Effect of Refrigerator on sales of Chocolates

Debarati | Kanika | Mudit | Anshumaan | Kaushik | Shreya | Pratik

Introduction

OBJECTIVE

**To study the effect of presence of refrigerator on sales ofChocolates in India

**To study the relative impact of factors such as fridge Volume, Retailer type, town etc. on sales of Chocolates

Summary

setwd("C:/Users/Anshumaan/Desktop/2018 DAM/PROJECT")
fulldata <-read.csv("DAM Project final data.csv")
head(fulldata)

  OutletCode TownClass     Town          State
1          1  TITANIUM     Pune    Maharashtra
2          2      GOLD  Gwalior Madhya Pradesh
3          3  TITANIUM    Nerul    Maharashtra
4          4    SILVER    KORBA    Chattisgarh
5          5  TITANIUM   Kalyan    Maharashtra
6          7    SILVER KANKAVLI    Maharashtra
                              RE                         RE_new
1 ERETAIL                                                OTHERS
2 HIGH END GROCER                HIGH END GROCER               
3 HIGH END GROCER                HIGH END GROCER               
4 HIGH END GROCER                HIGH END GROCER               
5 PANPLUS                                                OTHERS
6 CASH AND CARRY                                         OTHERS
  Fridge.Volume Has.Fridge Annual.Sales Parent.Firm CHOCO1 CHOCO2 CHOCO3
1           340          1    123860.13      71.60%  7.50% 10.90%  1.80%
2            50          1     79153.05      71.10%  6.40% 11.40%  0.50%
3            35          1    227851.06      71.60%  7.50% 10.90%  1.80%
4            35          1     31397.78      62.70%  6.60% 15.10%  0.00%
5            50          1     24210.18      71.60%  7.50% 10.90%  1.80%
6             0          0     20226.00      71.60%  7.50% 10.90%  1.80%
  CHOCO4 Sales.New
1  1.60% 123860.13
2  3.20%  79153.05
3  1.60% 227851.06
4  7.20%  31397.78
5  1.60%  24210.18
6  1.60%  20226.00

attach(fulldata)

Variable Description

**Outlet Code - Unique Code specific to Outlets

**Town Class - Titanium , Gold , Silver and Rest of Urban depending on the following two factors:

1) Revenue generated on an average from that Town

2) Disposable Income of the individuals staying there.

Titanium being highest, followed by Gold, Silver and Rest of Urban.

**Town- The town where the outlet concerned is located

**State - The state where the outlet concerned is located

**RE- Retailer type is dependant on two factors 1) Size of the Retail outlet 2) Types of goods stored there

**RE_new- Only the major 4 categories of the RE are retained and the remaining low frequency categories are clubbed under “OTHERS”

**Fridge - The volume of the Fridge in Litres. 0 meaning No Fridge

Variable Description

**Has Fridge - Binary variable: 1 -Has Fridge, 0 -No Fridge

**Sales New - Y Variable of concerned - Annual Sales generated by each store

**Parent Firm - The revenue share of the parent firm in that shop as compared with all the Chocolate firms which supply their products in that shop

**CHOCO 1, CHOCO 2, CHOCO 3 and CHOCO 4 are the revenue share of the other four chocolate firms which supply in that retail store

Data Structure

   OutletCode             TownClass             Town       
 Min.   :     1   GOLD         : 55639   Mumbai   : 30519  
 1st Qu.: 63576   REST OF URBAN: 20865   Ahmedabad: 15356  
 Median :126633   Silver       :  1541   Pune     : 11847  
 Mean   :126618   SILVER       : 37852   Surat    :  9820  
 3rd Qu.:189881   TITANIUM     :126698   Indore   :  6854  
 Max.   :252414                          Nagpur   :  6765  
                                         (Other)  :161434  
            State                                     RE        
 Chattisgarh   :  7973   LOW END GROCER                :158654  
 Gujarat       : 58437   CHEMIST                       : 32310  
 Madhya Pradesh: 33809   PANPLUS                       : 17094  
 Maharashtra   :142376   HIGH END GROCER               : 17082  
                         FOOD STORE                    : 12510  
                         NEW CHANNEL                   :  2408  
                         (Other)                       :  2537  
                            RE_new       Fridge.Volume      Has.Fridge    
 CHEMIST                       : 32330   Min.   :  0.00   Min.   :0.0000  
 FOOD STORE                    : 12558   1st Qu.:  0.00   1st Qu.:0.0000  
 HIGH END GROCER               : 17108   Median :  0.00   Median :0.0000  
 LOW END GROCER                :158803   Mean   : 46.15   Mean   :0.4311  
 OTHERS                        : 21796   3rd Qu.: 35.00   3rd Qu.:1.0000  
                                         Max.   :340.00   Max.   :1.0000  

