1. Prepare your data for modeling
## 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
## 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. :0.0001505
## 1st Qu.:0.2459924
## Median :0.4942164
## Mean :0.4970587
## 3rd Qu.:0.7476742
## Max. :0.9998803
##
## 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] 0.0765 0.5713 0.3018 0.2427 0.5339 ...
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 0.0001505 0.2459924 0.4942164 0.4970587 0.7476742 0.9998803
2. Develop a linear model to predict sales
##
## Call:
## lm(formula = Weekly_Sales ~ . - Date, data = trainlm)
##
## Residuals:
## Min 1Q Median 3Q Max
## -538619 -69911 -11523 40306 1831752
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 1277290.0 270928.5 4.714 2.50e-06 ***
## Store2 376185.6 22815.3 16.488 < 2e-16 ***
## Store3 -1177935.8 23612.2 -49.887 < 2e-16 ***
## Store4 752470.7 113219.6 6.646 3.37e-11 ***
## Store5 -1279970.8 23567.4 -54.311 < 2e-16 ***
## Store6 -12620.1 23289.8 -0.542 0.58793
## Store7 -923524.1 34275.8 -26.944 < 2e-16 ***
## Store8 -707956.0 23767.4 -29.787 < 2e-16 ***
## Store9 -1066350.4 24551.3 -43.433 < 2e-16 ***
## Store10 658995.0 110067.2 5.987 2.30e-09 ***
## Store11 -228922.0 22740.7 -10.067 < 2e-16 ***
## Store12 -130590.0 103479.0 -1.262 0.20702
## Store13 685363.7 111335.7 6.156 8.12e-10 ***
## Store14 567314.4 42175.9 13.451 < 2e-16 ***
## Store15 -676414.7 103202.8 -6.554 6.22e-11 ***
## Store16 -1015079.2 37890.5 -26.790 < 2e-16 ***
## Store17 -441065.9 112652.7 -3.915 9.16e-05 ***
## Store18 -199640.4 100798.8 -1.981 0.04770 *
## Store19 126915.3 102860.9 1.234 0.21732
## Store20 543513.8 24590.6 22.103 < 2e-16 ***
## Store21 -811479.9 22931.6 -35.387 < 2e-16 ***
## Store22 -282146.8 97540.3 -2.893 0.00384 **
## Store23 -9253.3 109856.4 -0.084 0.93288
## Store24 68029.0 102261.6 0.665 0.50593
## Store25 -840890.0 24662.3 -34.096 < 2e-16 ***
## Store26 -310573.0 102879.6 -3.019 0.00255 **
## Store27 488218.3 98293.7 4.967 7.05e-07 ***
## Store28 179423.4 103492.0 1.734 0.08304 .
## Store29 -718529.7 99164.2 -7.246 5.03e-13 ***
## Store30 -1121671.6 23109.7 -48.537 < 2e-16 ***
## Store31 -166114.4 22755.5 -7.300 3.38e-13 ***
## Store32 -307709.5 34086.5 -9.027 < 2e-16 ***
## Store33 -987021.2 109690.9 -8.998 < 2e-16 ***
## Store34 -285177.6 105176.9 -2.711 0.00673 **
## Store35 -377848.3 95884.3 -3.941 8.25e-05 ***
## Store36 -1177306.2 22336.6 -52.708 < 2e-16 ***
## Store37 -1032873.2 22950.4 -45.004 < 2e-16 ***
## Store38 -760356.8 103568.9 -7.342 2.49e-13 ***
## Store39 -112744.5 23462.5 -4.805 1.60e-06 ***
## Store40 -435204.7 109768.8 -3.965 7.46e-05 ***
## Store41 -248479.7 36882.3 -6.737 1.82e-11 ***
## Store42 -700178.0 110147.3 -6.357 2.26e-10 ***
## Store43 -849948.6 25597.6 -33.204 < 2e-16 ***
## Store44 -1018652.5 112030.3 -9.093 < 2e-16 ***
## Store45 -660285.7 42160.5 -15.661 < 2e-16 ***
## Holiday_Flag1 78741.6 9571.4 8.227 2.49e-16 ***
## Temperature -681.3 156.7 -4.348 1.41e-05 ***
## Fuel_Price -48630.5 8587.2 -5.663 1.58e-08 ***
## CPI 3072.2 1234.0 2.490 0.01282 *
## Unemployment -23643.2 5080.7 -4.654 3.36e-06 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 160000 on 4507 degrees of freedom
## Multiple R-squared: 0.9204, Adjusted R-squared: 0.9195
## F-statistic: 1063 on 49 and 4507 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
##
##
## Step => 0
## Model => Weekly_Sales ~ Store + Holiday_Flag + Temperature + Fuel_Price + CPI + Unemployment
## R2 => 0.92
##
## 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
## -538619 -69911 -11523 40306 1831752
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 1277290.0 270928.5 4.714 2.50e-06 ***
