4990746
## Mean :0.5017721
## 3rd Qu.:0.7480154
## Max. :0.9999758
## ## 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] 0.118 0.632 0.386 0.935 0.973 ...
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 0.0000049 0.2553981 0.4990746 0.5017721 0.7480154 0.99997583. Creating model and checking results
Important At the bottom of the data is R-squared percentage which tells us how correlated the data is.
##
## Call:
## lm(formula = Weekly_Sales ~ . - Date, data = trainlm)
##
## Residuals:
## Min 1Q Median 3Q Max
## -525229 -70856 -12219 39316 1842323
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 1067528.3 278137.5 3.838 0.000126 ***
## Store2 364064.7 23341.2 15.598 < 2e-16 ***
## Store3 -1173377.2 24044.0 -48.801 < 2e-16 ***
## Store4 850034.7 116869.9 7.273 4.12e-13 ***
## Store5 -1268813.7 23933.2 -53.015 < 2e-16 ***
## Store6 -22077.1 23418.4 -0.943 0.345872
## Store7 -894243.5 35735.5 -25.024 < 2e-16 ***
## Store8 -697747.6 24663.8 -28.290 < 2e-16 ***
## Store9 -1057109.2 24036.2 -43.980 < 2e-16 ***
## Store10 724913.8 112912.8 6.420 1.50e-10 ***
## Store11 -214922.0 23387.3 -9.190 < 2e-16 ***
## Store12 -69289.1 106126.8 -0.653 0.513861
## Store13 780241.1 114462.2 6.817 1.06e-11 ***
## Store14 600211.4 43394.5 13.832 < 2e-16 ***
## Store15 -607907.2 106088.8 -5.730 1.07e-08 ***
## Store16 -988525.2 39413.8 -25.081 < 2e-16 ***
## Store17 -361391.4 115449.4 -3.130 0.001758 **
## Store18 -154947.9 103382.9 -1.499 0.134002
## Store19 213743.8 106007.2 2.016 0.043827 *
## Store20 590819.2 25339.2 23.316 < 2e-16 ***
## Store21 -796391.1 22989.0 -34.642 < 2e-16 ***
## Store22 -224400.7 100135.5 -2.241 0.025077 *
## Store23 95265.3 112962.3 0.843 0.399085
## Store24 137157.7 104799.3 1.309 0.190681
## Store25 -837307.3 25270.2 -33.134 < 2e-16 ***
## Store26 -238478.4 105553.2 -2.259 0.023911 *
## Store27 532878.9 100870.5 5.283 1.33e-07 ***
## Store28 241476.4 105869.7 2.281 0.022602 *
## Store29 -651373.6 101765.4 -6.401 1.71e-10 ***
## Store30 -1111159.0 23120.6 -48.059 < 2e-16 ***
## Store31 -160870.7 23347.8 -6.890 6.35e-12 ***
## Store32 -285658.4 35031.9 -8.154 4.52e-16 ***
## Store33 -908025.0 112539.7 -8.068 9.07e-16 ***
## Store34 -206277.0 108100.3 -1.908 0.056429 .
## Store35 -311665.5 98829.5 -3.154 0.001624 **
## Store36 -1162570.1 23361.8 -49.764 < 2e-16 ***
## Store37 -1020966.4 23293.5 -43.831 < 2e-16 ***
## Store38 -692425.7 106024.5 -6.531 7.27e-11 ***
## Store39 -95946.6 22948.3 -4.181 2.96e-05 ***
## Store40 -346137.1 112863.2 -3.067 0.002176 **
## Store41 -227367.1 37895.4 -6.000 2.13e-09 ***
## Store42 -624190.0 112745.8 -5.536 3.27e-08 ***
## Store43 -839268.2 26464.2 -31.713 < 2e-16 ***
## Store44 -937498.8 115260.5 -8.134 5.34e-16 ***
## Store45 -626669.3 43375.9 -14.447 < 2e-16 ***
## Holiday_Flag1 63494.5 9744.2 6.516 8.01e-11 ***
## Temperature -869.9 160.5 -5.421 6.23e-08 ***
## Fuel_Price -45542.2 8656.9 -5.261 1.50e-07 ***
## CPI 3930.9 1258.1 3.124 0.001793 **
## Unemployment -20865.8 5265.2 -3.963 7.52e-05 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 162900 on 4468 degrees of freedom
## Multiple R-squared: 0.9178, Adjusted R-squared: 0.9169
## F-statistic: 1019 on 49 and 4468 DF, p-value: < 2.2e-164. Creating new model with backward selection
Important: With backward selection, you remove certain sections of the data to make r^2 more precise. In this instance, no data was removed.
## Backward Elimination Method
## ---------------------------
##
## Candidate Terms:
##
## 1. Store
## 2. Holiday_Flag
## 3. Temperature
## 4. Fuel_Price
## 5. CPI
## 6. Unemployment
##
##
## Step => 0
## Model => Weekly_Sales ~ Store + Holiday_Flag + Temperature + Fuel_Price + CPI + Unemployment
## R2 => 0.918
##
## Initiating stepwise selection...
##
##
## No more variables to be removed.##
## Call:
## lm(formula = paste(response, "~", paste(c(include, cterms), collapse = " + ")),
## data = l)
##
## Residuals:
## Min 1Q Median 3Q Max
## -525229 -70856 -12219 39316 1842323
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 1067528.3 278137.5 3.838 0.000126 ***
