Load packages and Data
General idea of the data
## 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
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. :0.0000653
## 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 ...
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 0.0000653 0.2527042 0.4945870 0.4980825 0.7453083 0.9999414
Creating the linear model
Checking results
##
## 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
Now creating a model with backward selection
## 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
## -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
Create a model with interactions
##
## Call:
## lm(formula = Weekly_Sales ~ (. - Date)^2, data = trainlm)
##
## Residuals:
## Min 1Q Median 3Q Max
## -595853 -56670 -9233 31098 1663498
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -1.814e+07 8.062e+06 -2.250 0.024511 *
## Store2 -8.331e+06 5.105e+06 -1.632 0.102745
## Store3 3.765e+05 4.068e+06 0.093 0.926263
## Store4 6.159e+06 7.469e+06 0.825 0.409655
## Store5 2.510e+06 4.114e+06 0.610 0.541772
## Store6 -1.580e+06 4.203e+06 -0.376 0.706981
## Store7 -6.242e+06 4.675e+06 -1.335 0.181873
## Store8 1.432e+06 3.929e+06 0.364 0.715508
## Store9 1.661e+05 4.227e+06 0.039 0.968652
## Store10 1.770e+07 6.886e+06 2.570 0.010201 *
## Store11 -2.909e+05 3.722e+06 -0.078 0.937700
## Store12 3.120e+06 5.194e+06 0.601 0.548010
## Store13 3.080e+07 9.377e+06 3.285 0.001029 **
## Store14 1.252e+07 2.922e+06 4.284 1.88e-05 ***
## Store15 8.150e+06 3.889e+06 2.095 0.036191 *
## Store16 1.208e+06 4.688e+06 0.258 0.796708
## Store17 8.361e+06 5.679e+06 1.472 0.140991
## Store18 6.954e+06 5.343e+06 1.301 0.193187
## Store19 9.525e+06 3.917e+06 2.432 0.015060 *
## Store20 3.499e+06 2.937e+06 1.192 0.233503
## Store21 -7.614e+06 5.407e+06 -1.408 0.159167
## Store22 9.818e+06 5.335e+06 1.840 0.065804 .
## Store23 1.253e+07 7.375e+06 1.699 0.089421 .
## Store24 7.089e+06 3.947e+06 1.796 0.072533 .
## Store25 3.174e+06 2.877e+06 1.103 0.270030
## Store26 8.832e+06 6.401e+06 1.380 0.167727
## Store27 9.699e+06 3.782e+06 2.564 0.010372 *
## Store28 5.353e+06 5.495e+06 0.974 0.330074
## Store29 4.681e+06 4.580e+06 1.022 0.306796
## Store30 4.165e+06 5.516e+06 0.755 0.450307
## Store31 -2.542e+06 5.151e+06 -0.493 0.621745
## Store32 -2.575e+06 4.584e+06 -0.562 0.574296
## Store33 8.365e+06 6.916e+06 1.209 0.226567
## Store34 8.236e+06 4.169e+06 1.975 0.048283 *
## Store35 8.761e+06 3.507e+06 2.498 0.012519 *
## Store36 7.062e+06 5.651e+06 1.250 0.211444
## Store37 3.599e+06 5.119e+06 0.703 0.482085
## Store38 4.123e+06 5.546e+06 0.743 0.457294
## Store39 -1.458e+07 5.140e+06 -2.836 0.004588 **
## Store40 1.089e+07 7.608e+06 1.432 0.152355
## Store41 -5.113e+05 5.599e+06 -0.091 0.927241
## Store42 1.157e+07 7.260e+06 1.593 0.111151
## Store43 3.284e+06 3.349e+06 0.981 0.326839
## Store44 1.331e+07 9.283e+06 1.434 