  Annual.Sales      Parent.Firm       CHOCO1          CHOCO2      
 Min.   :       0   62.70%:  7973   5.90%: 58437   10.40%: 58437  
 1st Qu.:    6333   71.00%: 58437   6.40%: 33809   10.90%:142376  
 Median :   18058   71.10%: 33809   6.60%:  7973   11.40%: 33809  
 Mean   :   51828   71.60%:142376   7.50%:142376   15.10%:  7973  
 3rd Qu.:   48606                                                 
 Max.   :28120118                                                 

   CHOCO3         CHOCO4         Sales.New     
 0.00%:  7973   1.60%:142376   Min.   :     0  
 0.50%: 33809   2.10%: 58437   1st Qu.:  6333  
 1.80%:142376   3.20%: 33809   Median : 18058  
 2.20%: 58437   7.20%:  7973   Mean   : 46288  
                               3rd Qu.: 48606  
                               Max.   :454670  


              vars      n      mean        sd    median   trimmed      mad
OutletCode       1 242595 126617.51  72905.95 126633.00 126672.70 93630.64
TownClass*       2 242595      3.66      1.68      5.00      3.82     0.00
Town*            3 242595    116.32     67.58    136.00    117.77    71.16
State*           4 242595      3.28      0.94      4.00      3.39     0.00
RE*              5 242595     18.26      7.06     21.00     18.79     0.00
RE_new*          6 242595      3.52      1.15      4.00      3.66     0.00
Fridge.Volume    7 242595     46.15     95.63      0.00     18.69     0.00
Has.Fridge       8 242595      0.43      0.50      0.00      0.41     0.00
Annual.Sales     9 242595  51828.05 151556.90  18058.44  27714.85 21270.67
Parent.Firm*    10 242595      3.28      0.94      4.00      3.39     0.00
CHOCO1*         11 242595      2.97      1.30      4.00      3.08     0.00
CHOCO2*         12 242595      1.96      0.71      2.00      1.91     0.00
CHOCO3*         13 242595      3.04      0.71      3.00      3.09     0.00
CHOCO4*         14 242595      1.62      0.84      1.00      1.48     0.00
Sales.New       15 242595  46288.43  77949.27  18058.44  27714.85 21270.67
              min        max      range  skew kurtosis     se
OutletCode      1   252414.0   252413.0 -0.01    -1.20 148.02
TownClass*      1        5.0        4.0 -0.72    -1.27   0.00
Town*           1      234.0      233.0 -0.24    -1.04   0.14
State*          1        4.0        3.0 -0.82    -0.82   0.00
RE*             1       36.0       35.0 -0.83     0.10   0.01
RE_new*         1        5.0        4.0 -1.26     0.43   0.00
Fridge.Volume   0      340.0      340.0  2.40     4.38   0.19
Has.Fridge      0        1.0        1.0  0.28    -1.92   0.00
Annual.Sales    0 28120117.7 28120117.7 43.20  5664.19 307.71
Parent.Firm*    1        4.0        3.0 -0.82    -0.82   0.00
CHOCO1*         1        4.0        3.0 -0.60    -1.46   0.00
CHOCO2*         1        4.0        3.0  0.59     0.58   0.00
CHOCO3*         1        4.0        3.0 -0.59     0.58   0.00
CHOCO4*         1        4.0        3.0  1.14     0.27   0.00
Sales.New       0   454669.8   454669.8  3.34    12.43 158.26

Removing Outliers

**Manually Removing points with sales less than 1000

**Box plot and Historam of Sales

plot of chunk unnamed-chunk-3

Fridge Vol VS Sales

plot of chunk unnamed-chunk-4

Fridge Vol VS Average Sales

Given the average sales based on fridge (has or not), we notice that having fridge increases sales significantly to close to Rs. 90,000 from Rs. 15,000 plot of chunk unnamed-chunk-5