## Store2 364064.7 23341.2 15.598 < 2e-16 ***
## Store3 -1173377.2 24044.0 -48.801 < 2e-16 ***
## Store4 850034.7 116869.9 7.273 4.12e-13 ***
## Store5 -1268813.7 23933.2 -53.015 < 2e-16 ***
## Store6 -22077.1 23418.4 -0.943 0.345872
## Store7 -894243.5 35735.5 -25.024 < 2e-16 ***
## Store8 -697747.6 24663.8 -28.290 < 2e-16 ***
## Store9 -1057109.2 24036.2 -43.980 < 2e-16 ***
## Store10 724913.8 112912.8 6.420 1.50e-10 ***
## Store11 -214922.0 23387.3 -9.190 < 2e-16 ***
## Store12 -69289.1 106126.8 -0.653 0.513861
## Store13 780241.1 114462.2 6.817 1.06e-11 ***
## Store14 600211.4 43394.5 13.832 < 2e-16 ***
## Store15 -607907.2 106088.8 -5.730 1.07e-08 ***
## Store16 -988525.2 39413.8 -25.081 < 2e-16 ***
## Store17 -361391.4 115449.4 -3.130 0.001758 **
## Store18 -154947.9 103382.9 -1.499 0.134002
## Store19 213743.8 106007.2 2.016 0.043827 *
## Store20 590819.2 25339.2 23.316 < 2e-16 ***
## Store21 -796391.1 22989.0 -34.642 < 2e-16 ***
## Store22 -224400.7 100135.5 -2.241 0.025077 *
## Store23 95265.3 112962.3 0.843 0.399085
## Store24 137157.7 104799.3 1.309 0.190681
## Store25 -837307.3 25270.2 -33.134 < 2e-16 ***
## Store26 -238478.4 105553.2 -2.259 0.023911 *
## Store27 532878.9 100870.5 5.283 1.33e-07 ***
## Store28 241476.4 105869.7 2.281 0.022602 *
## Store29 -651373.6 101765.4 -6.401 1.71e-10 ***
## Store30 -1111159.0 23120.6 -48.059 < 2e-16 ***
## Store31 -160870.7 23347.8 -6.890 6.35e-12 ***
## Store32 -285658.4 35031.9 -8.154 4.52e-16 ***
## Store33 -908025.0 112539.7 -8.068 9.07e-16 ***
## Store34 -206277.0 108100.3 -1.908 0.056429 .
## Store35 -311665.5 98829.5 -3.154 0.001624 **
## Store36 -1162570.1 23361.8 -49.764 < 2e-16 ***
## Store37 -1020966.4 23293.5 -43.831 < 2e-16 ***
## Store38 -692425.7 106024.5 -6.531 7.27e-11 ***
## Store39 -95946.6 22948.3 -4.181 2.96e-05 ***
## Store40 -346137.1 112863.2 -3.067 0.002176 **
## Store41 -227367.1 37895.4 -6.000 2.13e-09 ***
## Store42 -624190.0 112745.8 -5.536 3.27e-08 ***
## Store43 -839268.2 26464.2 -31.713 < 2e-16 ***
## Store44 -937498.8 115260.5 -8.134 5.34e-16 ***
## Store45 -626669.3 43375.9 -14.447 < 2e-16 ***
## Holiday_Flag1 63494.5 9744.2 6.516 8.01e-11 ***
## Temperature -869.9 160.5 -5.421 6.23e-08 ***
## Fuel_Price -45542.2 8656.9 -5.261 1.50e-07 ***
## CPI 3930.9 1258.1 3.124 0.001793 **
## Unemployment -20865.8 5265.2 -3.963 7.52e-05 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 162900 on 4468 degrees of freedom
## Multiple R-squared: 0.9178, Adjusted R-squared: 0.9169
## F-statistic: 1019 on 49 and 4468 DF, p-value: < 2.2e-165. Model with interactions (with backward selection)
##
## Call:
## lm(formula = Weekly_Sales ~ (. - Date)^2, data = trainlm)
##
## Residuals:
## Min 1Q Median 3Q Max
## -608696 -57493 -8887 33878 1670847
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -1.814e+07 8.304e+06 -2.184 0.028989 *