0.151653
## Store45 1.724e+06 3.065e+06 0.562 0.573828
## Holiday_Flag1 5.898e+05 1.229e+06 0.480 0.631282
## Temperature 5.782e+04 2.005e+04 2.883 0.003958 **
## Fuel_Price 1.940e+06 9.748e+05 1.990 0.046601 *
## CPI 9.192e+04 3.752e+04 2.450 0.014330 *
## Unemployment 8.046e+05 8.959e+05 0.898 0.369154
## Store2:Holiday_Flag1 -6.298e+04 9.041e+04 -0.697 0.486094
## Store3:Holiday_Flag1 -9.216e+04 9.262e+04 -0.995 0.319760
## Store4:Holiday_Flag1 -1.427e+05 5.318e+05 -0.268 0.788436
## Store5:Holiday_Flag1 -1.316e+05 9.508e+04 -1.384 0.166313
## Store6:Holiday_Flag1 -5.437e+04 9.331e+04 -0.583 0.560107
## Store7:Holiday_Flag1 2.854e+03 1.522e+05 0.019 0.985038
## Store8:Holiday_Flag1 -1.029e+05 1.016e+05 -1.013 0.311222
## Store9:Holiday_Flag1 -1.575e+05 9.449e+04 -1.667 0.095633 .
## Store10:Holiday_Flag1 -4.117e+04 5.120e+05 -0.080 0.935918
## Store11:Holiday_Flag1 -1.514e+05 1.011e+05 -1.497 0.134419
## Store12:Holiday_Flag1 2.152e+05 4.889e+05 0.440 0.659752
## Store13:Holiday_Flag1 -3.399e+04 5.142e+05 -0.066 0.947296
## Store14:Holiday_Flag1 3.479e+04 1.921e+05 0.181 0.856301
## Store15:Holiday_Flag1 -1.332e+05 4.835e+05 -0.275 0.783029
## Store16:Holiday_Flag1 -1.200e+05 1.731e+05 -0.693 0.488480
## Store17:Holiday_Flag1 -6.268e+04 5.202e+05 -0.120 0.904095
## Store18:Holiday_Flag1 1.021e+05 4.744e+05 0.215 0.829576
## Store19:Holiday_Flag1 6.892e+04 4.810e+05 0.143 0.886067
## Store20:Holiday_Flag1 -5.090e+04 1.016e+05 -0.501 0.616558
## Store21:Holiday_Flag1 -8.772e+04 8.957e+04 -0.979 0.327420
## Store22:Holiday_Flag1 -7.716e+04 4.563e+05 -0.169 0.865740
## Store23:Holiday_Flag1 -7.343e+04 5.082e+05 -0.144 0.885121
## Store24:Holiday_Flag1 7.853e+04 4.791e+05 0.164 0.869816
## Store25:Holiday_Flag1 -3.724e+04 1.065e+05 -0.350 0.726486
## Store26:Holiday_Flag1 7.173e+03 4.818e+05 0.015 0.988123
## Store27:Holiday_Flag1 1.067e+05 4.582e+05 0.233 0.815834
## Store28:Holiday_Flag1 2.523e+05 4.899e+05 0.515 0.606670
## Store29:Holiday_Flag1 6.965e+04 4.680e+05 0.149 0.881703
## Store30:Holiday_Flag1 -1.108e+05 9.073e+04 -1.222 0.221875
## Store31:Holiday_Flag1 1.405e+03 8.970e+04 0.016 0.987506
## Store32:Holiday_Flag1 -5.212e+04 1.529e+05 -0.341 0.733298
## Store33:Holiday_Flag1 -1.330e+05 5.136e+05 -0.259 0.795731
## Store34:Holiday_Flag1 3.104e+04 4.911e+05 0.063 0.949597
## Store35:Holiday_Flag1 1.075e+05 4.488e+05 0.240 0.810666
## Store36:Holiday_Flag1 -1.031e+05 9.148e+04 -1.127 0.259926
## Store37:Holiday_Flag1 -1.230e+05 8.919e+04 -1.380 0.167809
## Store38:Holiday_Flag1 8.040e+04 4.907e+05 0.164 0.869851
## Store39:Holiday_Flag1 1.467e+04 8.953e+04 0.164 0.869811
## Store40:Holiday_Flag1 -1.706e+05 5.075e+05 -0.336 0.736710
## Store41:Holiday_Flag1 -6.340e+04 1.633e+05 -0.388 0.697848
## Store42:Holiday_Flag1 -5.911e+04 5.160e+05 -0.115 0.908803
## Store43:Holiday_Flag1 -1.034e+04 1.062e+05 -0.097 0.922422
## Store44:Holiday_Flag1 -1.780e+05 5.179e+05 -0.344 0.731127
## Store45:Holiday_Flag1 -5.190e+04 2.014e+05 -0.258 0.796624
## Store2:Temperature -3.422e+02 1.589e+03 -0.215 0.829459
## Store3:Temperature 1.367e+03 1.788e+03 0.764 0.444622
## Store4:Temperature -2.901e+04 8.502e+03 -3.413 0.000650 ***
## Store5:Temperature 1.004e+03 1.796e+03 0.559 0.576016
## Store6:Temperature 1.287e+03 1.644e+03 0.783 0.433843
## Store7:Temperature -2.781e+03 2.488e+03 -1.118 0.263621
## Store8:Temperature -1.247e+03 1.668e+03 -0.748 0.454675
## Store9:Temperature 1.095e+03 1.680e+03 0.652 0.514718
## Store10:Temperature -3.373e+04 8.335e+03 -4.047 5.27e-05 ***
## Store11:Temperature -2.239e+03 1.951e+03 -1.148 0.251214
## Store12:Temperature -2.324e+04 7.968e+03 -2.917 0.003551 **
## Store13:Temperature -2.788e+04 8.417e+03 -3.313 0.000931 ***
## Store14:Temperature -7.534e+03 3.148e+03 -2.393 0.016735 *
## Store15:Temperature -2.231e+04 7.775e+03 -2.869 0.004133 **
## Store16:Temperature -3.202e+03 2.708e+03 -1.182 0.237079
## Store17:Temperature -2.320e+04 8.447e+03 -2.746 0.006055 **
## Store18:Temperature -2.182e+04 7.671e+03 -2.845 0.004467 **
## Store19:Temperature -2.033e+04 7.771e+03 -2.616 0.008941 **
## Store20:Temperature -6.782e+03 1.744e+03 -3.889 0.000102 ***
## Store21:Temperature 1.255e+03 1.620e+03 0.774 0.438867
## Store22:Temperature -2.015e+04 7.391e+03 -2.726 0.006441 **
## Store23:Temperature -2.249e+04 8.148e+03 -2.761 0.005795 **
## Store24:Temperature -1.998e+04 7.714e+03 -2.590 0.009623 **
## Store25:Temperature -8.659e+02 1.695e+03 -0.511 0.609419
## Store26:Temperature -1.945e+04 7.774e+03 -2.503 0.012368 *
## Store27:Temperature -1.708e+04 7.444e+03 -2.295 0.021780 *
## Store28:Temperature -2.404e+04 7.976e+03 -3.014 0.002593 **
## Store29:Temperature -2.161e+04 7.557e+03 -2.860 0.004254 **
## Store30:Temperature 1.313e+03 1.571e+03 0.836 0.403253
## Store31:Temperature -1.742e+02 1.561e+03 -0.112 0.911142
## Store32:Temperature -3.208e+03 2.467e+03 -1.301 0.193485
## Store33:Temperature -2.304e+04 8.315e+03 -2.771 0.005610 **
## Store34:Temperature -2.286e+04 7.973e+03 -2.868 0.004155 **
## Store35:Temperature -1.777e+04 7.258e+03 -2.449 0.014380 *
## Store36:Temperature 1.871e+03 1.846e+03 1.013 0.310967
## Store37:Temperature 6.751e+02 1.887e+03 0.358 0.720565
## Store38:Temperature -2.042e+04 7.966e+03 -2.563 0.010417 *
## Store39:Temperature 2.146e+03 1.859e+03 1.154 0.248437
## Store40:Temperature -2.277e+04 8.144e+03 -2.796 0.005205 **
## Store41:Temperature -3.442e+03 2.626e+03 -1.311 0.190021
## Store42:Temperature -2.449e+04 8.350e+03 -2.933 0.003375 **
## Store43:Temperature 1.737e+03 1.876e+03 0.926 0.354702
## Store44:Temperature -2.378e+04 8.441e+03 -2.817 0.004874 **
## Store45:Temperature -8.208e+03 3.146e+03 -2.609 0.009117 **
## Store2:Fuel_Price -2.059e+05 9.131e+04 -2.254 0.024216 *
## Store3:Fuel_Price 5.882e+04 