## Store2 376185.6 22815.3 16.488 < 2e-16 ***
## Store3 -1177935.8 23612.2 -49.887 < 2e-16 ***
## Store4 752470.7 113219.6 6.646 3.37e-11 ***
## Store5 -1279970.8 23567.4 -54.311 < 2e-16 ***
## Store6 -12620.1 23289.8 -0.542 0.58793
## Store7 -923524.1 34275.8 -26.944 < 2e-16 ***
## Store8 -707956.0 23767.4 -29.787 < 2e-16 ***
## Store9 -1066350.4 24551.3 -43.433 < 2e-16 ***
## Store10 658995.0 110067.2 5.987 2.30e-09 ***
## Store11 -228922.0 22740.7 -10.067 < 2e-16 ***
## Store12 -130590.0 103479.0 -1.262 0.20702
## Store13 685363.7 111335.7 6.156 8.12e-10 ***
## Store14 567314.4 42175.9 13.451 < 2e-16 ***
## Store15 -676414.7 103202.8 -6.554 6.22e-11 ***
## Store16 -1015079.2 37890.5 -26.790 < 2e-16 ***
## Store17 -441065.9 112652.7 -3.915 9.16e-05 ***
## Store18 -199640.4 100798.8 -1.981 0.04770 *
## Store19 126915.3 102860.9 1.234 0.21732
## Store20 543513.8 24590.6 22.103 < 2e-16 ***
## Store21 -811479.9 22931.6 -35.387 < 2e-16 ***
## Store22 -282146.8 97540.3 -2.893 0.00384 **
## Store23 -9253.3 109856.4 -0.084 0.93288
## Store24 68029.0 102261.6 0.665 0.50593
## Store25 -840890.0 24662.3 -34.096 < 2e-16 ***
## Store26 -310573.0 102879.6 -3.019 0.00255 **
## Store27 488218.3 98293.7 4.967 7.05e-07 ***
## Store28 179423.4 103492.0 1.734 0.08304 .
## Store29 -718529.7 99164.2 -7.246 5.03e-13 ***
## Store30 -1121671.6 23109.7 -48.537 < 2e-16 ***
## Store31 -166114.4 22755.5 -7.300 3.38e-13 ***
## Store32 -307709.5 34086.5 -9.027 < 2e-16 ***
## Store33 -987021.2 109690.9 -8.998 < 2e-16 ***
## Store34 -285177.6 105176.9 -2.711 0.00673 **
## Store35 -377848.3 95884.3 -3.941 8.25e-05 ***
## Store36 -1177306.2 22336.6 -52.708 < 2e-16 ***
## Store37 -1032873.2 22950.4 -45.004 < 2e-16 ***
## Store38 -760356.8 103568.9 -7.342 2.49e-13 ***
## Store39 -112744.5 23462.5 -4.805 1.60e-06 ***
## Store40 -435204.7 109768.8 -3.965 7.46e-05 ***
## Store41 -248479.7 36882.3 -6.737 1.82e-11 ***
## Store42 -700178.0 110147.3 -6.357 2.26e-10 ***
## Store43 -849948.6 25597.6 -33.204 < 2e-16 ***
## Store44 -1018652.5 112030.3 -9.093 < 2e-16 ***
## Store45 -660285.7 42160.5 -15.661 < 2e-16 ***
## Holiday_Flag1 78741.6 9571.4 8.227 2.49e-16 ***
## Temperature -681.3 156.7 -4.348 1.41e-05 ***
## Fuel_Price -48630.5 8587.2 -5.663 1.58e-08 ***
## CPI 3072.2 1234.0 2.490 0.01282 *
## Unemployment -23643.2 5080.7 -4.654 3.36e-06 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 160000 on 4507 degrees of freedom
## Multiple R-squared: 0.9204, Adjusted R-squared: 0.9195
## F-statistic: 1063 on 49 and 4507 DF, p-value: < 2.2e-16
##
## Call:
## lm(formula = Weekly_Sales ~ (. - Date)^2, data = trainlm)
##
## Residuals:
## Min 1Q Median 3Q Max
## -682241 -54563 -9320 31979 1661245
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -2.176e+07 8.030e+06 -2.709 0.006768 **