## Store2 3.745e+06 5.715e+06 0.655 0.512310
## Store3 2.851e+06 3.866e+06 0.737 0.460921
## Store4 3.465e+06 7.708e+06 0.450 0.653092
## Store5 1.679e+06 3.960e+06 0.424 0.671550
## Store6 -1.064e+07 4.181e+06 -2.544 0.010997 *
## Store7 -6.467e+06 4.638e+06 -1.394 0.163305
## Store8 1.356e+06 3.793e+06 0.358 0.720734
## Store9 2.035e+06 4.314e+06 0.472 0.637161
## Store10 1.241e+07 6.838e+06 1.815 0.069632 .
## Store11 -2.402e+06 3.893e+06 -0.617 0.537244
## Store12 4.373e+06 5.172e+06 0.845 0.397921
## Store13 2.009e+07 8.994e+06 2.233 0.025570 *
## Store14 9.701e+06 3.065e+06 3.165 0.001561 **
## Store15 9.128e+06 3.958e+06 2.306 0.021146 *
## Store16 3.696e+06 4.658e+06 0.794 0.427527
## Store17 9.953e+06 5.563e+06 1.789 0.073639 .
## Store18 1.335e+07 5.186e+06 2.573 0.010105 *
## Store19 6.876e+06 3.975e+06 1.730 0.083737 .
## Store20 4.736e+06 2.857e+06 1.657 0.097520 .
## Store21 -4.378e+06 4.965e+06 -0.882 0.377875
## Store22 4.923e+06 5.151e+06 0.956 0.339218
## Store23 8.971e+06 7.185e+06 1.249 0.211908
## Store24 5.695e+06 4.014e+06 1.419 0.156086
## Store25 1.529e+06 2.828e+06 0.541 0.588849
## Store26 6.019e+06 6.690e+06 0.900 0.368314
## Store27 1.016e+07 3.815e+06 2.664 0.007747 **
## Store28 5.151e+06 4.947e+06 1.041 0.297822
## Store29 5.784e+06 4.701e+06 1.230 0.218598
## Store30 5.154e+06 5.512e+06 0.935 0.349764
## Store31 -7.961e+06 5.504e+06 -1.446 0.148143
## Store32 -7.065e+06 4.495e+06 -1.572 0.116092
## Store33 8.404e+06 7.090e+06 1.185 0.235985
## Store34 4.043e+06 4.347e+06 0.930 0.352365
## Store35 8.911e+06 3.632e+06 2.453 0.014195 *
## Store36 7.620e+06 5.564e+06 1.370 0.170902
## Store37 3.988e+06 5.224e+06 0.763 0.445333
## Store38 5.311e+06 5.566e+06 0.954 0.340050
## Store39 -1.349e+07 4.930e+06 -2.735 0.006260 **
## Store40 1.030e+07 7.184e+06 1.434 0.151649
## Store41 -2.191e+06 5.574e+06 -0.393 0.694231
## Store42 1.148e+07 7.104e+06 1.616 0.106188
## Store43 4.200e+06 3.262e+06 1.287 0.198006
## Store44 1.257e+07 1.002e+07 1.255 0.209578
## Store45 2.409e+06 2.961e+06 0.813 0.415989
## Holiday_Flag1 4.483e+05 1.199e+06 0.374 0.708591
## Temperature 6.296e+04 2.018e+04 3.120 0.001822 **
## Fuel_Price 2.753e+06 9.577e+05 2.875 0.004059 **
## CPI 9.075e+04 3.870e+04 2.345 0.019078 *
## Unemployment 4.772e+05 9.168e+05 0.521 0.602736
## Store2:Holiday_Flag1 6.946e+04 8.315e+04 0.835 0.403556
## Store3:Holiday_Flag1 -9.540e+04 8.601e+04 -1.109 0.267440
## Store4:Holiday_Flag1 -8.546e+04 5.139e+05 -0.166 0.867929
## Store5:Holiday_Flag1 -9.569e+04 8.144e+04 -1.175 0.240080
## Store6:Holiday_Flag1 8.985e+03 8.291e+04 0.108 0.913707
## Store7:Holiday_Flag1 1.893e+05 1.507e+05 1.256 0.209100
## Store8:Holiday_Flag1 -3.538e+04 9.581e+04 -0.369 0.711986
## Store9:Holiday_Flag1 -9.178e+04 9.408e+04 -0.976 0.329311
## Store10:Holiday_Flag1 9.823e+04 5.111e+05 0.192 0.847587
## Store11:Holiday_Flag1 -4.844e+04 8.481e+04 -0.571 0.567882
## Store12:Holiday_Flag1 4.047e+05 5.017e+05 0.807 0.419873
## Store13:Holiday_Flag1 6.337e+04 5.111e+05 0.124 0.901339
## Store14:Holiday_Flag1 1.527e+05 1.926e+05 0.793 0.427737
## Store15:Holiday_Flag1 1.361e+05 4.811e+05 0.283 0.777299
## Store16:Holiday_Flag1 -2.137e+04 1.586e+05 -0.135 0.892802
## Store17:Holiday_Flag1 9.680e+04 5.139e+05 0.188 0.850600
## Store18:Holiday_Flag1 9.925e+04 4.708e+05 0.211 0.833056
## Store19:Holiday_Flag1 2.178e+05 4.819e+05 0.452 0.651368
## Store20:Holiday_Flag1 -7.711e+03 9.687e+04 -0.080 0.936554
## Store21:Holiday_Flag1 -5.643e+04 8.238e+04 -0.685 0.493360
## Store22:Holiday_Flag1 1.157e+05 4.516e+05 0.256 0.797865
## Store23:Holiday_Flag1 -1.219e+05 4.970e+05 -0.245 0.806334
## Store24:Holiday_Flag1 2.224e+05 4.769e+05 0.466 0.641017
## Store25:Holiday_Flag1 5.064e+04 9.499e+04 0.533 0.593964
## Store26:Holiday_Flag1 1.896e+05 4.778e+05 0.397 0.691606
## Store27:Holiday_Flag1 2.864e+05 4.584e+05 0.625 0.532116
## Store28:Holiday_Flag1 4.544e+05 5.012e+05 0.907 0.364652
## Store29:Holiday_Flag1 2.693e+05 4.688e+05 0.575 0.565632
## Store30:Holiday_Flag1 -4.589e+04 8.614e+04 -0.533 0.594217
## Store31:Holiday_Flag1 5.478e+04 8.321e+04 0.658 0.510336
## Store32:Holiday_Flag1 8.669e+04 1.484e+05 0.584 0.559048
## Store33:Holiday_Flag1 5.629e+04 5.120e+05 0.110 0.912457
## Store34:Holiday_Flag1 2.762e+05 4.951e+05 0.558 0.576983
## Store35:Holiday_Flag1 2.126e+05 4.494e+05 0.473 0.636087
## Store36:Holiday_Flag1 -3.544e+04 9.980e+04 -0.355 0.722562
## Store37:Holiday_Flag1 -4.067e+04 9.842e+04 -0.413 0.679454
## Store38:Holiday_Flag1 3.685e+05 4.995e+05 0.738 0.460724
## Store39:Holiday_Flag1 -8.082e+03 7.846e+04 -0.103 0.917959
## Store40:Holiday_Flag1 -1.057e+05 4.963e+05 -0.213 0.831429
## Store41:Holiday_Flag1 -1.351e+04 1.528e+05 -0.088 0.929544
## Store42:Holiday_Flag1 6.628e+04 5.110e+05 0.130 0.896811
## Store43:Holiday_Flag1 1.529e+05 1.255e+05 1.219 0.223017
## Store44:Holiday_Flag1 -2.872e+04 5.109e+05 -0.056 0.955176
## Store45:Holiday_Flag1 7.457e+04 1.948e+05 0.383 0.701931
## Store2:Temperature -3.912e+02 1.581e+03 -0.247 0.804545
## Store3:Temperature 1.552e+03 1.830e+03 0.848 0.396450
## Store4:Temperature -3.122e+04 8.565e+03 -3.646 0.000270 ***
## Store5:Temperature 1.476e+03 1.740e+03 0.848 0.396619
## Store6:Temperature 1.978e+03 1.669e+03 1.185 0.236125
## Store7:Temperature -2.494e+03 2.549e+03 -0.978 0.327921
## Store8:Temperature 9.016e+02 1.694e+03 0.532 0.594494
## Store9:Temperature 1.815e+03 1.689e+03 1.075 0.282652
## Store10:Temperature -3.391e+04 8.405e+03 -4.035 5.57e-05 ***
## Store11:Temperature -4.923e+02 1.785e+03 -0.276 0.782708
## Store12:Temperature -2.501e+04 8.039e+03 -3.111 0.001877 **
## Store13:Temperature -2.832e+04 8.452e+03 -3.351 0.000814 ***
## Store14:Temperature -1.010e+04 3.220e+03 -3.136 0.001724 **
## Store15:Temperature -2.312e+04 7.850e+03 -2.945 0.003242 **
## Store16:Temperature -3.331e+03 2.729e+03 -1.221 0.222238