1.076e+05 0.547 0.584670
## Store4:Fuel_Price -8.848e+05 3.750e+05 -2.359 0.018349 *
## Store5:Fuel_Price 5.886e+04 9.816e+04 0.600 0.548748
## Store6:Fuel_Price -3.611e+04 9.315e+04 -0.388 0.698308
## Store7:Fuel_Price -1.687e+05 1.208e+05 -1.397 0.162473
## Store8:Fuel_Price 7.439e+04 1.001e+05 0.743 0.457445
## Store9:Fuel_Price 7.942e+04 9.941e+04 0.799 0.424402
## Store10:Fuel_Price -8.946e+05 3.527e+05 -2.537 0.011227 *
## Store11:Fuel_Price 1.153e+03 1.045e+05 0.011 0.991198
## Store12:Fuel_Price -8.630e+05 3.271e+05 -2.638 0.008366 **
## Store13:Fuel_Price -6.703e+05 3.762e+05 -1.782 0.074881 .
## Store14:Fuel_Price -2.311e+05 1.418e+05 -1.630 0.103259
## Store15:Fuel_Price -7.849e+05 3.362e+05 -2.335 0.019599 *
## Store16:Fuel_Price -1.252e+05 1.498e+05 -0.836 0.403408
## Store17:Fuel_Price -7.646e+05 3.799e+05 -2.013 0.044215 *
## Store18:Fuel_Price -8.899e+05 3.246e+05 -2.741 0.006145 **
## Store19:Fuel_Price -7.829e+05 3.354e+05 -2.334 0.019626 *
## Store20:Fuel_Price -7.169e+04 1.008e+05 -0.711 0.477062
## Store21:Fuel_Price -3.853e+04 9.499e+04 -0.406 0.685019
## Store22:Fuel_Price -7.208e+05 3.181e+05 -2.266 0.023525 *
## Store23:Fuel_Price -7.726e+05 3.743e+05 -2.064 0.039041 *
## Store24:Fuel_Price -8.527e+05 3.315e+05 -2.572 0.010145 *
## Store25:Fuel_Price -5.260e+04 9.616e+04 -0.547 0.584389
## Store26:Fuel_Price -7.797e+05 3.361e+05 -2.319 0.020419 *
## Store27:Fuel_Price -8.610e+05 3.201e+05 -2.690 0.007180 **
## Store28:Fuel_Price -9.208e+05 3.272e+05 -2.814 0.004908 **
## Store29:Fuel_Price -8.172e+05 3.144e+05 -2.600 0.009366 **
## Store30:Fuel_Price 4.174e+04 9.389e+04 0.445 0.656662
## Store31:Fuel_Price 3.539e+04 9.159e+04 0.386 0.699226
## Store32:Fuel_Price -1.293e+05 1.192e+05 -1.085 0.278162
## Store33:Fuel_Price -8.203e+05 3.521e+05 -2.330 0.019868 *
## Store34:Fuel_Price -8.139e+05 3.385e+05 -2.404 0.016245 *
## Store35:Fuel_Price -6.846e+05 3.127e+05 -2.189 0.028643 *
## Store36:Fuel_Price 5.524e+04 1.020e+05 0.542 0.588124
## Store37:Fuel_Price 6.730e+04 9.923e+04 0.678 0.497685
## Store38:Fuel_Price -8.276e+05 3.280e+05 -2.523 0.011672 *
## Store39:Fuel_Price -1.944e+05 9.995e+04 -1.945 0.051816 .
## Store40:Fuel_Price -7.718e+05 3.729e+05 -2.070 0.038551 *
## Store41:Fuel_Price -1.438e+05 1.362e+05 -1.056 0.291110
## Store42:Fuel_Price -7.562e+05 3.541e+05 -2.136 0.032759 *
## Store43:Fuel_Price -1.170e+04 1.171e+05 -0.100 0.920464
## Store44:Fuel_Price -7.429e+05 3.805e+05 -1.952 0.050960 .
## Store45:Fuel_Price -2.830e+05 1.450e+05 -1.952 0.050994 .
## Store2:CPI 3.688e+04 2.024e+04 1.822 0.068475 .