## Store2 -2.238e+06 5.158e+06 -0.434 0.664391
## Store3 5.106e+06 4.011e+06 1.273 0.203114
## Store4 5.807e+06 7.343e+06 0.791 0.429115
## Store5 3.935e+06 4.168e+06 0.944 0.345281
## Store6 -3.750e+06 4.318e+06 -0.869 0.385164
## Store7 -3.481e+06 4.772e+06 -0.730 0.465710
## Store8 5.121e+06 3.854e+06 1.329 0.183986
## Store9 9.315e+05 4.496e+06 0.207 0.835883
## Store10 1.567e+07 6.707e+06 2.336 0.019516 *
## Store11 -8.264e+05 3.631e+06 -0.228 0.819966
## Store12 7.006e+06 5.083e+06 1.378 0.168183
## Store13 1.617e+07 8.845e+06 1.828 0.067597 .
## Store14 1.285e+07 3.126e+06 4.111 4.01e-05 ***
## Store15 1.125e+07 3.965e+06 2.837 0.004578 **
## Store16 3.831e+06 4.708e+06 0.814 0.415776
## Store17 1.450e+07 5.434e+06 2.668 0.007658 **
## Store18 1.154e+07 5.271e+06 2.190 0.028575 *
## Store19 1.301e+07 3.936e+06 3.305 0.000959 ***
## Store20 3.354e+06 2.923e+06 1.147 0.251335
## Store21 -1.317e+06 5.673e+06 -0.232 0.816422
## Store22 6.718e+06 5.158e+06 1.302 0.192838
## Store23 1.167e+07 6.920e+06 1.687 0.091748 .
## Store24 8.602e+06 4.002e+06 2.149 0.031658 *
## Store25 3.694e+06 2.956e+06 1.250 0.211490
## Store26 1.024e+07 6.625e+06 1.545 0.122383
## Store27 1.301e+07 3.787e+06 3.435 0.000598 ***
## Store28 8.012e+06 4.900e+06 1.635 0.102122
## Store29 8.139e+06 4.658e+06 1.747 0.080646 .
## Store30 6.326e+06 5.576e+06 1.135 0.256633
## Store31 -3.427e+06 5.128e+06 -0.668 0.504008
## Store32 -4.454e+06 4.659e+06 -0.956 0.339106
## Store33 1.027e+07 6.564e+06 1.564 0.117908
## Store34 1.124e+07 4.272e+06 2.630 0.008561 **
## Store35 9.568e+06 3.569e+06 2.681 0.007371 **
## Store36 8.751e+06 5.097e+06 1.717 0.086106 .
## Store37 5.357e+06 4.950e+06 1.082 0.279228
## Store38 5.764e+06 5.071e+06 1.137 0.255728
## Store39 -1.024e+07 5.674e+06 -1.804 0.071263 .
## Store40 1.170e+07 6.995e+06 1.673 0.094389 .
## Store41 -8.925e+06 5.812e+06 -1.536 0.124722
## Store42 1.381e+07 7.102e+06 1.944 0.051949 .
## Store43 5.367e+06 3.398e+06 1.579 0.114314
## Store44 1.366e+07 9.230e+06 1.480 0.139019
## Store45 3.703e+06 3.019e+06 1.227 0.220060
## Holiday_Flag1 2.705e+05 1.166e+06 0.232 0.816549
## Temperature 6.302e+04 1.959e+04 3.218 0.001303 **
## Fuel_Price 2.562e+06 9.387e+05 2.729 0.006383 **
## CPI 1.069e+05 3.732e+04 2.865 0.004192 **
## Unemployment 7.956e+05 8.870e+05 0.897 0.369804
## Store2:Holiday_Flag1 8.883e+04 8.290e+04 1.072 0.283985
## Store3:Holiday_Flag1 -7.263e+04 8.340e+04 -0.871 0.383838
## Store4:Holiday_Flag1 6.961e+04 4.977e+05 0.140 0.888781
## Store5:Holiday_Flag1 -6.369e+04 8.766e+04 -0.727 0.467512
## Store6:Holiday_Flag1 1.687e+04 8.701e+04 0.194 0.846281
## Store7:Holiday_Flag1 8.325e+04 1.422e+05 0.585 0.558387
## Store8:Holiday_Flag1 -4.697e+04 8.789e+04 -0.534 0.593054
## Store9:Holiday_Flag1 -4.801e+04 9.331e+04 -0.515 0.606909
## Store10:Holiday_Flag1 1.012e+05 4.891e+05 0.207 0.836078
## Store11:Holiday_Flag1 -1.220e+05 8.464e+04 -1.441 0.149705
## Store12:Holiday_Flag1 1.062e+05 4.683e+05 0.227 0.820537
## Store13:Holiday_Flag1 -7.326e+04 4.877e+05 -0.150 0.880597
## Store14:Holiday_Flag1 1.291e+05 1.841e+05 0.702 0.482992
## Store15:Holiday_Flag1 1.839e+04 4.578e+05 0.040 0.967960
## Store16:Holiday_Flag1 -9.811e+03 1.534e+05 -0.064 0.949019
## Store17:Holiday_Flag1 -1.095e+03 4.934e+05 -0.002 0.998230
## Store18:Holiday_Flag1 -5.685e+04 4.491e+05 -0.127 0.899271
## Store19:Holiday_Flag1 -2.700e+04 4.578e+05 -0.059 0.952972
## Store20:Holiday_Flag1 1.205e+05 9.254e+04 1.302 0.192955
## Store21:Holiday_Flag1 -7.135e+03 7.859e+04 -0.091 0.927660
## Store22:Holiday_Flag1 -6.371e+04 4.344e+05 -0.147 0.883416
## Store23:Holiday_Flag1 5.674e+04 4.813e+05 0.118 0.906161
## Store24:Holiday_Flag1 8.787e+04 4.564e+05 0.193 0.847337
## Store25:Holiday_Flag1 -6.784e+04 9.641e+04 -0.704 0.481665
## Store26:Holiday_Flag1 3.240e+04 4.546e+05 0.071 0.943187
## Store27:Holiday_Flag1 5.021e+03 4.371e+05 0.011 0.990835
## Store28:Holiday_Flag1 7.459e+04 4.681e+05 0.159 0.873401
## Store29:Holiday_Flag1 6.354e+03 4.461e+05 0.014 0.988635
## Store30:Holiday_Flag1 -7.241e+04 9.163e+04 -0.790 0.429406
## Store31:Holiday_Flag1 -1.204e+04 8.032e+04 -0.150 0.880898
## Store32:Holiday_Flag1 3.468e+04 1.427e+05 0.243 0.808042
## Store33:Holiday_Flag1 -1.042e+05 4.850e+05 -0.215 0.829822
## Store34:Holiday_Flag1 6.938e+04 4.661e+05 0.149 0.881688
## Store35:Holiday_Flag1 2.171e+05 4.274e+05 0.508 0.611566
## Store36:Holiday_Flag1 -8.699e+04 8.342e+04 -1.043 0.297104
## Store37:Holiday_Flag1 -9.670e+04 8.815e+04 -1.097 0.272719
## Store38:Holiday_Flag1 -5.076e+04 4.711e+05 -0.108 0.914204
## Store39:Holiday_Flag1 4.988e+04 9.069e+04 0.550 0.582305
## Store40:Holiday_Flag1 -4.238e+04 4.803e+05 -0.088 0.929680
## Store41:Holiday_Flag1 -3.551e+04 1.523e+05 -0.233 0.815702
## Store42:Holiday_Flag1 -1.082e+05 4.896e+05 -0.221 0.825172
## Store43:Holiday_Flag1 -4.641e+04 9.803e+04 -0.473 0.635958
## Store44:Holiday_Flag1 -9.148e+04 4.941e+05 -0.185 0.853145
## Store45:Holiday_Flag1 -8.255e+04 1.887e+05 -0.437 0.661867
## Store2:Temperature -1.976e+03 1.580e+03 -1.251 0.210939
## Store3:Temperature 1.013e+03 1.817e+03 0.558 0.577061
## Store4:Temperature -2.915e+04 8.320e+03 -3.504 0.000463 ***
## Store5:Temperature 1.124e+03 1.670e+03 0.673 0.501094
## Store6:Temperature 1.502e+03 1.645e+03 0.913 0.361249
## Store7:Temperature -1.724e+03 2.422e+03 -0.712 0.476685
## Store8:Temperature -5.713e+01 1.617e+03 -0.035 0.971817
## Store9:Temperature 1.378e+03 1.665e+03 0.827 0.408114
## Store10:Temperature -3.370e+04 8.153e+03 -4.134 3.63e-05 ***
## Store11:Temperature -8.676e+02 1.738e+03 -0.499 0.617563
## Store12:Temperature -2.362e+04 7.800e+03 -3.029 0.002472 **
## Store13:Temperature -2.670e+04 8.190e+03 -3.260 0.001123 **
## Store14:Temperature -8.356e+03 3.089e+03 -2.705 0.006853 **
## Store15:Temperature -2.313e+04 7.608e+03 -3.040 0.002381 **
## Store16:Temperature -3.703e+03 2.601e+03 -1.424 0.154522
## Store17:Temperature -2.469e+04 8.240e+03 -2.997 0.002743 **
## Store18:Temperature -2.185e+04 7.483e+03 -2.919 0.003528 **
## Store19:Temperature -2.267e+04 7.588e+03 -2.988 0.002826 **
## Store20:Temperature -2.150e+03 1.651e+03 -1.302 0.192945
## Store21:Temperature 