## Store17:Temperature -2.514e+04 8.494e+03 -2.960 0.003095 **
## Store18:Temperature -2.111e+04 7.718e+03 -2.735 0.006267 **
## Store19:Temperature -2.223e+04 7.843e+03 -2.834 0.004616 **
## Store20:Temperature -5.481e+03 1.681e+03 -3.260 0.001121 **
## Store21:Temperature 1.342e+03 1.595e+03 0.841 0.400196
## Store22:Temperature -2.189e+04 7.414e+03 -2.953 0.003168 **
## Store23:Temperature -2.540e+04 8.192e+03 -3.101 0.001943 **
## Store24:Temperature -2.092e+04 7.761e+03 -2.696 0.007055 **
## Store25:Temperature 1.084e+03 1.689e+03 0.642 0.521096
## Store26:Temperature -2.126e+04 7.828e+03 -2.716 0.006635 **
## Store27:Temperature -1.804e+04 7.462e+03 -2.417 0.015689 *
## Store28:Temperature -2.407e+04 8.020e+03 -3.001 0.002705 **
## Store29:Temperature -2.255e+04 7.611e+03 -2.963 0.003065 **
## Store30:Temperature 2.162e+03 1.598e+03 1.353 0.176118
## Store31:Temperature 1.691e+03 1.589e+03 1.064 0.287272
## Store32:Temperature -4.207e+03 2.464e+03 -1.707 0.087869 .
## Store33:Temperature -2.488e+04 8.365e+03 -2.975 0.002949 **
## Store34:Temperature -2.424e+04 8.039e+03 -3.015 0.002581 **
## Store35:Temperature -1.850e+04 7.331e+03 -2.523 0.011656 *
## Store36:Temperature 2.826e+03 1.848e+03 1.529 0.126313
## Store37:Temperature 1.477e+03 1.894e+03 0.780 0.435486
## Store38:Temperature -2.176e+04 8.028e+03 -2.711 0.006735 **
## Store39:Temperature 3.773e+03 1.752e+03 2.153 0.031377 *
## Store40:Temperature -2.408e+04 8.191e+03 -2.939 0.003307 **
## Store41:Temperature -3.125e+03 2.620e+03 -1.193 0.232999
## Store42:Temperature -2.539e+04 8.390e+03 -3.026 0.002494 **
## Store43:Temperature 2.110e+03 1.882e+03 1.121 0.262342
## Store44:Temperature -2.558e+04 8.520e+03 -3.002 0.002695 **
## Store45:Temperature -8.667e+03 3.194e+03 -2.713 0.006687 **
## Store2:Fuel_Price -1.269e+05 9.679e+04 -1.311 0.189999
## Store3:Fuel_Price 8.265e+04 1.057e+05 0.782 0.434304
## Store4:Fuel_Price -1.251e+06 3.696e+05 -3.385 0.000719 ***
## Store5:Fuel_Price -1.991e+03 9.473e+04 -0.021 0.983233
## Store6:Fuel_Price -1.444e+05 8.997e+04 -1.605 0.108480
## Store7:Fuel_Price -2.514e+05 1.209e+05 -2.080 0.037557 *
## Store8:Fuel_Price 3.823e+04 9.722e+04 0.393 0.694174
## Store9:Fuel_Price 6.005e+04 9.864e+04 0.609 0.542726
## Store10:Fuel_Price -1.214e+06 3.514e+05 -3.455 0.000556 ***
## Store11:Fuel_Price -6.151e+04 1.057e+05 -0.582 0.560518
## Store12:Fuel_Price -1.104e+06 3.266e+05 -3.379 0.000734 ***
## Store13:Fuel_Price -1.035e+06 3.716e+05 -2.785 0.005373 **
## Store14:Fuel_Price -3.837e+05 1.430e+05 -2.683 0.007319 **
## Store15:Fuel_Price -9.405e+05 3.353e+05 -2.805 0.005052 **
## Store16:Fuel_Price -3.300e+05 1.480e+05 -2.229 0.025876 *
## Store17:Fuel_Price -1.016e+06 3.750e+05 -2.708 0.006797 **
## Store18:Fuel_Price -1.122e+06 3.225e+05 -3.478 0.000510 ***
## Store19:Fuel_Price -1.222e+06 3.331e+05 -3.668 0.000248 ***
## Store20:Fuel_Price -1.871e+05 9.328e+04 -2.006 0.044914 *
## Store21:Fuel_Price -5.882e+04 9.125e+04 -0.645 0.519188
## Store22:Fuel_Price -9.976e+05 3.142e+05 -3.175 0.001509 **
## Store23:Fuel_Price -1.182e+06 3.667e+05 -3.222 0.001281 **
## Store24:Fuel_Price -1.130e+06 3.294e+05 -3.431 0.000607 ***
## Store25:Fuel_Price -1.378e+05 9.620e+04 -1.433 0.152002
## Store26:Fuel_Price -1.023e+06 3.337e+05 -3.064 0.002195 **
## Store27:Fuel_Price -1.077e+06 3.176e+05 -3.391 0.000702 ***
## Store28:Fuel_Price -1.146e+06 3.270e+05 -3.505 0.000462 ***
## Store29:Fuel_Price -1.018e+06 3.136e+05 -3.247 0.001174 **
## Store30:Fuel_Price 1.481e+04 9.235e+04 0.160 0.872603
## Store31:Fuel_Price -6.887e+04 9.400e+04 -0.733 0.463820
## Store32:Fuel_Price -2.255e+05 1.179e+05 -1.913 0.055769 .
## Store33:Fuel_Price -1.108e+06 3.493e+05 -3.173 0.001522 **
## Store34:Fuel_Price -1.207e+06 3.405e+05 -3.545 0.000396 ***
## Store35:Fuel_Price -9.228e+05 3.137e+05 -2.941 0.003287 **
## Store36:Fuel_Price 1.435e+04 9.813e+04 0.146 0.883720
## Store37:Fuel_Price 3.679e+04 1.015e+05 0.362 0.717090
## Store38:Fuel_Price -1.056e+06 3.290e+05 -3.211 0.001334 **
## Store39:Fuel_Price -1.677e+05 9.572e+04 -1.753 0.079754 .
## Store40:Fuel_Price -1.120e+06 3.670e+05 -3.051 0.002297 **
## Store41:Fuel_Price -1.945e+05 1.329e+05 -1.463 0.143579
## Store42:Fuel_Price -1.091e+06 3.524e+05 -3.097 0.001968 **
## Store43:Fuel_Price -2.144e+04 1.176e+05 -0.182 0.855326
## Store44:Fuel_Price -1.065e+06 3.793e+05 -2.808 0.005012 **
## Store45:Fuel_Price -3.645e+05 1.425e+05 -2.558 0.010569 *
## Store2:CPI -1.157e+04 2.267e+04 -0.510 0.609771
## Store3:CPI -1.703e+04 1.533e+04 -1.110 0.266874
## Store4:CPI 4.691e+04 4.543e+04 1.033 0.301784
## Store5:CPI -1.232e+04 1.579e+04 -0.780 0.435324
## Store6:CPI 4.137e+04 1.666e+04 2.483 0.013082 *
## Store7:CPI 2.816e+04 1.878e+04 1.499 0.133898
## Store8:CPI -9.328e+03 1.532e+04 -0.609 0.542772
## Store9:CPI -1.409e+04 1.756e+04 -0.803 0.422121
## Store10:CPI -2.169e+04 4.266e+04 -0.508 0.611210
## Store11:CPI 9.009e+03 1.550e+04 0.581 0.561189
## Store12:CPI 2.052e+04 4.338e+04 0.473 0.636195
## Store13:CPI -8.289e+04 5.865e+04 -1.413 0.157597
## Store14:CPI -3.856e+04 1.208e+04 -3.193 0.001419 **
## Store15:CPI -3.388e+04 1.788e+04 -1.895 0.058103 .
## Store16:CPI -1.172e+04 1.728e+04 -0.678 0.497578
## Store17:CPI -2.130e+04 2.564e+04 -0.831 0.406063
## Store18:CPI -3.559e+04 2.695e+04 -1.320 0.186747
## Store19:CPI 1.369e+04 1.785e+04 0.767 0.443074
## Store20:CPI -8.131e+03 1.094e+04 -0.744 0.457211
## Store21:CPI 1.222e+04 1.967e+04 0.621 0.534444
## Store22:CPI 4.403e+03 2.408e+04 0.183 0.854909
## Store23:CPI -5.547e+03 3.462e+04 -0.160 0.872722
## Store24:CPI 1.734e+04 2.352e+04 0.737 0.461109
## Store25:CPI -6.674e+03 1.102e+04 -0.606 0.544848
## Store26:CPI 1.411e+03 3.098e+04 0.046 0.963676
## Store27:CPI -1.838e+04 1.796e+04 -1.023 0.306220
## Store28:CPI 1.674e+04 4.169e+04 0.402 0.688019
## Store29:CPI -4.391e+02 2.611e+04 -0.017 0.986585
## Store30:CPI -2.570e+04 2.172e+04 -1.183 0.236762
## Store31:CPI 3.001e+04 2.177e+04 1.378 0.168132
## Store32:CPI 3.144e+04 1.845e+04 1.704 0.088534 .