Main sales drivers

                              RE         x
1 CHEMIST                         49980.94
2 FOOD STORE                     180629.79
3 HIGH END GROCER                149307.75
4 LOW END GROCER                  27197.38
5                         OTHERS  39135.34

      TownClass        x
1          GOLD 46066.47
2 REST OF URBAN 29472.93
3        Silver 34455.96
4        SILVER 33538.91
5      TITANIUM 57234.99

Through this we found that food store and high end grocers drive the highest sales

gold and titanium town class drive the highest sales

[1] "GOLD"          "REST OF URBAN" "Silver"        "SILVER"       
[5] "TITANIUM"     

[1] "REST OF URBAN" "GOLD"          "Silver"        "SILVER"       
[5] "TITANIUM"     

[1] "CHEMIST                       " "FOOD STORE                    "
[3] "HIGH END GROCER               " "LOW END GROCER                "
[5] "OTHERS"                        

[1] "OTHERS"                         "CHEMIST                       "
[3] "FOOD STORE                    " "HIGH END GROCER               "
[5] "LOW END GROCER                "

'data.frame':   232145 obs. of  16 variables:
 $ OutletCode   : int  1 2 3 4 5 7 8 10 11 12 ...
 $ TownClass    : Factor w/ 5 levels "REST OF URBAN",..: 5 2 5 4 5 4 4 4 4 4 ...
 $ Town         : Factor w/ 234 levels "Ahmedabad","Ahmednagar",..: 171 77 148 114 99 101 84 84 84 84 ...
 $ State        : Factor w/ 4 levels "Chattisgarh",..: 4 3 4 1 4 4 4 4 4 4 ...
 $ RE           : Factor w/ 36 levels "CASH AND CARRY                ",..: 5 13 13 13 30 1 1 1 1 1 ...
 $ RE_new       : Factor w/ 5 levels "OTHERS","CHEMIST                       ",..: 1 4 4 4 1 1 1 1 1 1 ...
 $ Fridge.Volume: int  340 50 35 35 50 0 0 0 0 340 ...
 $ Has.Fridge   : Factor w/ 2 levels "0","1": 2 2 2 2 2 1 1 1 1 2 ...
 $ Annual.Sales : num  123860 79153 227851 31398 24210 ...
 $ Parent.Firm  : Factor w/ 4 levels "62.70%","71.00%",..: 4 3 4 1 4 4 4 4 4 4 ...
 $ CHOCO1       : Factor w/ 4 levels "5.90%","6.40%",..: 4 2 4 3 4 4 4 4 4 4 ...
 $ CHOCO2       : Factor w/ 4 levels "10.40%","10.90%",..: 2 3 2 4 2 2 2 2 2 2 ...
 $ CHOCO3       : Factor w/ 4 levels "0.00%","0.50%",..: 3 2 3 1 3 3 3 3 3 3 ...
 $ CHOCO4       : Factor w/ 4 levels "1.60%","2.10%",..: 1 3 1 4 1 1 1 1 1 1 ...
 $ Sales.New    : num  123860 79153 227851 31398 24210 ...
 $ Has.State    : Factor w/ 4 levels "Chattisgarh",..: 4 3 4 1 4 4 4 4 4 4 ...

Regression Models

** Transformation of variables to Factor variables and defined levels for Townclass and Retailer**

** Model 1 : Regression Output: We tried to find out Effect of presence of Fridge in sales revenue **

The p value < .05 , implying that the variables Sales.New and Fridge.Volume are significantly related. With 1 litre increment in fridge colume, the annual sales of the shop increase by 360 Rs INR.


Call:
lm(formula = fulldata$Sales.New ~ fulldata$Fridge.Volume)

Residuals:
    Min      1Q  Median      3Q     Max 
-152874  -26681  -17726    5111  423204 

Coefficients:
                        Estimate Std. Error t value Pr(>|t|)    
(Intercept)            31466.154    164.422   191.4   <2e-16 ***
fulldata$Fridge.Volume   360.043      1.542   233.5   <2e-16 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Residual standard error: 71150 on 232143 degrees of freedom
Multiple R-squared:  0.1902,    Adjusted R-squared:  0.1902 
F-statistic: 5.452e+04 on 1 and 232143 DF,  p-value: < 2.2e-16

Regression Models

Effect of other factors -Linear Linear

The p-value of the model is less that .05, implying the X variables are related with Y variables. All the X variables are related to the Y variables as their individual P values are < .05. The adjusted R square value of the model is 37%.