## Store3:CPI -7.412e+03 1.624e+04 -0.456 0.648055
## Store4:CPI 2.624e+04 4.374e+04 0.600 0.548500
## Store5:CPI -1.609e+04 1.631e+04 -0.986 0.324195
## Store6:CPI 5.210e+03 1.689e+04 0.308 0.757798
## Store7:CPI 2.733e+04 1.910e+04 1.431 0.152523
## Store8:CPI -1.058e+04 1.598e+04 -0.662 0.507894
## Store9:CPI -7.305e+03 1.717e+04 -0.426 0.670458
## Store10:CPI -5.707e+04 4.366e+04 -1.307 0.191258
## Store11:CPI 4.976e+02 1.485e+04 0.034 0.973267
## Store12:CPI 3.336e+04 4.353e+04 0.766 0.443464
## Store13:CPI -1.583e+05 6.233e+04 -2.539 0.011148 *
## Store14:CPI -4.655e+04 1.176e+04 -3.960 7.62e-05 ***
## Store15:CPI -1.025e+04 1.728e+04 -0.593 0.553195
## Store16:CPI -6.055e+03 1.734e+04 -0.349 0.727012
## Store17:CPI -6.740e+03 2.757e+04 -0.245 0.806851
## Store18:CPI 3.141e+03 2.828e+04 0.111 0.911564
## Store19:CPI -1.499e+04 1.734e+04 -0.864 0.387380
## Store20:CPI -5.219e+03 1.166e+04 -0.448 0.654367
## Store21:CPI 2.478e+04 2.146e+04 1.154 0.248416
## Store22:CPI -1.878e+04 2.584e+04 -0.727 0.467536
## Store23:CPI -3.343e+04 3.696e+04 -0.904 0.365844
## Store24:CPI 2.776e+03 2.303e+04 0.121 0.904090
## Store25:CPI -1.357e+04 1.121e+04 -1.210 0.226193
## Store26:CPI -1.067e+04 2.930e+04 -0.364 0.715677
## Store27:CPI 1.328e+03 1.825e+04 0.073 0.942004
## Store28:CPI 2.206e+04 4.526e+04 0.488 0.625925
## Store29:CPI 1.314e+04 2.519e+04 0.521 0.602100
## Store30:CPI -2.168e+04 2.195e+04 -0.988 0.323342
## Store31:CPI 8.565e+03 2.039e+04 0.420 0.674404
## Store32:CPI 1.246e+04 1.866e+04 0.668 0.504277
## Store33:CPI -1.223e+04 4.423e+04 -0.277 0.782172
## Store34:CPI -5.265e+03 2.446e+04 -0.215 0.829578
## Store35:CPI -4.556e+04 1.572e+04 -2.898 0.003772 **
## Store36:CPI -3.577e+04 2.328e+04 -1.536 0.124498
## Store37:CPI -1.929e+04 2.094e+04 -0.921 0.357078
## Store38:CPI 2.079e+04 4.613e+04 0.451 0.652188
## Store39:CPI 6.311e+04 2.102e+04 3.003 0.002691 **
## Store40:CPI -2.548e+04 3.894e+04 -0.654 0.512993
## Store41:CPI 1.030e+04 2.152e+04 0.478 0.632354
## Store42:CPI -3.252e+04 4.623e+04 -0.704 0.481732
## Store43:CPI -1.396e+04 1.571e+04 -0.888 0.374546
## Store44:CPI -4.823e+04 6.132e+04 -0.787 0.431597
## Store45:CPI -1.242e+03 1.242e+04 -0.100 0.920353
## Store2:Unemployment 1.864e+05 1.287e+05 1.449 0.147481
## Store3:Unemployment -3.037e+04 1.183e+05 -0.257 0.797327
## Store4:Unemployment -3.970e+05 3.966e+05 -1.001 0.316892
## Store5:Unemployment -7.319e+04 1.329e+05 -0.551 0.581842
## Store6:Unemployment 7.442e+04 1.197e+05 0.622 0.534185
## Store7:Unemployment 1.055e+05 1.695e+05 0.622 0.533826
## Store8:Unemployment 1.655e+04 1.282e+05 0.129 0.897298
## Store9:Unemployment 1.826e+04 1.282e+05 0.142 0.886743
## Store10:Unemployment -4.471e+05 4.030e+05 -1.109 0.267314
## Store11:Unemployment 1.818e+04 1.108e+05 0.164 0.869630
## Store12:Unemployment -3.227e+05 3.994e+05 -0.808 0.419130
## Store13:Unemployment -6.448e+05 4.048e+05 -1.593 0.111318
## Store14:Unemployment -2.179e+05 2.224e+05 -0.980 0.327117
## Store15:Unemployment -3.235e+05 3.896e+05 -0.830 0.406368
## Store16:Unemployment 9.924e+03 2.102e+05 0.047 0.962354
## Store17:Unemployment -3.783e+05 4.033e+05 -0.938 0.348287
## Store18:Unemployment -3.073e+05 