## Store33:CPI -1.464e+04 4.541e+04 -0.322 0.747101
## Store34:CPI 2.515e+04 2.613e+04 0.963 0.335736
## Store35:CPI -5.167e+04 1.732e+04 -2.984 0.002863 **
## Store36:CPI -3.804e+04 2.266e+04 -1.679 0.093204 .
## Store37:CPI -2.101e+04 2.139e+04 -0.982 0.326018
## Store38:CPI 8.277e+03 4.596e+04 0.180 0.857083
## Store39:CPI 5.716e+04 2.000e+04 2.858 0.004284 **
## Store40:CPI -2.000e+04 3.444e+04 -0.581 0.561540
## Store41:CPI 1.469e+04 2.158e+04 0.681 0.496129
## Store42:CPI -3.227e+04 4.466e+04 -0.723 0.470009
## Store43:CPI -1.921e+04 1.533e+04 -1.253 0.210268
## Store44:CPI -4.390e+04 6.762e+04 -0.649 0.516169
## Store45:CPI -6.593e+03 1.195e+04 -0.552 0.581053
## Store2:Unemployment -5.909e+04 1.425e+05 -0.415 0.678399
## Store3:Unemployment -9.181e+04 1.170e+05 -0.785 0.432548
## Store4:Unemployment -2.214e+05 4.056e+05 -0.546 0.585198
## Store5:Unemployment -4.730e+04 1.269e+05 -0.373 0.709430
## Store6:Unemployment 2.994e+05 1.212e+05 2.471 0.013503 *
## Store7:Unemployment 1.484e+05 1.741e+05 0.852 0.394056
## Store8:Unemployment -2.504e+04 1.283e+05 -0.195 0.845239
## Store9:Unemployment -4.403e+04 1.282e+05 -0.343 0.731328
## Store10:Unemployment -2.269e+05 4.130e+05 -0.549 0.582780
## Store11:Unemployment 6.225e+04 1.166e+05 0.534 0.593520
## Store12:Unemployment -1.591e+05 4.086e+05 -0.389 0.697038
## Store13:Unemployment -3.474e+05 4.125e+05 -0.842 0.399663
## Store14:Unemployment 2.032e+04 2.390e+05 0.085 0.932255
## Store15:Unemployment 1.896e+04 4.022e+05 0.047 0.962397
## Store16:Unemployment -1.131e+05 2.083e+05 -0.543 0.587163
## Store17:Unemployment -2.275e+05 4.094e+05 -0.556 0.578570
## Store18:Unemployment -3.422e+05 3.895e+05 -0.879 0.379643
## Store19:Unemployment -2.815e+05 3.996e+05 -0.704 0.481180
## Store20:Unemployment -1.917e+05 1.224e+05 -1.566 0.117391
## Store21:Unemployment 1.379e+05 1.258e+05 1.096 0.272943
## Store22:Unemployment -4.569e+04 3.775e+05 -0.121 0.903676
## Store23:Unemployment -2.506e+05 4.091e+05 -0.613 0.540226
## Store24:Unemployment -2.526e+05 3.916e+05 -0.645 0.519013
## Store25:Unemployment -6.442e+04 1.173e+05 -0.549 0.582794
## Store26:Unemployment -1.142e+05 4.282e+05 -0.267 0.789753
## Store27:Unemployment -2.021e+05 3.824e+05 -0.528 0.597302
## Store28:Unemployment -1.516e+05 4.092e+05 -0.371 0.710989
## Store29:Unemployment -1.217e+05 3.859e+05 -0.315 0.752495
## Store30:Unemployment -1.202e+05 1.399e+05 -0.860 0.390044
## Store31:Unemployment 1.877e+05 1.386e+05 1.355 0.175647
## Store32:Unemployment 2.134e+05 1.654e+05 1.290 0.197137
## Store33:Unemployment -1.765e+05 4.120e+05 -0.428 0.668461
## Store34:Unemployment -1.569e+05 4.054e+05 -0.387 0.698808
## Store35:Unemployment 3.127e+05 3.835e+05 0.816 0.414792
## Store36:Unemployment -1.096e+05 1.242e+05 -0.882 0.377613
## Store37:Unemployment -9.141e+04 1.177e+05 -0.776 0.437567
## Store38:Unemployment -1.884e+05 4.093e+05 -0.460 0.645299
## Store39:Unemployment 1.760e+05 1.157e+05 1.521 0.128297
## Store40:Unemployment -2.710e+05 4.093e+05 -0.662 0.508031
## Store41:Unemployment 3.962e+04 2.121e+05 0.187 0.851848
## Store42:Unemployment -2.407e+05 4.134e+05 -0.582 0.560405
## Store43:Unemployment -1.222e+05 1.020e+05 -1.199 0.230777
## Store44:Unemployment -2.430e+05 4.136e+05 -0.588 0.556872
## Store45:Unemployment 1.492e+04 2.279e+05 0.065 0.947814
## Holiday_Flag1:Temperature 1.381e+03 5.972e+02 2.312 0.020821 *
## Holiday_Flag1:Fuel_Price -4.665e+04 4.862e+04 -0.959 0.337439
## Holiday_Flag1:CPI 6.661e+02 5.718e+03 0.116 0.907270
## Holiday_Flag1:Unemployment -6.261e+04 2.174e+04 -2.879 0.004007 **
## Temperature:Fuel_Price 2.234e+03 6.996e+02 3.193 0.001419 **
## Temperature:CPI -3.136e+02 9.376e+01 -3.344 0.000833 ***
## Temperature:Unemployment -6.836e+02 3.733e+02 -1.831 0.067137 .
## Fuel_Price:CPI -1.328e+04 3.981e+03 -3.336 0.000857 ***
## Fuel_Price:Unemployment -1.002e+04 2.311e+04 -0.434 0.664636
## CPI:Unemployment -1.656e+03 4.359e+03 -0.380 0.704049
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 154000 on 4238 degrees of freedom
## Multiple R-squared: 0.9304, Adjusted R-squared: 0.9258
## F-statistic: 202.9 on 279 and 4238 DF, p-value: < 2.2e-16## 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 => 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 => 0.93036
##
## Step => 2
## 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:Unemployment + Temperature:Fuel_Price + Temperature:CPI + Temperature:Unemployment + Fuel_Price:CPI + Fuel_Price:Unemployment + CPI:Unemployment
## R2 => 0.93036
##
## Step => 3
## 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 + Fuel_Price:Unemployment
## R2 => 0.93036
##
## 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 + Holiday_Flag:Unemployment + Temperature:Fuel_Price + Temperature:CPI + Temperature:Unemployment + Fuel_Price:CPI
## R2 => 0.93035
##
## Step => 5
## Removed => Store:Holiday_Flag
## Model => Weekly_Sales ~ Store + Holiday_Flag + Temperature + Fuel_Price + CPI + 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 => 0.92961
##
## Step => 6
## Removed => Holiday_Flag:Temperature
## Model => Weekly_Sales ~ Store + Holiday_Flag + Temperature + Fuel_Price + CPI + Store:Temperature + Store:Fuel_Price + Store:CPI + Store:Unemployment + Holiday_Flag:Fuel_Price + Holiday_Flag:Unemployment + Temperature:Fuel_Price + Temperature:CPI + Temperature:Unemployment + Fuel_Price:CPI
## R2 => 0.9296
##
## Step => 7
## Removed => Holiday_Flag:Unemployment
## Model => Weekly_Sales ~ Store + Holiday_Flag + Temperature + Fuel_Price + CPI + Store:Temperature + Store:Fuel_Price + Store:CPI + Store:Unemployment + Holiday_Flag:Fuel_Price + Temperature:Fuel_Price + Temperature:CPI + Temperature:Unemployment + Fuel_Price:CPI