1.597e+03 1.596e+03 1.000 0.317156
## Store22:Temperature -2.237e+04 7.183e+03 -3.114 0.001858 **
## Store23:Temperature -2.236e+04 7.949e+03 -2.813 0.004936 **
## Store24:Temperature -2.047e+04 7.549e+03 -2.711 0.006730 **
## Store25:Temperature -9.531e+02 1.647e+03 -0.579 0.562833
## Store26:Temperature -2.103e+04 7.620e+03 -2.760 0.005801 **
## Store27:Temperature -2.002e+04 7.233e+03 -2.768 0.005666 **
## Store28:Temperature -2.418e+04 7.805e+03 -3.098 0.001958 **
## Store29:Temperature -2.168e+04 7.380e+03 -2.938 0.003319 **
## Store30:Temperature 1.393e+03 1.597e+03 0.872 0.383185
## Store31:Temperature -9.609e+01 1.556e+03 -0.062 0.950776
## Store32:Temperature -3.923e+03 2.408e+03 -1.629 0.103299
## Store33:Temperature -2.398e+04 8.108e+03 -2.958 0.003114 **
## Store34:Temperature -2.301e+04 7.782e+03 -2.957 0.003125 **
## Store35:Temperature -1.808e+04 7.081e+03 -2.553 0.010726 *
## Store36:Temperature 2.288e+03 1.734e+03 1.320 0.187068
## Store37:Temperature 1.238e+03 1.799e+03 0.688 0.491267
## Store38:Temperature -2.081e+04 7.795e+03 -2.670 0.007608 **
## Store39:Temperature 4.433e+03 1.799e+03 2.464 0.013783 *
## Store40:Temperature -2.341e+04 7.937e+03 -2.949 0.003205 **
## Store41:Temperature -3.551e+03 2.567e+03 -1.383 0.166698
## Store42:Temperature -2.462e+04 8.162e+03 -3.017 0.002567 **
## Store43:Temperature 1.953e+03 1.841e+03 1.061 0.288808
## Store44:Temperature -2.464e+04 8.213e+03 -3.000 0.002715 **
## Store45:Temperature -8.494e+03 3.100e+03 -2.740 0.006171 **
## Store2:Fuel_Price -1.279e+05 9.121e+04 -1.402 0.161013
## Store3:Fuel_Price 1.528e+05 1.042e+05 1.467 0.142541
## Store4:Fuel_Price -1.163e+06 3.625e+05 -3.209 0.001343 **
## Store5:Fuel_Price 5.690e+04 9.934e+04 0.573 0.566781
## Store6:Fuel_Price -1.219e+05 9.009e+04 -1.353 0.176048
## Store7:Fuel_Price -1.562e+05 1.164e+05 -1.342 0.179706
## Store8:Fuel_Price 1.191e+05 9.514e+04 1.252 0.210679
## Store9:Fuel_Price 8.456e+04 9.868e+04 0.857 0.391569
## Store10:Fuel_Price -1.152e+06 3.431e+05 -3.359 0.000790 ***
## Store11:Fuel_Price -2.264e+04 9.614e+04 -0.236 0.813824
## Store12:Fuel_Price -9.720e+05 3.181e+05 -3.056 0.002259 **
## Store13:Fuel_Price -9.945e+05 3.648e+05 -2.726 0.006429 **
## Store14:Fuel_Price -2.635e+05 1.389e+05 -1.897 0.057878 .
## Store15:Fuel_Price -9.007e+05 3.256e+05 -2.766 0.005692 **
## Store16:Fuel_Price -1.777e+05 1.396e+05 -1.273 0.203240
## Store17:Fuel_Price -8.570e+05 3.682e+05 -2.327 0.019987 *
## Store18:Fuel_Price -1.048e+06 3.136e+05 -3.341 0.000842 ***
## Store19:Fuel_Price -8.191e+05 3.248e+05 -2.522 0.011709 *
## Store20:Fuel_Price -8.340e+04 9.210e+04 -0.906 0.365221
## Store21:Fuel_Price 5.369e+04 9.615e+04 0.558 0.576585
## Store22:Fuel_Price -9.692e+05 3.062e+05 -3.166 0.001558 **
## Store23:Fuel_Price -9.739e+05 3.584e+05 -2.717 0.006609 **
## Store24:Fuel_Price -1.034e+06 3.214e+05 -3.217 0.001303 **
## Store25:Fuel_Price -5.683e+04 9.235e+04 -0.615 0.538380
## Store26:Fuel_Price -9.408e+05 3.255e+05 -2.891 0.003863 **
## Store27:Fuel_Price -9.427e+05 3.098e+05 -3.043 0.002353 **
## Store28:Fuel_Price -1.051e+06 3.166e+05 -3.319 0.000912 ***
## Store29:Fuel_Price -9.716e+05 3.060e+05 -3.176 0.001505 **
## Store30:Fuel_Price 8.151e+04 9.392e+04 0.868 0.385533
## Store31:Fuel_Price 3.145e+04 9.198e+04 0.342 0.732437
## Store32:Fuel_Price -1.776e+05 1.166e+05 -1.523 0.127793
## Store33:Fuel_Price -1.013e+06 3.411e+05 -2.971 0.002986 **
## Store34:Fuel_Price -9.641e+05 3.300e+05 -2.922 0.003498 **
## Store35:Fuel_Price -1.001e+06 3.031e+05 -3.303 0.000966 ***
## Store36:Fuel_Price 7.986e+04 9.369e+04 0.852 0.394061
## Store37:Fuel_Price 9.164e+04 9.742e+04 0.941 0.346923
## Store38:Fuel_Price -9.896e+05 3.202e+05 -3.091 0.002009 **
## Store39:Fuel_Price -1.392e+05 1.015e+05 -1.371 0.170295
## Store40:Fuel_Price -9.853e+05 3.582e+05 -2.751 0.005967 **
## Store41:Fuel_Price -1.343e+05 1.332e+05 -1.008 0.313403
## Store42:Fuel_Price -9.663e+05 3.447e+05 -2.803 0.005084 **
## Store43:Fuel_Price 1.520e+04 1.128e+05 0.135 0.892867
## Store44:Fuel_Price -9.733e+05 3.644e+05 -2.671 0.007595 **
## Store45:Fuel_Price -2.753e+05 1.372e+05 -2.006 0.044877 *
## Store2:CPI 1.211e+04 2.047e+04 0.592 0.554156
## Store3:CPI -2.709e+04 1.598e+04 -1.695 0.090056 .
## Store4:CPI 4.033e+04 4.301e+04 0.938 0.348480
## Store5:CPI -2.218e+04 1.657e+04 -1.338 0.180874
## Store6:CPI 1.431e+04 1.723e+04 0.830 0.406326
## Store7:CPI 1.449e+04 1.938e+04 0.748 0.454515
## Store8:CPI -2.519e+04 1.558e+04 -1.617 0.105962
## Store9:CPI -1.066e+04 1.815e+04 -0.588 0.556861
## Store10:CPI -3.190e+04 4.209e+04 -0.758 0.448599
## Store11:CPI 1.858e+03 1.444e+04 0.129 0.897659
## Store12:CPI 1.128e+04 4.191e+04 0.269 0.787820
## Store13:CPI -4.340e+04 5.777e+04 -0.751 0.452532
## Store14:CPI -5.200e+04 1.268e+04 -4.100 4.21e-05 ***
## Store15:CPI -3.142e+04 1.836e+04 -1.712 0.087052 .
## Store16:CPI -1.605e+04 1.769e+04 -0.907 0.364212
## Store17:CPI -4.300e+04 2.587e+04 -1.662 0.096647 .
## Store18:CPI -1.765e+04 2.719e+04 -0.649 0.516227
## Store19:CPI -4.748e+04 1.800e+04 -2.637 0.008384 **
## Store20:CPI -7.458e+03 1.133e+04 -0.658 0.510289
## Store21:CPI -1.708e+03 2.254e+04 -0.076 0.939616
## Store22:CPI 5.513e+03 2.434e+04 0.227 0.820816
## Store23:CPI -2.122e+04 3.312e+04 -0.641 0.521823
## Store24:CPI 7.683e+03 2.326e+04 0.330 0.741203
## Store25:CPI -1.578e+04 1.151e+04 -1.371 0.170489
## Store26:CPI -1.509e+04 3.051e+04 -0.494 0.620986
## Store27:CPI -2.971e+04 1.832e+04 -1.621 0.105010
## Store28:CPI 8.637e+03 4.067e+04 0.212 0.831849
## Store29:CPI -3.101e+03 2.592e+04 -0.120 0.904746
## Store30:CPI -3.105e+04 2.207e+04 -1.407 0.159455
## Store31:CPI 1.122e+04 2.034e+04 0.552 0.581260
## Store32:CPI 2.135e+04 1.924e+04 1.109 0.267297
## Store33:CPI -1.693e+04 4.149e+04 -0.408 0.683158
## Store34:CPI -1.869e+04 2.545e+04 -0.734 0.462807
## Store35:CPI -3.146e+04 1.625e+04 -1.936 0.052878 .
## Store36:CPI -4.323e+04 2.085e+04 -2.073 0.038202 *
## Store37:CPI -2.703e+04 2.019e+04 -1.339 0.180593
## Store38:CPI 1.662e+04 4.246e+04 0.391 0.695573
## Store39:CPI 4.455e+04 2.315e+04 1.924 0.054397 .
## Store40:CPI -2.270e+04 3.392e+04 -0.669 0.503461
## Store41:CPI 4.104e+04 2.258e+04 1.817 0.069220 .