3.833e+05 -0.802 0.422848
## Store19:Unemployment -3.305e+05 3.899e+05 -0.848 0.396660
## Store20:Unemployment -1.476e+05 1.247e+05 -1.184 0.236418
## Store21:Unemployment 1.970e+05 1.348e+05 1.461 0.143975
## Store22:Unemployment -3.797e+05 3.730e+05 -1.018 0.308816
## Store23:Unemployment -4.261e+05 4.055e+05 -1.051 0.293313
## Store24:Unemployment -3.083e+05 3.841e+05 -0.803 0.422236
## Store25:Unemployment -1.124e+05 1.204e+05 -0.933 0.350724
## Store26:Unemployment -3.772e+05 4.177e+05 -0.903 0.366554
## Store27:Unemployment -5.802e+05 3.753e+05 -1.546 0.122159
## Store28:Unemployment -3.391e+05 3.995e+05 -0.849 0.395959
## Store29:Unemployment -2.968e+05 3.782e+05 -0.785 0.432601
## Store30:Unemployment -1.088e+05 1.354e+05 -0.804 0.421387
## Store31:Unemployment 5.690e+04 1.303e+05 0.437 0.662380
## Store32:Unemployment 6.996e+04 1.699e+05 0.412 0.680477
## Store33:Unemployment -3.428e+05 4.027e+05 -0.851 0.394789
## Store34:Unemployment -3.548e+05 3.965e+05 -0.895 0.370974
## Store35:Unemployment 1.251e+05 3.743e+05 0.334 0.738222
## Store36:Unemployment -1.108e+05 1.217e+05 -0.910 0.362673
## Store37:Unemployment -9.578e+04 1.147e+05 -0.835 0.403602
## Store38:Unemployment -3.481e+05 3.992e+05 -0.872 0.383256
## Store39:Unemployment 1.783e+05 1.167e+05 1.528 0.126469
## Store40:Unemployment -3.931e+05 4.087e+05 -0.962 0.336210
## Store41:Unemployment -9.309e+04 2.170e+05 -0.429 0.667978
## Store42:Unemployment -3.934e+05 4.055e+05 -0.970 0.332042
## Store43:Unemployment -1.481e+05 9.918e+04 -1.493 0.135427
## Store44:Unemployment -4.131e+05 4.045e+05 -1.021 0.307146
## Store45:Unemployment -6.143e+04 2.234e+05 -0.275 0.783374
## Holiday_Flag1:Temperature 1.680e+03 5.993e+02 2.803 0.005089 **
## Holiday_Flag1:Fuel_Price -4.141e+04 4.670e+04 -0.887 0.375264
## Holiday_Flag1:CPI -6.259e+02 5.717e+03 -0.109 0.912830
## Holiday_Flag1:Unemployment -4.157e+04 2.359e+04 -1.763 0.078039 .
## Temperature:Fuel_Price 2.144e+03 6.999e+02 3.064 0.002200 **
## Temperature:CPI -2.865e+02 9.339e+01 -3.068 0.002169 **
## Temperature:Unemployment -6.384e+02 3.686e+02 -1.732 0.083361 .
## Fuel_Price:CPI -1.013e+04 4.026e+03 -2.516 0.011910 *
## Fuel_Price:Unemployment 3.937e+03 2.348e+04 0.168 0.866853
## CPI:Unemployment -3.307e+03 4.262e+03 -0.776 0.437856
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 154000 on 4245 degrees of freedom
## Multiple R-squared: 0.9303, Adjusted R-squared: 0.9257
## F-statistic: 203 on 279 and 4245 DF, p-value: < 2.2e-16
Now doing the backward selection process on the model with
interactions
## 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
##
## 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
scoring the validation dataset
3 Predictors
- When fuel prices go up, sales go down
- When there is a holiday, sales go up
- When there is high unemployment, sales go down
How to calculate R^2
## [1] 0.9252588