## R2 => 0.92959
##
##
## No more variables to be removed.
##
## Variables Removed:
##
## => Holiday_Flag:CPI
## => Unemployment
## => CPI:Unemployment
## => Fuel_Price:Unemployment
## => Store:Holiday_Flag
## => Holiday_Flag:Temperature
## => Holiday_Flag:Unemployment##
## Call:
## lm(formula = paste(response, "~", paste(c(include, cterms), collapse = " + ")),
## data = l)
##
## Residuals:
## Min 1Q Median 3Q Max
## -615719 -59058 -9155 33518 1674732
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -1.277e+07 3.137e+06 -4.071 4.77e-05 ***
## Store2 4.203e+06 5.658e+06 0.743 0.457586
## Store3 2.803e+06 3.857e+06 0.727 0.467536
## Store4 5.929e+05 6.196e+06 0.096 0.923772
## Store5 1.097e+06 3.746e+06 0.293 0.769596
## Store6 -1.135e+07 4.112e+06 -2.759 0.005816 **
## Store7 -7.360e+06 4.566e+06 -1.612 0.107079
## Store8 3.934e+05 3.568e+06 0.110 0.912217
## Store9 1.491e+06 4.140e+06 0.360 0.718759
## Store10 1.121e+07 6.153e+06 1.821 0.068610 .
## Store11 -2.594e+06 3.884e+06 -0.668 0.504352
## Store12 5.488e+06 5.018e+06 1.094 0.274188
## Store13 1.806e+07 8.208e+06 2.200 0.027835 *
## Store14 9.815e+06 3.009e+06 3.262 0.001116 **
## Store15 7.643e+06 2.668e+06 2.864 0.004199 **
## Store16 2.956e+06 4.178e+06 0.708 0.479176
## Store17 7.823e+06 3.941e+06 1.985 0.047188 *
## Store18 1.298e+07 4.595e+06 2.824 0.004764 **
## Store19 5.225e+06 2.689e+06 1.943 0.052044 .
## Store20 4.746e+06 2.731e+06 1.738 0.082365 .
## Store21 -3.896e+06 4.880e+06 -0.798 0.424637
## Store22 3.375e+06 4.327e+06 0.780 0.435426
## Store23 6.687e+06 5.097e+06 1.312 0.189608
## Store24 3.795e+06 2.959e+06 1.282 0.199835
## Store25 1.449e+06 2.690e+06 0.538 0.590293
## Store26 3.642e+06 5.849e+06 0.623 0.533470
## Store27 8.426e+06 2.650e+06 3.180 0.001483 **
## Store28 5.842e+06 4.725e+06 1.236 0.216354
## Store29 4.123e+06 4.195e+06 0.983 0.325735
## Store30 5.491e+06 5.461e+06 1.006 0.314675
## Store31 -7.471e+06 5.453e+06 -1.370 0.170741
## Store32 -6.955e+06 4.473e+06 -1.555 0.120054
## Store33 6.588e+06 6.482e+06 1.016 0.309514
## Store34 2.256e+06 3.728e+06 0.605 0.545107
## Store35 7.541e+06 2.779e+06 2.714 0.006680 **
## Store36 7.611e+06 5.431e+06 1.401 0.161156
## Store37 4.588e+06 5.068e+06 0.905 0.365430
## Store38 6.907e+06 5.357e+06 1.289 0.197296
## Store39 -1.295e+07 4.832e+06 -2.681 0.007368 **
## Store40 7.306e+06 5.095e+06 1.434 0.151625
## Store41 -2.652e+06 5.355e+06 -0.495 0.620409
## Store42 9.420e+06 6.442e+06 1.462 0.143767
## Store43 4.522e+06 2.931e+06 1.543 0.122958
## Store44 1.071e+07 9.309e+06 1.150 0.250157
## Store45 2.392e+06 2.911e+06 0.822 0.411270
## Holiday_Flag1 -1.126e+05 7.170e+04 -1.571 0.116285
## Temperature 5.884e+04 1.962e+04 2.999 0.002728 **
## Fuel_Price 2.027e+06 6.696e+05 3.028 0.002477 **
## CPI 6.774e+04 1.381e+04 4.906 9.65e-07 ***
## Store2:Temperature -6.368e+02 1.550e+03 -0.411 0.681300
## Store3:Temperature 1.865e+03 1.785e+03 1.045 0.296199
## Store4:Temperature -2.944e+04 8.308e+03 -3.544 0.000399 ***
## Store5:Temperature 1.686e+03 1.715e+03 0.983 0.325483
## Store6:Temperature 1.938e+03 1.652e+03 1.173 0.240748
## Store7:Temperature -2.616e+03 2.475e+03 -1.057 0.290484
## Store8:Temperature 8.720e+02 1.665e+03 0.524 0.600424
## Store9:Temperature 1.919e+03 1.669e+03 1.150 0.250246
## Store10:Temperature -3.280e+04 8.138e+03 -4.030 5.67e-05 ***
## Store11:Temperature -5.356e+02 1.767e+03 -0.303 0.761869
## Store12:Temperature -2.460e+04 7.746e+03 -3.175 0.001507 **
## Store13:Temperature -2.710e+04 8.201e+03 -3.305 0.000958 ***
## Store14:Temperature -9.899e+03 3.133e+03 -3.159 0.001592 **
## Store15:Temperature -2.216e+04 7.610e+03 -2.912 0.003609 **
## Store16:Temperature -3.038e+03 2.660e+03 -1.142 0.253557
## Store17:Temperature -2.409e+04 8.242e+03 -2.923 0.003482 **
## Store18:Temperature -1.978e+04 7.476e+03 -2.645 0.008187 **
## Store19:Temperature -2.156e+04 7.608e+03 -2.833 0.004628 **
## Store20:Temperature -5.401e+03 1.658e+03 -3.258 0.001131 **
## Store21:Temperature 1.453e+03 1.576e+03 0.922 0.356699
## Store22:Temperature -2.097e+04 7.193e+03 -2.915 0.003573 **
## Store23:Temperature -2.385e+04 7.966e+03 -2.994 0.002773 **
## Store24:Temperature -2.024e+04 7.527e+03 -2.690 0.007182 **
## Store25:Temperature 9.776e+02 1.660e+03 0.589 0.556047
## Store26:Temperature -2.048e+04 7.600e+03 -2.695 0.007069 **
## Store27:Temperature -1.774e+04 7.237e+03 -2.452 0.014260 *
## Store28:Temperature -2.375e+04 7.726e+03 -3.074 0.002125 **
## Store29:Temperature -2.202e+04 7.366e+03 -2.989 0.002814 **
## Store30:Temperature 2.172e+03 1.580e+03 1.375 0.169277
## Store31:Temperature 1.501e+03 1.558e+03 0.964 0.335305
## Store32:Temperature -4.047e+03 2.398e+03 -1.688 0.091578 .