## Store42:CPI -3.971e+04 4.556e+04 -0.871 0.383531
## Store43:CPI -2.290e+04 1.581e+04 -1.448 0.147617
## Store44:CPI -4.086e+04 6.065e+04 -0.674 0.500576
## Store45:CPI -1.339e+04 1.226e+04 -1.092 0.274719
## Store2:Unemployment 7.008e+04 1.305e+05 0.537 0.591385
## Store3:Unemployment -1.288e+05 1.188e+05 -1.084 0.278621
## Store4:Unemployment -3.817e+05 3.910e+05 -0.976 0.328988
## Store5:Unemployment -8.773e+04 1.352e+05 -0.649 0.516419
## Store6:Unemployment 1.464e+05 1.239e+05 1.182 0.237269
## Store7:Unemployment 8.120e+04 1.719e+05 0.472 0.636615
## Store8:Unemployment -1.005e+05 1.281e+05 -0.785 0.432380
## Store9:Unemployment 6.844e+03 1.364e+05 0.050 0.959995
## Store10:Unemployment -4.115e+05 3.989e+05 -1.031 0.302380
## Store11:Unemployment 4.372e+04 1.100e+05 0.397 0.691193
## Store12:Unemployment -3.229e+05 3.954e+05 -0.817 0.414107
## Store13:Unemployment -4.297e+05 4.001e+05 -1.074 0.282858
## Store14:Unemployment -9.779e+04 2.266e+05 -0.432 0.666021
## Store15:Unemployment -2.261e+05 3.853e+05 -0.587 0.557365
## Store16:Unemployment -3.768e+04 2.024e+05 -0.186 0.852315
## Store17:Unemployment -4.435e+05 3.948e+05 -1.123 0.261371
## Store18:Unemployment -3.784e+05 3.800e+05 -0.996 0.319361
## Store19:Unemployment -1.133e+05 3.840e+05 -0.295 0.767907
## Store20:Unemployment -9.332e+04 1.229e+05 -0.759 0.447812
## Store21:Unemployment 7.662e+04 1.425e+05 0.538 0.590856
## Store22:Unemployment -2.221e+05 3.669e+05 -0.605 0.545062
## Store23:Unemployment -3.289e+05 3.946e+05 -0.834 0.404565
## Store24:Unemployment -4.183e+05 3.805e+05 -1.100 0.271606
## Store25:Unemployment -1.106e+05 1.211e+05 -0.913 0.361153
## Store26:Unemployment -3.233e+05 4.183e+05 -0.773 0.439522
## Store27:Unemployment -3.273e+05 3.730e+05 -0.877 0.380325
## Store28:Unemployment -3.246e+05 3.953e+05 -0.821 0.411584
## Store29:Unemployment -3.103e+05 3.734e+05 -0.831 0.406098
## Store30:Unemployment -1.456e+05 1.406e+05 -1.036 0.300317
## Store31:Unemployment 9.781e+04 1.311e+05 0.746 0.455771
## Store32:Unemployment 1.288e+05 1.664e+05 0.774 0.438959
## Store33:Unemployment -3.361e+05 3.977e+05 -0.845 0.398166
## Store34:Unemployment -3.651e+05 3.914e+05 -0.933 0.350987
## Store35:Unemployment 3.699e+02 3.704e+05 0.001 0.999203
## Store36:Unemployment -1.357e+05 1.165e+05 -1.165 0.243912
## Store37:Unemployment -1.235e+05 1.164e+05 -1.061 0.288727
## Store38:Unemployment -3.377e+05 3.947e+05 -0.856 0.392314
## Store39:Unemployment 8.617e+04 1.291e+05 0.668 0.504436
## Store40:Unemployment -3.615e+05 3.951e+05 -0.915 0.360378
## Store41:Unemployment 2.817e+05 2.188e+05 1.287 0.197998
## Store42:Unemployment -3.884e+05 3.993e+05 -0.973 0.330798
## Store43:Unemployment -1.796e+05 1.036e+05 -1.734 0.082987 .
## Store44:Unemployment -3.874e+05 4.006e+05 -0.967 0.333515
## Store45:Unemployment -6.137e+03 2.238e+05 -0.027 0.978125
## Holiday_Flag1:Temperature 1.647e+03 6.042e+02 2.725 0.006454 **
## Holiday_Flag1:Fuel_Price -3.893e+04 4.691e+04 -0.830 0.406702
## Holiday_Flag1:CPI -3.465e+02 5.449e+03 -0.064 0.949297
## Holiday_Flag1:Unemployment -1.241e+04 2.284e+04 -0.543 0.586931
## Temperature:Fuel_Price 1.800e+03 6.870e+02 2.620 0.008826 **
## Temperature:CPI -3.030e+02 9.131e+01 -3.319 0.000912 ***
## Temperature:Unemployment -7.452e+02 3.641e+02 -2.047 0.040767 *
## Fuel_Price:CPI -1.273e+04 3.901e+03 -3.264 0.001106 **
## Fuel_Price:Unemployment -4.475e+03 2.261e+04 -0.198 0.843126
## CPI:Unemployment -3.004e+03 4.227e+03 -0.711 0.477359
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 151700 on 4277 degrees of freedom
## Multiple R-squared: 0.9321, Adjusted R-squared: 0.9277
## F-statistic: 210.4 on 279 and 4277 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 => 0.932
##
## Initiating stepwise selection...
##
## Step => 1
## Removed => Holiday_Flag:CPI
## Model => Weekly_Sales ~ Store + Holiday_Flag + Temperature + Fuel_Price + CPI + Unemployment + Store:Holiday_Flag + Store:Temperature + Store:Fuel_Price + Store:CPI + Store:Unemployment + Holiday_Flag:Temperature + Holiday_Flag:Fuel_Price + Holiday_Flag:Unemployment + Temperature:Fuel_Price + Temperature:CPI + Temperature:Unemployment + Fuel_Price:CPI + Fuel_Price:Unemployment + CPI:Unemployment
## R2 => 0.93208
##
## Step => 2
## Removed => Fuel_Price:Unemployment
## Model => Weekly_Sales ~ Store + Holiday_Flag + Temperature + Fuel_Price + CPI + Unemployment + Store:Holiday_Flag + Store:Temperature + Store:Fuel_Price + Store:CPI + Store:Unemployment + Holiday_Flag:Temperature + Holiday_Flag:Fuel_Price + Holiday_Flag:Unemployment + Temperature:Fuel_Price + Temperature:CPI + Temperature:Unemployment + Fuel_Price:CPI + CPI:Unemployment
## R2 => 0.93208
##
## Step => 3
## Removed => Holiday_Flag:Unemployment
## Model => Weekly_Sales ~ Store + Holiday_Flag + Temperature + Fuel_Price + CPI + Unemployment + Store:Holiday_Flag + Store:Temperature + Store:Fuel_Price + Store:CPI + Store:Unemployment + Holiday_Flag:Temperature + Holiday_Flag:Fuel_Price + Temperature:Fuel_Price + Temperature:CPI + Temperature:Unemployment + Fuel_Price:CPI + CPI:Unemployment
## R2 => 0.93208
##
## Step => 4
## Removed => Unemployment
## Model => Weekly_Sales ~ Store + Holiday_Flag + Temperature + Fuel_Price + CPI + Store:Holiday_Flag + Store:Temperature + Store:Fuel_Price + Store:CPI + Store:Unemployment + Holiday_Flag:Temperature + Holiday_Flag:Fuel_Price + Temperature:Fuel_Price + Temperature:CPI + Temperature:Unemployment + Fuel_Price:CPI + CPI:Unemployment
## R2 => 0.93208
##
## Step => 5
## 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 + Temperature:Fuel_Price + Temperature:CPI + Temperature:Unemployment + Fuel_Price:CPI
## R2 => 0.93206
##
##
## No more variables to be removed.
##
## Variables Removed:
##
## => Holiday_Flag:CPI
## => Fuel_Price:Unemployment
## => Holiday_Flag:Unemployment
## => Unemployment
## => CPI:Unemployment
##
## Call:
## lm(formula = paste(response, "~", paste(c(include, cterms), collapse = " + ")),
## data = l)
##
## Residuals:
## Min 1Q Median 3Q Max
## -678244 -54709 -9704 32041 1659453
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -1.511e+07 3.294e+06 -4.587 4.62e-06 ***