Call:
lm(formula = Sales.New ~ Fridge.Volume + TownClass + RE_new + 
    State)

Residuals:
    Min      1Q  Median      3Q     Max 
-218068  -20794   -9153    9549  442088 

Coefficients:
                                       Estimate Std. Error t value
(Intercept)                           35896.333    794.484  45.182
Fridge.Volume                           201.045      1.435 140.127
TownClassREST OF URBAN                -4757.955    505.165  -9.419
TownClassSilver                      -14368.160   1602.649  -8.965
TownClassSILVER                       -4055.606    416.307  -9.742
TownClassTITANIUM                      3568.373    325.027  10.979
RE_newFOOD STORE                     107818.711    668.907 161.187
RE_newHIGH END GROCER                 84556.842    593.835 142.391
RE_newLOW END GROCER                 -16395.815    380.739 -43.063
RE_newOTHERS                          -6071.191    550.422 -11.030
StateGujarat                          -2863.446    760.953  -3.763
StateMadhya Pradesh                   -4437.455    775.332  -5.723
StateMaharashtra                       2428.831    733.479   3.311
                                     Pr(>|t|)    
(Intercept)                           < 2e-16 ***
Fridge.Volume                         < 2e-16 ***
TownClassREST OF URBAN                < 2e-16 ***
TownClassSilver                       < 2e-16 ***
TownClassSILVER                       < 2e-16 ***
TownClassTITANIUM                     < 2e-16 ***
RE_newFOOD STORE                      < 2e-16 ***
RE_newHIGH END GROCER                 < 2e-16 ***
RE_newLOW END GROCER                  < 2e-16 ***
RE_newOTHERS                          < 2e-16 ***
StateGujarat                         0.000168 ***
StateMadhya Pradesh                  1.05e-08 ***
StateMaharashtra                     0.000928 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Residual standard error: 61870 on 242582 degrees of freedom
Multiple R-squared:  0.3701,    Adjusted R-squared:  0.3701 
F-statistic: 1.188e+04 on 12 and 242582 DF,  p-value: < 2.2e-16

Considering Interactions

With interactions considered, the Adjusted R square value is improving fom 37% to 38.92%


Call:
lm(formula = Sales.New ~ Fridge.Volume + TownClass + RE_new + 
    State + TownClass * Fridge.Volume + RE_new * Fridge.Volume)

Residuals:
    Min      1Q  Median      3Q     Max 
-245885  -21154   -9691    9299  440945 