## Store33:Temperature -2.362e+04 8.100e+03 -2.916 0.003562 **
## Store34:Temperature -2.369e+04 7.774e+03 -3.047 0.002327 **
## Store35:Temperature -1.777e+04 7.106e+03 -2.500 0.012439 *
## Store36:Temperature 2.846e+03 1.827e+03 1.558 0.119311
## Store37:Temperature 1.570e+03 1.862e+03 0.843 0.399067
## Store38:Temperature -2.140e+04 7.736e+03 -2.767 0.005688 **
## Store39:Temperature 3.876e+03 1.722e+03 2.250 0.024472 *
## Store40:Temperature -2.264e+04 7.969e+03 -2.841 0.004525 **
## Store41:Temperature -2.794e+03 2.559e+03 -1.092 0.274931
## Store42:Temperature -2.410e+04 8.126e+03 -2.965 0.003040 **
## Store43:Temperature 1.802e+03 1.842e+03 0.978 0.328039
## Store44:Temperature -2.410e+04 8.264e+03 -2.917 0.003556 **
## Store45:Temperature -8.399e+03 3.113e+03 -2.698 0.007010 **
## Store2:Fuel_Price -1.216e+05 9.670e+04 -1.258 0.208552
## Store3:Fuel_Price 8.158e+04 1.055e+05 0.774 0.439214
## Store4:Fuel_Price -9.807e+05 2.847e+05 -3.445 0.000577 ***
## Store5:Fuel_Price 1.094e+04 9.043e+04 0.121 0.903686
## Store6:Fuel_Price -1.481e+05 8.738e+04 -1.695 0.090165 .
## Store7:Fuel_Price -1.963e+05 1.140e+05 -1.722 0.085076 .
## Store8:Fuel_Price 3.536e+04 9.228e+04 0.383 0.701634
## Store9:Fuel_Price 6.690e+04 9.447e+04 0.708 0.478872
## Store10:Fuel_Price -9.529e+05 2.844e+05 -3.350 0.000815 ***
## Store11:Fuel_Price -6.592e+04 1.055e+05 -0.625 0.531963
## Store12:Fuel_Price -8.780e+05 2.851e+05 -3.080 0.002086 **
## Store13:Fuel_Price -7.723e+05 2.931e+05 -2.635 0.008444 **
## Store14:Fuel_Price -3.100e+05 1.286e+05 -2.410 0.015996 *
## Store15:Fuel_Price -6.977e+05 2.702e+05 -2.582 0.009852 **
## Store16:Fuel_Price -2.506e+05 1.245e+05 -2.013 0.044199 *
## Store17:Fuel_Price -7.445e+05 2.894e+05 -2.573 0.010127 *
## Store18:Fuel_Price -8.827e+05 2.666e+05 -3.311 0.000939 ***
## Store19:Fuel_Price -9.909e+05 2.681e+05 -3.696 0.000222 ***
## Store20:Fuel_Price -1.600e+05 8.976e+04 -1.782 0.074764 .
## Store21:Fuel_Price -5.369e+04 9.099e+04 -0.590 0.555188
## Store22:Fuel_Price -7.714e+05 2.547e+05 -3.029 0.002470 **
## Store23:Fuel_Price -9.052e+05 2.644e+05 -3.424 0.000623 ***
## Store24:Fuel_Price -9.064e+05 2.657e+05 -3.411 0.000653 ***
## Store25:Fuel_Price -1.068e+05 9.261e+04 -1.153 0.249002
## Store26:Fuel_Price -7.872e+05 2.682e+05 -2.935 0.003354 **
## Store27:Fuel_Price -8.655e+05 2.558e+05 -3.383 0.000723 ***
## Store28:Fuel_Price -9.318e+05 2.854e+05 -3.265 0.001105 **
## Store29:Fuel_Price -8.041e+05 2.666e+05 -3.017 0.002570 **
## Store30:Fuel_Price 2.301e+04 9.201e+04 0.250 0.802516
## Store31:Fuel_Price -6.409e+04 9.388e+04 -0.683 0.494881
## Store32:Fuel_Price -1.672e+05 1.110e+05 -1.506 0.132167
## Store33:Fuel_Price -8.545e+05 2.850e+05 -2.999 0.002728 **
## Store34:Fuel_Price -9.770e+05 2.891e+05 -3.379 0.000733 ***
## Store35:Fuel_Price -7.140e+05 2.574e+05 -2.774 0.005558 **
## Store36:Fuel_Price 1.752e+04 9.708e+04 0.180 0.856834
## Store37:Fuel_Price 4.617e+04 1.004e+05 0.460 0.645580
## Store38:Fuel_Price -8.171e+05 2.874e+05 -2.843 0.004492 **
## Store39:Fuel_Price -1.640e+05 9.504e+04 -1.725 0.084538 .
## Store40:Fuel_Price -8.449e+05 2.649e+05 -3.190 0.001435 **
## Store41:Fuel_Price -1.189e+05 1.133e+05 -1.049 0.294335
## Store42:Fuel_Price -8.359e+05 2.860e+05 -2.923 0.003487 **
## Store43:Fuel_Price -1.918e+04 1.053e+05 -0.182 0.855379
## Store44:Fuel_Price -7.895e+05 2.995e+05 -2.636 0.008428 **
## Store45:Fuel_Price -2.798e+05 1.288e+05 -2.172 0.029890 *
## Store2:CPI -1.335e+04 2.244e+04 -0.595 0.551895
## Store3:CPI -1.663e+04 1.526e+04 -1.090 0.275811
## Store4:CPI 5.254e+04 4.397e+04 1.195 0.232167
## Store5:CPI -1.000e+04 1.462e+04 -0.684 0.493763
## Store6:CPI 4.451e+04 1.623e+04 2.743 0.006112 **
## Store7:CPI 2.930e+04 1.805e+04 1.623 0.104608
## Store8:CPI -5.244e+03 1.386e+04 -0.378 0.705251
## Store9:CPI -1.163e+04 1.645e+04 -0.707 0.479638
## Store10:CPI -2.781e+04 4.235e+04 -0.657 0.511423
## Store11:CPI 1.002e+04 1.543e+04 0.649 0.516067
## Store12:CPI -9.234e+02 3.475e+04 -0.027 0.978799
## Store13:CPI -8.299e+04 5.838e+04 -1.422 0.155188
## Store14:CPI -4.113e+04 1.127e+04 -3.648 0.000267 ***
## Store15:CPI -3.647e+04 1.775e+04 -2.055 0.039962 *
## Store16:CPI -1.064e+04 1.595e+04 -0.667 0.504553
## Store17:CPI -2.053e+04 2.500e+04 -0.821 0.411713
## Store18:CPI -4.506e+04 2.601e+04 -1.732 0.083328 .