## Store2 -1.558e+06 5.073e+06 -0.307 0.758825
## Store3 4.982e+06 4.008e+06 1.243 0.213933
## Store4 1.732e+06 5.954e+06 0.291 0.771172
## Store5 3.013e+06 4.032e+06 0.747 0.455027
## Store6 -4.094e+06 4.295e+06 -0.953 0.340581
## Store7 -3.438e+06 4.758e+06 -0.723 0.469972
## Store8 4.263e+06 3.702e+06 1.152 0.249580
## Store9 2.253e+05 4.417e+06 0.051 0.959322
## Store10 1.349e+07 6.127e+06 2.201 0.027769 *
## Store11 -9.379e+05 3.628e+06 -0.259 0.795990
## Store12 7.502e+06 4.920e+06 1.525 0.127395
## Store13 1.320e+07 8.116e+06 1.626 0.104015
## Store14 1.269e+07 3.092e+06 4.105 4.12e-05 ***
## Store15 9.080e+06 2.879e+06 3.153 0.001625 **
## Store16 2.389e+06 4.311e+06 0.554 0.579537
## Store17 1.143e+07 4.024e+06 2.841 0.004519 **
## Store18 9.739e+06 4.806e+06 2.027 0.042771 *
## Store19 1.084e+07 2.849e+06 3.805 0.000144 ***
## Store20 2.978e+06 2.824e+06 1.055 0.291678
## Store21 -6.575e+05 5.596e+06 -0.118 0.906465
## Store22 4.542e+06 4.473e+06 1.015 0.309935
## Store23 7.596e+06 5.002e+06 1.519 0.128907
## Store24 6.535e+06 3.111e+06 2.100 0.035760 *
## Store25 3.252e+06 2.849e+06 1.142 0.253634
## Store26 7.659e+06 5.904e+06 1.297 0.194590
## Store27 1.096e+07 2.799e+06 3.916 9.13e-05 ***
## Store28 8.566e+06 4.713e+06 1.818 0.069179 .
## Store29 6.463e+06 4.275e+06 1.512 0.130668
## Store30 6.999e+06 5.495e+06 1.274 0.202848
## Store31 -2.760e+06 5.046e+06 -0.547 0.584423
## Store32 -4.427e+06 4.651e+06 -0.952 0.341190
## Store33 8.257e+06 5.997e+06 1.377 0.168572
## Store34 9.328e+06 3.757e+06 2.483 0.013073 *
## Store35 7.790e+06 2.836e+06 2.747 0.006048 **
## Store36 9.687e+06 4.939e+06 1.961 0.049894 *
## Store37 6.195e+06 4.820e+06 1.285 0.198749
## Store38 6.365e+06 4.939e+06 1.289 0.197566
## Store39 -9.360e+06 5.562e+06 -1.683 0.092457 .
## Store40 7.606e+06 5.085e+06 1.496 0.134800
## Store41 -1.003e+07 5.642e+06 -1.778 0.075426 .
## Store42 1.168e+07 6.578e+06 1.776 0.075769 .
## Store43 6.237e+06 3.078e+06 2.027 0.042771 *
## Store44 1.047e+07 8.470e+06 1.236 0.216508
## Store45 3.545e+06 2.983e+06 1.188 0.234754
## Holiday_Flag1 6.876e+04 9.586e+04 0.717 0.473213
## Temperature 6.136e+04 1.907e+04 3.218 0.001299 **
## Fuel_Price 2.091e+06 6.573e+05 3.182 0.001475 **
## CPI 7.699e+04 1.434e+04 5.369 8.33e-08 ***
## Store2:Holiday_Flag1 8.976e+04 8.285e+04 1.083 0.278698
## Store3:Holiday_Flag1 -6.689e+04 8.143e+04 -0.821 0.411431
## Store4:Holiday_Flag1 1.216e+05 8.097e+04 1.502 0.133158
## Store5:Holiday_Flag1 -4.564e+04 8.219e+04 -0.555 0.578708
## Store6:Holiday_Flag1 2.960e+04 8.388e+04 0.353 0.724146
## Store7:Holiday_Flag1 8.051e+04 8.444e+04 0.953 0.340407
## Store8:Holiday_Flag1 -2.754e+04 8.056e+04 -0.342 0.732485
## Store9:Holiday_Flag1 -2.810e+04 8.555e+04 -0.328 0.742551
## Store10:Holiday_Flag1 1.183e+05 8.587e+04 1.377 0.168452
## Store11:Holiday_Flag1 -1.167e+05 8.259e+04 -1.413 0.157871
## Store12:Holiday_Flag1 6.265e+04 8.123e+04 0.771 0.440586
## Store13:Holiday_Flag1 -3.582e+04 8.048e+04 -0.445 0.656314
## Store14:Holiday_Flag1 1.258e+05 8.240e+04 1.527 0.126838
## Store15:Holiday_Flag1 3.933e+04 7.796e+04 0.504 0.613958
## Store16:Holiday_Flag1 1.262e+04 7.787e+04 0.162 0.871235
## Store17:Holiday_Flag1 4.459e+04 9.216e+04 0.484 0.628525
## Store18:Holiday_Flag1 -4.579e+04 8.732e+04 -0.524 0.600011
## Store19:Holiday_Flag1 -6.132e+03 8.605e+04 -0.071 0.943191
## Store20:Holiday_Flag1 1.246e+05 7.920e+04 1.573 0.115696
## Store21:Holiday_Flag1 -6.059e+03 7.853e+04 -0.077 0.938507
## Store22:Holiday_Flag1 -4.472e+04 8.485e+04 -0.527 0.598201
## Store23:Holiday_Flag1 1.168e+05 8.053e+04 1.450 0.147008
## Store24:Holiday_Flag1 1.073e+05 9.111e+04 1.178 0.238860
## Store25:Holiday_Flag1 -6.163e+04 8.341e+04 -0.739 0.460025
## Store26:Holiday_Flag1 5.542e+04 7.856e+04 0.706 0.480520
## Store27:Holiday_Flag1 2.578e+04 8.446e+04 0.305 0.760211
## Store28:Holiday_Flag1 3.194e+04 8.452e+04 0.378 0.705537
## Store29:Holiday_Flag1 5.169e+03 8.772e+04 0.059 0.953014
## Store30:Holiday_Flag1 -7.115e+04 9.144e+04 -0.778 0.436588
## Store31:Holiday_Flag1 -1.070e+04 8.027e+04 -0.133 0.893968
## Store32:Holiday_Flag1 3.022e+04 8.345e+04 0.362 0.717255
## Store33:Holiday_Flag1 -8.976e+04 9.996e+04 -0.898 0.369260
## Store34:Holiday_Flag1 7.290e+04 8.468e+04 0.861 0.389346
## Store35:Holiday_Flag1 2.278e+05 8.710e+04 2.615 0.008957 **
## Store36:Holiday_Flag1 -8.897e+04 8.287e+04 -1.074 0.283079
## Store37:Holiday_Flag1 -9.941e+04 8.779e+04 -1.132 0.257539
## Store38:Holiday_Flag1 -9.134e+04 8.294e+04 -1.101 0.270840
## Store39:Holiday_Flag1 4.792e+04 9.012e+04 0.532 0.594953
## Store40:Holiday_Flag1 1.689e+04 8.394e+04 0.201 0.840530
## Store41:Holiday_Flag1 -1.876e+04 8.923e+04 -0.210 0.833452
## Store42:Holiday_Flag1 -8.786e+04 9.890e+04 -0.888 0.374426
## Store43:Holiday_Flag1 -6.968e+04 8.191e+04 -0.851 0.395006
## Store44:Holiday_Flag1 -4.699e+04 9.099e+04 -0.516 0.605547
## Store45:Holiday_Flag1 -8.766e+04 9.076e+04 -0.966 0.334198
## Store2:Temperature -1.956e+03 1.579e+03 -1.239 0.215486
## Store3:Temperature 9.730e+02 1.815e+03 0.536 0.591920
## Store4:Temperature -2.828e+04 8.095e+03 -3.494 0.000481 ***
## Store5:Temperature 1.082e+03 1.664e+03 0.650 0.515731
## Store6:Temperature 1.481e+03 1.643e+03 0.901 0.367443
## Store7:Temperature -1.484e+03 2.374e+03 -0.625 0.531972
## Store8:Temperature -8.101e+01 1.612e+03 -0.050 0.959929
## Store9:Temperature 1.344e+03 1.660e+03 0.810 0.418204
## Store10:Temperature -3.290e+04 7.925e+03 -4.151 3.37e-05 ***
## Store11:Temperature -9.130e+02 1.734e+03 -0.527 0.598529
## Store12:Temperature -2.276e+04 7.560e+03 -3.010 0.002628 **
## Store13:Temperature -2.587e+04 7.964e+03 -3.248 0.001169 **
## Store14:Temperature -8.075e+03 3.026e+03 -2.669 0.007640 **
## Store15:Temperature -2.242e+04 7.408e+03 -3.027 0.002483 **
## Store16:Temperature -3.527e+03 2.551e+03 -1.382 0.166934
## Store17:Temperature -2.399e+04 8.020e+03 -2.991 0.002795 **
## Store18:Temperature -2.110e+04 7.283e+03 -2.897 0.003789 **
## Store19:Temperature -2.197e+04 7.386e+03 -2.975 0.002950 **
## Store20:Temperature -2.148e+03 1.645e+03 -1.306 0.191762
## Store21:Temperature 1.627e+03 1.595e+03 1.020 0.307842
## Store22:Temperature -2.173e+04 6.994e+03 -3.107 0.001900 **
## Store23:Temperature -2.176e+04 7.748e+03 -2.808 0.005002 **
## Store24:Temperature -1.981e+04 7.346e+03 -2.697 0.007031 **
## Store25:Temperature -9.362e+02 1.638e+03 -0.572 0.567540
## Store26:Temperature -2.035e+04 7.422e+03 -2.741 0.006144 **
## Store27:Temperature -1.937e+04 7.043e+03 -2.750 0.005985 **
## Store28:Temperature -2.331e+04 7.568e+03 -3.080 0.002080 **
## Store29:Temperature -2.098e+04 7.181e+03 -2.922 0.003496 **
## Store30:Temperature 1.421e+03 1.596e+03 0.890 0.373323
## Store31:Temperature -8.119e+01 1.556e+03 -0.052 0.958380
## Store32:Temperature -3.684e+03 2.361e+03 -1.560 0.118816
## Store33:Temperature -2.318e+04 7.883e+03 -2.941 0.003287 **
## Store34:Temperature -2.222e+04 7.561e+03 -2.938 0.003317 **
## Store35:Temperature -1.740e+04 6.890e+03 -2.525 0.011591 *
## Store36:Temperature 2.273e+03 1.733e+03 1.312 0.189605
## Store37:Temperature 1.242e+03 1.798e+03 0.691 0.489736
## Store38:Temperature -1.994e+04 7.557e+03 -2.639 0.008343 **
## Store39:Temperature 4.467e+03 1.798e+03 2.484 0.013018 *
## Store40:Temperature -2.280e+04 7.739e+03 -2.946 0.003235 **
## Store41:Temperature -3.366e+03 2.523e+03 -1.334 0.182196
## Store42:Temperature -2.381e+04 7.933e+03 -3.001 0.002705 **
## Store43:Temperature 2.116e+03 1.823e+03 1.160 0.246027
## Store44:Temperature -2.381e+04 7.989e+03 -2.980 0.002899 **
## Store45:Temperature -8.214e+03 3.036e+03 -2.705 0.006847 **
## Store2:Fuel_Price -1.267e+05 9.103e+04 -1.392 0.164032
## Store3:Fuel_Price 1.520e+05 1.040e+05 1.461 0.144031
## Store4:Fuel_Price -9.977e+05 2.815e+05 -3.545 0.000397 ***
## Store5:Fuel_Price 6.226e+04 9.618e+04 0.647 0.517463
## Store6:Fuel_Price -1.211e+05 8.852e+04 -1.368 0.171383
## Store7:Fuel_Price -1.195e+05 1.098e+05 -1.089 0.276413
## Store8:Fuel_Price 1.218e+05 9.209e+04 1.323 0.185977
## Store9:Fuel_Price 8.597e+04 9.623e+04 0.893 0.371700
## Store10:Fuel_Price -9.836e+05 2.803e+05 -3.509 0.000454 ***
## Store11:Fuel_Price -2.278e+04 9.593e+04 -0.237 0.812312
## Store12:Fuel_Price -8.160e+05 2.795e+05 -2.919 0.003525 **
## Store13:Fuel_Price -8.257e+05 2.900e+05 -2.847 0.004437 **
## Store14:Fuel_Price -2.073e+05 1.259e+05 -1.647 0.099729 .
## Store15:Fuel_Price -7.415e+05 2.642e+05 -2.807 0.005024 **
## Store16:Fuel_Price -1.322e+05 1.164e+05 -1.135 0.256401
## Store17:Fuel_Price -6.746e+05 2.853e+05 -2.365 0.018084 *
## Store18:Fuel_Price -8.915e+05 2.600e+05 -3.429 0.000612 ***
## Store19:Fuel_Price -6.588e+05 2.625e+05 -2.510 0.012112 *
## Store20:Fuel_Price -6.665e+04 8.871e+04 -0.751 0.452535
## Store21:Fuel_Price 5.540e+04 9.591e+04 0.578 0.563543
## Store22:Fuel_Price -8.171e+05 2.490e+05 -3.281 0.001042 **
## Store23:Fuel_Price -8.010e+05 2.592e+05 -3.090 0.002015 **
## Store24:Fuel_Price -8.707e+05 2.600e+05 -3.349 0.000817 ***
## Store25:Fuel_Price -4.126e+04 8.919e+04 -0.463 0.643696
## Store26:Fuel_Price -7.799e+05 2.622e+05 -2.975 0.002946 **
## Store27:Fuel_Price -7.886e+05 2.501e+05 -3.153 0.001625 **
## Store28:Fuel_Price -8.941e+05 2.776e+05 -3.220 0.001291 **
## Store29:Fuel_Price -8.223e+05 2.615e+05 -3.145 0.001674 **
## Store30:Fuel_Price 8.244e+04 9.374e+04 0.879 0.379202
## Store31:Fuel_Price 3.204e+04 9.183e+04 0.349 0.727186
## Store32:Fuel_Price -1.414e+05 1.103e+05 -1.283 0.199677
## Store33:Fuel_Price -8.450e+05 2.778e+05 -3.042 0.002366 **
## Store34:Fuel_Price -7.983e+05 2.809e+05 -2.842 0.004503 **
## Store35:Fuel_Price -8.476e+05 2.494e+05 -3.399 0.000682 ***
## Store36:Fuel_Price 8.570e+04 9.250e+04 0.927 0.354201
## Store37:Fuel_Price 9.572e+04 9.658e+04 0.991 0.321694
## Store38:Fuel_Price -8.311e+05 2.816e+05 -2.952 0.003177 **
## Store39:Fuel_Price -1.343e+05 1.006e+05 -1.334 0.182161
## Store40:Fuel_Price -8.124e+05 2.588e+05 -3.139 0.001705 **
## Store41:Fuel_Price -9.115e+04 1.152e+05 -0.791 0.428894
## Store42:Fuel_Price -7.978e+05 2.820e+05 -2.829 0.004692 **
## Store43:Fuel_Price 2.191e+04 1.012e+05 0.216 0.828697
## Store44:Fuel_Price -8.040e+05 2.875e+05 -2.797 0.005186 **
## Store45:Fuel_Price -2.184e+05 1.239e+05 -1.763 0.078045 .
## Store2:CPI 9.449e+03 2.013e+04 0.469 0.638741
## Store3:CPI -2.613e+04 1.595e+04 -1.639 0.101320
## Store4:CPI 5.115e+04 4.172e+04 1.226 0.220270
## Store5:CPI -1.809e+04 1.578e+04 -1.146 0.251773
## Store6:CPI 1.622e+04 1.703e+04 0.952 0.340918
## Store7:CPI 1.112e+04 1.879e+04 0.592 0.554007
## Store8:CPI -2.097e+04 1.452e+04 -1.444 0.148709
## Store9:CPI -6.993e+03 1.752e+04 -0.399 0.689801
## Store10:CPI -3.537e+04 4.193e+04 -0.844 0.398993
## Store11:CPI 2.757e+03 1.441e+04 0.191 0.848331
## Store12:CPI -1.184e+04 3.354e+04 -0.353 0.724004
## Store13:CPI -4.086e+04 5.759e+04 -0.710 0.478029
## Store14:CPI -5.579e+04 1.189e+04 -4.692 2.79e-06 ***
## Store15:CPI -3.322e+04 1.824e+04 -1.821 0.068646 .