Coefficients:
                                                     Estimate Std. Error
(Intercept)                                         33344.355    808.167
Fridge.Volume                                         258.653      4.224
TownClassREST OF URBAN                              -2410.948    535.628
TownClassSilver                                     -8188.731   1742.869
TownClassSILVER                                     -2905.563    445.974
TownClassTITANIUM                                    6537.487    359.313
RE_newFOOD STORE                                    91520.870    942.426
RE_newHIGH END GROCER                               82478.259    766.541
RE_newLOW END GROCER                               -13345.772    417.858
RE_newOTHERS                                       -12537.905    595.362
StateGujarat                                        -2997.379    755.908
StateMadhya Pradesh                                 -4671.002    769.377
StateMaharashtra                                     2155.947    728.481
Fridge.Volume:TownClassREST OF URBAN                  -51.629      7.651
Fridge.Volume:TownClassSilver                        -132.509     17.643
Fridge.Volume:TownClassSILVER                         -17.265      5.387
Fridge.Volume:TownClassTITANIUM                       -55.977      3.389
Fridge.Volume:RE_newFOOD STORE                         91.027      5.279
Fridge.Volume:RE_newHIGH END GROCER                     4.955      4.981
Fridge.Volume:RE_newLOW END GROCER                    -92.655      3.826
Fridge.Volume:RE_newOTHERS                            180.335      5.619
                                                   t value Pr(>|t|)    
(Intercept)                                         41.259  < 2e-16 ***
Fridge.Volume                                       61.241  < 2e-16 ***
TownClassREST OF URBAN                              -4.501 6.76e-06 ***
TownClassSilver                                     -4.698 2.62e-06 ***
TownClassSILVER                                     -6.515 7.28e-11 ***
TownClassTITANIUM                                   18.194  < 2e-16 ***
RE_newFOOD STORE                                    97.112  < 2e-16 ***
RE_newHIGH END GROCER                              107.598  < 2e-16 ***
RE_newLOW END GROCER                               -31.939  < 2e-16 ***
RE_newOTHERS                                       -21.059  < 2e-16 ***
StateGujarat                                        -3.965 7.33e-05 ***
StateMadhya Pradesh                                 -6.071 1.27e-09 ***
StateMaharashtra                                     2.960  0.00308 ** 
Fridge.Volume:TownClassREST OF URBAN                -6.748 1.50e-11 ***
Fridge.Volume:TownClassSilver                       -7.511 5.90e-14 ***
Fridge.Volume:TownClassSILVER                       -3.205  0.00135 ** 
Fridge.Volume:TownClassTITANIUM                    -16.515  < 2e-16 ***
Fridge.Volume:RE_newFOOD STORE                      17.245  < 2e-16 ***
Fridge.Volume:RE_newHIGH END GROCER                  0.995  0.31990    
Fridge.Volume:RE_newLOW END GROCER                 -24.218  < 2e-16 ***
Fridge.Volume:RE_newOTHERS                          32.095  < 2e-16 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Residual standard error: 61340 on 242574 degrees of freedom
Multiple R-squared:  0.3808,    Adjusted R-squared:  0.3808 
F-statistic:  7459 on 20 and 242574 DF,  p-value: < 2.2e-16

Step Function

The previous model fit 3 is declared the best model by step function


Call:
lm(formula = Sales.New ~ Fridge.Volume + TownClass + RE_new + 
    State + TownClass * Fridge.Volume + RE_new * Fridge.Volume)

Residuals:
    Min      1Q  Median      3Q     Max 
-245885  -21154   -9691    9299  440945 

Coefficients:
                                                     Estimate Std. Error
(Intercept)                                         33344.355    808.167
Fridge.Volume                                         258.653      4.224
TownClassREST OF URBAN                              -2410.948    535.628
TownClassSilver                                     -8188.731   1742.869
TownClassSILVER                                     -2905.563    445.974
TownClassTITANIUM                                    6537.487    359.313
RE_newFOOD STORE                                    91520.870    942.426
RE_newHIGH END GROCER                               82478.259    766.541
RE_newLOW END GROCER                               -13345.772    417.858
RE_newOTHERS                                       -12537.905    595.362
StateGujarat                                        -2997.379    755.908
StateMadhya Pradesh                                 -4671.002    769.377
StateMaharashtra                                     2155.947    728.481
Fridge.Volume:TownClassREST OF URBAN                  -51.629      7.651
Fridge.Volume:TownClassSilver                        -132.509     17.643
Fridge.Volume:TownClassSILVER                         -17.265      5.387
Fridge.Volume:TownClassTITANIUM                       -55.977      3.389
Fridge.Volume:RE_newFOOD STORE                         91.027      5.279
Fridge.Volume:RE_newHIGH END GROCER                     4.955      4.981
Fridge.Volume:RE_newLOW END GROCER                    -92.655      3.826
Fridge.Volume:RE_newOTHERS                            180.335      5.619
                                                   t value Pr(>|t|)    
(Intercept)                                         41.259  < 2e-16 ***
Fridge.Volume                                       61.241  < 2e-16 ***
TownClassREST OF URBAN                              -4.501 6.76e-06 ***
TownClassSilver                                     -4.698 2.62e-06 ***
TownClassSILVER                                     -6.515 7.28e-11 ***
TownClassTITANIUM                                   18.194  < 2e-16 ***
RE_newFOOD STORE                                    97.112  < 2e-16 ***
RE_newHIGH END GROCER                              107.598  < 2e-16 ***
RE_newLOW END GROCER                               -31.939  < 2e-16 ***
RE_newOTHERS                                       -21.059  < 2e-16 ***
StateGujarat                                        -3.965 7.33e-05 ***
StateMadhya Pradesh                                 -6.071 1.27e-09 ***
StateMaharashtra                                     2.960  0.00308 ** 
Fridge.Volume:TownClassREST OF URBAN                -6.748 1.50e-11 ***
Fridge.Volume:TownClassSilver                       -7.511 5.90e-14 ***
Fridge.Volume:TownClassSILVER                       -3.205  0.00135 ** 
Fridge.Volume:TownClassTITANIUM                    -16.515  < 2e-16 ***
Fridge.Volume:RE_newFOOD STORE                      17.245  < 2e-16 ***
Fridge.Volume:RE_newHIGH END GROCER                  0.995  0.31990    
Fridge.Volume:RE_newLOW END GROCER                 -24.218  < 2e-16 ***
Fridge.Volume:RE_newOTHERS                          32.095  < 2e-16 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Residual standard error: 61340 on 242574 degrees of freedom
Multiple R-squared:  0.3808,    Adjusted R-squared:  0.3808 
F-statistic:  7459 on 20 and 242574 DF,  p-value: < 2.2e-16