## Store19:CPI 1.363e+04 1.765e+04 0.772 0.439885
## Store20:CPI -8.889e+03 1.068e+04 -0.832 0.405212
## Store21:CPI 1.024e+04 1.931e+04 0.530 0.596107
## Store22:CPI 2.789e+03 2.385e+04 0.117 0.906915
## Store23:CPI -3.701e+03 3.080e+04 -0.120 0.904372
## Store24:CPI 2.045e+04 2.313e+04 0.884 0.376623
## Store25:CPI -7.277e+03 1.073e+04 -0.678 0.497658
## Store26:CPI 4.147e+03 3.085e+04 0.134 0.893089
## Store27:CPI -1.637e+04 1.780e+04 -0.920 0.357672
## Store28:CPI -1.187e+03 3.249e+04 -0.037 0.970853
## Store29:CPI -1.600e+03 2.408e+04 -0.066 0.947017
## Store30:CPI -2.719e+04 2.150e+04 -1.264 0.206238
## Store31:CPI 2.811e+04 2.156e+04 1.304 0.192364
## Store32:CPI 2.871e+04 1.783e+04 1.610 0.107472
## Store33:CPI -1.647e+04 4.522e+04 -0.364 0.715776
## Store34:CPI 2.387e+04 2.414e+04 0.989 0.322677
## Store35:CPI -5.317e+04 1.648e+04 -3.226 0.001266 **
## Store36:CPI -3.820e+04 2.202e+04 -1.734 0.082912 .
## Store37:CPI -2.372e+04 2.064e+04 -1.149 0.250624
## Store38:CPI -1.718e+04 3.753e+04 -0.458 0.647098
## Store39:CPI 5.489e+04 1.950e+04 2.815 0.004907 **
## Store40:CPI -1.355e+04 3.077e+04 -0.440 0.659677
## Store41:CPI 1.445e+04 2.116e+04 0.683 0.494646
## Store42:CPI -3.242e+04 4.454e+04 -0.728 0.466699
## Store43:CPI -2.174e+04 1.204e+04 -1.805 0.071105 .
## Store44:CPI -4.562e+04 6.731e+04 -0.678 0.497964
## Store45:CPI -9.723e+03 1.115e+04 -0.872 0.383347
## Store1:Unemployment 7.025e+04 7.515e+04 0.935 0.349930
## Store2:Unemployment 2.374e+03 1.259e+05 0.019 0.984961
## Store3:Unemployment -3.043e+04 9.617e+04 -0.316 0.751704
## Store4:Unemployment 2.042e+03 4.926e+04 0.041 0.966940
## Store5:Unemployment 2.512e+04 1.082e+05 0.232 0.816380
## Store6:Unemployment 3.762e+05 1.010e+05 3.725 0.000198 ***
## Store7:Unemployment 2.829e+05 1.224e+05 2.310 0.020915 *
## Store8:Unemployment 5.781e+04 1.074e+05 0.538 0.590421
## Store9:Unemployment 2.159e+04 1.072e+05 0.201 0.840359
## Store10:Unemployment -1.402e+04 7.372e+04 -0.190 0.849205
## Store11:Unemployment 1.302e+05 9.633e+04 1.352 0.176427
## Store12:Unemployment 4.343e+04 4.395e+04 0.988 0.323106
## Store13:Unemployment -1.301e+05 9.566e+04 -1.360 0.173821
## Store14:Unemployment 1.111e+05 1.710e+05 0.650 0.515797
## Store15:Unemployment 2.200e+05 1.289e+05 1.707 0.087839 .
## Store16:Unemployment -1.097e+04 1.623e+05 -0.068 0.946140
## Store17:Unemployment -1.496e+04 7.574e+04 -0.198 0.843433
## Store18:Unemployment -1.623e+05 1.086e+05 -1.494 0.135269
## Store19:Unemployment -9.431e+04 1.227e+05 -0.769 0.442069
## Store20:Unemployment -1.146e+05 8.543e+04 -1.342 0.179716
## Store21:Unemployment 1.977e+05 1.067e+05 1.853 0.063969 .
## Store22:Unemployment 1.547e+05 1.083e+05 1.429 0.153102
## Store23:Unemployment -4.589e+04 1.351e+05 -0.340 0.734125
## Store24:Unemployment -8.271e+04 1.248e+05 -0.663 0.507528
## Store25:Unemployment 2.054e+04 7.663e+04 0.268 0.788677
## Store26:Unemployment 1.136e+05 1.915e+05 0.593 0.553035
## Store27:Unemployment -2.867e+04 1.277e+05 -0.224 0.822382
## Store28:Unemployment 5.270e+04 4.137e+04 1.274 0.202739
## Store29:Unemployment 9.266e+04 7.836e+04 1.183 0.237028
## Store30:Unemployment -5.558e+04 1.236e+05 -0.450 0.652999
## Store31:Unemployment 2.479e+05 1.223e+05 2.028 0.042648 *
## Store32:Unemployment 3.148e+05 1.139e+05 2.765 0.005725 **
## Store33:Unemployment 4.501e+04 7.065e+04 0.637 0.524159
## Store34:Unemployment 6.776e+04 4.691e+04 1.445 0.148654
## Store35:Unemployment 4.998e+05 1.125e+05 4.444 9.06e-06 ***
## Store36:Unemployment -3.494e+04 1.060e+05 -0.330 0.741684
## Store37:Unemployment -2.768e+04 9.763e+04 -0.283 0.776810
## Store38:Unemployment 1.309e+04 4.586e+04 0.285 0.775324
## Store39:Unemployment 2.387e+05 9.628e+04 2.480 0.013188 *
## Store40:Unemployment -4.474e+04 1.339e+05 -0.334 0.738357
## Store41:Unemployment 1.407e+05 1.705e+05 0.825 0.409329
## Store42:Unemployment -1.643e+04 7.814e+04 -0.210 0.833469
## Store43:Unemployment -2.495e+04 5.679e+04 -0.439 0.660478
## Store44:Unemployment -2.832e+04 1.030e+05 -0.275 0.783475
## Store45:Unemployment 1.276e+05 1.588e+05 0.803 0.421947
## Holiday_Flag1:Fuel_Price 5.219e+04 2.183e+04 2.391 0.016867 *
## Temperature:Fuel_Price 2.333e+03 6.910e+02 3.376 0.000742 ***
## Temperature:CPI -2.996e+02 9.086e+01 -3.297 0.000986 ***
## Temperature:Unemployment -5.607e+02 3.649e+02 -1.537 0.124454
## Fuel_Price:CPI -1.033e+04 3.082e+03 -3.352 0.000810 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 153900 on 4287 degrees of freedom
## Multiple R-squared: 0.9296, Adjusted R-squared: 0.9258
## F-statistic: 246.1 on 230 and 4287 DF, p-value: < 2.2e-166. Scoring with validation set
7. Calculating R^2
Conclusion: This model, using the training data, has an R^2 of 0.934. The model, using the validation data, has an R^2 of 0.912