## Store16:CPI -1.230e+04 1.669e+04 -0.737 0.461411
## Store17:CPI -3.994e+04 2.542e+04 -1.571 0.116189
## Store18:CPI -2.217e+04 2.659e+04 -0.834 0.404419
## Store19:CPI -4.938e+04 1.787e+04 -2.763 0.005756 **
## Store20:CPI -7.091e+03 1.114e+04 -0.637 0.524276
## Store21:CPI -4.317e+03 2.222e+04 -0.194 0.845969
## Store22:CPI 4.221e+03 2.427e+04 0.174 0.861924
## Store23:CPI -1.007e+04 2.977e+04 -0.338 0.735224
## Store24:CPI 5.479e+03 2.309e+04 0.237 0.812468
## Store25:CPI -1.515e+04 1.131e+04 -1.339 0.180629
## Store26:CPI -1.476e+04 3.049e+04 -0.484 0.628326
## Store27:CPI -3.149e+04 1.822e+04 -1.728 0.084075 .
## Store28:CPI -1.491e+04 3.174e+04 -0.470 0.638519
## Store29:CPI -8.796e+03 2.439e+04 -0.361 0.718393
## Store30:CPI -3.369e+04 2.174e+04 -1.549 0.121394
## Store31:CPI 8.627e+03 2.001e+04 0.431 0.666454
## Store32:CPI 1.802e+04 1.866e+04 0.965 0.334472
## Store33:CPI -2.168e+04 4.119e+04 -0.526 0.598710
## Store34:CPI -2.446e+04 2.332e+04 -1.049 0.294353
## Store35:CPI -3.588e+04 1.542e+04 -2.326 0.020044 *
## Store36:CPI -4.720e+04 2.012e+04 -2.347 0.018995 *
## Store37:CPI -3.061e+04 1.957e+04 -1.564 0.117925
## Store38:CPI -7.307e+03 3.399e+04 -0.215 0.829811
## Store39:CPI 4.078e+04 2.261e+04 1.803 0.071423 .
## Store40:CPI -1.141e+04 3.059e+04 -0.373 0.709196
## Store41:CPI 4.318e+04 2.233e+04 1.933 0.053262 .
## Store42:CPI -4.357e+04 4.538e+04 -0.960 0.337052
## Store43:CPI -2.874e+04 1.269e+04 -2.264 0.023612 *
## Store44:CPI -3.676e+04 6.039e+04 -0.609 0.542788
## Store45:CPI -1.724e+04 1.143e+04 -1.508 0.131526
## Store1:Unemployment 1.235e+05 8.083e+04 1.528 0.126603
## Store2:Unemployment 1.794e+05 1.079e+05 1.663 0.096358 .
## Store3:Unemployment -1.647e+04 9.330e+04 -0.177 0.859893
## Store4:Unemployment 1.832e+04 4.391e+04 0.417 0.676578
## Store5:Unemployment 3.741e+04 1.144e+05 0.327 0.743615
## Store6:Unemployment 2.583e+05 9.996e+04 2.584 0.009796 **
## Store7:Unemployment 2.690e+05 1.236e+05 2.176 0.029575 *
## Store8:Unemployment 1.047e+04 1.037e+05 0.101 0.919602
## Store9:Unemployment 1.139e+05 1.133e+05 1.005 0.314931
## Store10:Unemployment -1.995e+04 7.137e+04 -0.280 0.779833
## Store11:Unemployment 1.558e+05 8.165e+04 1.909 0.056370 .
## Store12:Unemployment 6.162e+04 4.168e+04 1.478 0.139371
## Store13:Unemployment -3.701e+04 9.498e+04 -0.390 0.696803
## Store14:Unemployment 1.148e+05 1.602e+05 0.716 0.473744
## Store15:Unemployment 1.411e+05 1.148e+05 1.230 0.218839
## Store16:Unemployment 1.582e+05 1.552e+05 1.020 0.307885
## Store17:Unemployment -5.313e+04 7.071e+04 -0.751 0.452405
## Store18:Unemployment -8.990e+03 1.160e+05 -0.078 0.938201
## Store19:Unemployment 2.546e+05 1.113e+05 2.287 0.022260 *
## Store20:Unemployment 6.203e+04 8.330e+04 0.745 0.456538
## Store21:Unemployment 1.869e+05 1.227e+05 1.524 0.127699
## Store22:Unemployment 1.409e+05 1.123e+05 1.255 0.209696
## Store23:Unemployment 5.700e+04 1.281e+05 0.445 0.656330
## Store24:Unemployment -5.808e+04 1.230e+05 -0.472 0.636703
## Store25:Unemployment 4.641e+04 7.960e+04 0.583 0.559902
## Store26:Unemployment 5.869e+04 1.944e+05 0.302 0.762734
## Store27:Unemployment 2.689e+04 1.351e+05 0.199 0.842242
## Store28:Unemployment 5.945e+04 3.934e+04 1.511 0.130803
## Store29:Unemployment 6.557e+04 7.788e+04 0.842 0.399843
## Store30:Unemployment -3.596e+04 1.200e+05 -0.300 0.764430
## Store31:Unemployment 2.073e+05 1.086e+05 1.909 0.056269 .
## Store32:Unemployment 3.178e+05 1.162e+05 2.734 0.006280 **
## Store33:Unemployment 5.462e+04 6.390e+04 0.855 0.392742
## Store34:Unemployment 2.961e+04 4.575e+04 0.647 0.517526
## Store35:Unemployment 3.667e+05 1.107e+05 3.314 0.000929 ***
## Store36:Unemployment -2.404e+04 9.130e+04 -0.263 0.792359
## Store37:Unemployment -9.595e+03 9.152e+04 -0.105 0.916503
## Store38:Unemployment 4.599e+04 4.115e+04 1.117 0.263863
## Store39:Unemployment 1.999e+05 1.075e+05 1.859 0.063062 .
## Store40:Unemployment 2.515e+04 1.289e+05 0.195 0.845273
## Store41:Unemployment 4.760e+05 1.791e+05 2.658 0.007892 **
## Store42:Unemployment 2.039e+03 7.787e+04 0.026 0.979114
## Store43:Unemployment -1.693e+04 5.498e+04 -0.308 0.758172
## Store44:Unemployment 7.250e+03 9.649e+04 0.075 0.940105
## Store45:Unemployment 2.069e+05 1.563e+05 1.323 0.185780
## Holiday_Flag1:Temperature 1.622e+03 6.004e+02 2.701 0.006936 **
## Holiday_Flag1:Fuel_Price -2.864e+04 2.723e+04 -1.052 0.292970
## Temperature:Fuel_Price 1.801e+03 6.811e+02 2.644 0.008228 **
## Temperature:CPI -2.945e+02 8.876e+01 -3.318 0.000913 ***
## Temperature:Unemployment -7.708e+02 3.560e+02 -2.165 0.030417 *
## Fuel_Price:CPI -1.072e+04 3.035e+03 -3.533 0.000416 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 151600 on 4281 degrees of freedom
## Multiple R-squared: 0.9321, Adjusted R-squared: 0.9277
## F-statistic: 213.6 on 275 and 4281 DF, p-value: < 2.2e-16
3. Interpret 3 predictors
Fuel Price: When fuel prices go up, sales go down
Holiday_Flag1: Sales increase during holidays
CPI: As the CPI goes up, so do sales
4. What is the R^2 of the model (calculated on the validation
data)
mean_sales_val <- mean(validationlm$Weekly_Sales)
vallmR2 <- validationlm %>%
mutate(res2 = (Weekly_Sales - sales_predicted)^2 ,
tot2 = (Weekly_Sales - mean_sales_val )^2)
r2 <- 1- sum(vallmR2$res2)/sum(vallmR2$tot2)
mean_sales_val = 1051995.39232258
r2 = 0.91771756274538