plot of chunk unnamed-chunk-11

Checking outliers

[1] 232145     16

       rstudent unadjusted p-value Bonferonni p
37     5.431844         5.5828e-08   1.3544e-02
289    5.231629         1.6816e-07   4.0795e-02
369    6.026807         1.6747e-09   4.0627e-04
391    6.358144         2.0457e-10   4.9627e-05
430    5.604676         2.0887e-08   5.0671e-03
583    5.604676         2.0887e-08   5.0671e-03
695    5.815250         6.0619e-09   1.4706e-03
745    5.604676         2.0887e-08   5.0671e-03
748    6.001158         1.9619e-09   4.7595e-04
1681   5.604676         2.0887e-08   5.0671e-03
1901   5.345845         9.0077e-08   2.1852e-02
1989   5.328810         9.8946e-08   2.4004e-02
2015   5.264444         1.4073e-07   3.4141e-02
2102   5.199987         1.9946e-07   4.8389e-02
2255   6.409673         1.4610e-10   3.5443e-05
2256   5.604676         2.0887e-08   5.0671e-03
2372   6.686751         2.2867e-11   5.5474e-06
2394   5.306590         1.1179e-07   2.7120e-02
2528   5.264444         1.4073e-07   3.4141e-02
2657   5.264444         1.4073e-07   3.4141e-02
3231   6.461633         1.0377e-10   2.5175e-05
3689   6.447109         1.1422e-10   2.7708e-05
3893   6.352231         2.1259e-10   5.1573e-05
4555   5.440623         5.3146e-08   1.2893e-02
7363   5.711760         1.1194e-08   2.7157e-03
7543   5.348509         8.8762e-08   2.1533e-02
7619   5.711760         1.1194e-08   2.7157e-03
7739   5.607745         2.0520e-08   4.9781e-03
7834   6.881162         5.9509e-12   1.4437e-06
7862   6.845630         7.6320e-12   1.8515e-06
7893   5.355268         8.5507e-08   2.0744e-02
8380   6.529421         6.6154e-11   1.6049e-05
8492   6.052711         1.4264e-09   3.4603e-04
8537   5.264444         1.4073e-07   3.4141e-02
8566   5.604676         2.0887e-08   5.0671e-03
8576   5.348509         8.8762e-08   2.1533e-02
8753   6.545790         5.9299e-11   1.4386e-05
8904   6.137418         8.4003e-10   2.0379e-04
9167   6.837639         8.0698e-12   1.9577e-06
9668   6.626688         3.4402e-11   8.3457e-06
9697   5.367298         7.9998e-08   1.9407e-02
9940   5.604676         2.0887e-08   5.0671e-03
10012  5.213536         1.8543e-07   4.4984e-02
10134  5.344162         9.0918e-08   2.2056e-02
10453  5.508208         3.6287e-08   8.8031e-03
10476  5.379606         7.4718e-08   1.8126e-02
10757  6.099920         1.0628e-09   2.5783e-04
11119  6.248560         4.1494e-10   1.0066e-04
11799  5.353772         8.6218e-08   2.0916e-02
11885  6.419769         1.3673e-10   3.3170e-05
11992  6.419769         1.3673e-10   3.3170e-05
14640  7.016322         2.2838e-12   5.5403e-07
14691  5.643249         1.6706e-08   4.0527e-03
14694  5.480462         4.2464e-08   1.0301e-02
14734  6.001158         1.9619e-09   4.7595e-04
14735  5.767583         8.0514e-09   1.9532e-03
14756  6.125063         9.0786e-10   2.2024e-04
14997  5.450512         5.0274e-08   1.2196e-02
15027  5.990510         2.0948e-09   5.0818e-04
15090  5.367298         7.9998e-08   1.9407e-02
15092  5.383021         7.3314e-08   1.7786e-02
15098  5.604676         2.0887e-08   5.0671e-03
15479  6.612054         3.7981e-11   9.2139e-06
16004  5.604676         2.0887e-08   5.0671e-03
16036  5.604676         2.0887e-08   5.0671e-03
16037  5.682973         1.3252e-08   3.2150e-03
16237  5.226784         1.7263e-07   4.1878e-02
16268  5.199544         1.9994e-07   4.8504e-02
16518  5.604676         2.0887e-08   5.0671e-03
16650  5.220408         1.7868e-07   4.3346e-02
16659  5.328810         9.8946e-08   2.4004e-02
16895  6.612054         3.7981e-11   9.2139e-06
16986  6.066894         1.3060e-09   3.1683e-04
16996  5.396400         6.8055e-08   1.6510e-02
17068  5.423201         5.8597e-08   1.4215e-02
17103  6.248560         4.1494e-10   1.0066e-04
17302  5.604676         2.0887e-08   5.0671e-03
17332  5.604676         2.0887e-08   5.0671e-03
18401  6.335678         2.3671e-10   5.7425e-05
19311  6.586573         4.5101e-11   1.0941e-05
21089  6.335678         2.3671e-10   5.7425e-05
21415  7.038969         1.9418e-12   4.7107e-07
21451  6.026807         1.6747e-09   4.0627e-04
21496  5.604676         2.0887e-08   5.0671e-03
21538  6.932289         4.1511e-12   1.0070e-06
21950  6.026807         1.6747e-09   4.0627e-04
23259  5.250219         1.5205e-07   3.6886e-02
23264  5.339128         9.3478e-08   2.2677e-02
23291  5.231629         1.6816e-07   4.0795e-02
23339  5.209265         1.8974e-07   4.6031e-02
23903  5.367298         7.9998e-08   1.9407e-02
23937  5.261783         1.4279e-07   3.4639e-02
24106  5.264444         1.4073e-07   3.4141e-02
24238  5.604676         2.0887e-08   5.0671e-03
24500  5.289337         1.2287e-07   2.9807e-02
24739  5.604676         2.0887e-08   5.0671e-03
24782  5.688221         1.2852e-08   3.1177e-03
24930  7.051951         1.7689e-12   4.2914e-07
25020  6.594889         4.2644e-11   1.0345e-05
25210  5.781311         7.4211e-09   1.8003e-03
26155  6.132428         8.6681e-10   2.1028e-04
26382  5.225814         1.7353e-07   4.2098e-02
26383  6.586573         4.5101e-11   1.0941e-05
27411  6.455999         1.0771e-10   2.6130e-05
28460  5.339128         9.3478e-08   2.2677e-02
28461  6.713648         1.9023e-11   4.6150e-06
28487  5.767583         8.0514e-09   1.9532e-03
28607  7.068591         1.5693e-12   3.8071e-07
28735  6.335678         2.3671e-10   5.7425e-05
28782  6.335678         2.3671e-10   5.7425e-05
28890  7.016322         2.2838e-12   5.5403e-07
28921  5.220408         1.7868e-07   4.3346e-02
28970  5.711760         1.1194e-08   2.7157e-03
29126  6.182870         6.3046e-10   1.5295e-04
29130  5.683534         1.3209e-08   3.2044e-03
29161  5.604676         2.0887e-08   5.0671e-03
29328  6.001158         1.9619e-09   4.7595e-04
29330  6.899771         5.2213e-12   1.2667e-06
29388  5.408186         6.3726e-08   1.5460e-02
29504  5.390289         7.0410e-08   1.7081e-02
29516  6.788361         1.1367e-11   2.7577e-06
29644  6.945295         3.7861e-12   9.1850e-07
29867  5.840676         5.2056e-09   1.2628e-03
31070  6.529421         6.6154e-11   1.6049e-05
31477  5.328810         9.8946e-08   2.4004e-02
31650  6.510756         7.4918e-11   1.8175e-05
31724  5.264444         1.4073e-07   3.4141e-02
31816  5.354016         8.6101e-08   2.0888e-02
32118  6.066894         1.3060e-09   3.1683e-04
32256  5.247731         1.5411e-07   3.7387e-02
32397  5.604676         2.0887e-08   5.0671e-03
32453  5.604676         2.0887e-08   5.0671e-03
32459  7.189800         6.5072e-13   1.5786e-07
32555  5.604676         2.0887e-08   5.0671e-03
32663  5.981476         2.2143e-09   5.3718e-04
33286  7.029371         2.0801e-12   5.0462e-07
33330  5.778765         7.5343e-09   1.8278e-03
34836  7.189800         6.5072e-13   1.5786e-07
36256  5.264444         1.4073e-07   3.4141e-02
36258  5.304473         1.1310e-07   2.7437e-02
36282  5.226784         1.7263e-07   4.1878e-02
36426  6.573358         4.9292e-11   1.1958e-05
36634  5.264444         1.4073e-07   3.4141e-02
36795  5.408008         6.3790e-08   1.5475e-02
36809  5.489663         4.0310e-08   9.7791e-03
36850  6.248560         4.1494e-10   1.0066e-04
36983  5.203430         1.9580e-07   4.7501e-02
37190  5.991124         2.0869e-09   5.0627e-04
37192  5.991124         2.0869e-09   5.0627e-04
37730  6.085208         1.1651e-09   2.8266e-04
37863  5.543925         2.9607e-08   7.1826e-03
38280  5.383021         7.3314e-08   1.7786e-02
38451  5.311345         1.0891e-07   2.6422e-02
38458  5.348509         8.8762e-08   2.1533e-02
38499  5.224875         1.7442e-07   4.2313e-02
38714  6.066894         1.3060e-09   3.1683e-04
39010  5.604676         2.0887e-08   5.0671e-03
39070  5.604676         2.0887e-08   5.0671e-03
40369  6.200582         5.6345e-10   1.3669e-04
40498  6.335678         2.3671e-10   5.7425e-05
40668  6.461633         1.0377e-10   2.5175e-05
40944  5.382544         7.3508e-08   1.7833e-02
41598  5.324578         1.0128e-07   2.4569e-02
41821  6.855579         7.1193e-12   1.7271e-06
42882  5.704441         1.1686e-08   2.8350e-03
43323  5.683534         1.3209e-08   3.2044e-03
43337  6.788361         1.1367e-11   2.7577e-06
43525  5.328810         9.8946e-08   2.4004e-02
43582  6.612054         3.7981e-11   9.2139e-06
43620  5.407110         6.4110e-08   1.5553e-02
43743  7.123013         1.0588e-12   2.5687e-07
44038  5.953209         2.6329e-09   6.3874e-04
44121  6.612054         3.7981e-11   9.2139e-06
44603  6.022835         1.7163e-09   4.1637e-04
44903  7.091379         1.3314e-12   3.2300e-07
45382  5.604676         2.0887e-08   5.0671e-03
45426  6.529421         6.6154e-11   1.6049e-05
45448  6.066894         1.3060e-09   3.1683e-04
45450  6.612054         3.7981e-11   9.2139e-06
45616  5.332688         9.6856e-08   2.3497e-02
45651  5.374581         7.6832e-08   1.8639e-02
45662  5.307819         1.1104e-07   2.6938e-02
45771  5.264444         1.4073e-07   3.4141e-02
45879  5.381829         7.3801e-08   1.7904e-02
45900  5.348509         8.8762e-08   2.1533e-02
45958  5.199987         1.9946e-07   4.8389e-02
45991  5.211586         1.8739e-07   4.5459e-02
46011  5.604676         2.0887e-08   5.0671e-03
46139  5.199987         1.9946e-07   4.8389e-02
46213  5.342432         9.1790e-08   2.2268e-02
46557  5.407310         6.4039e-08   1.5535e-02
46600  5.317688         1.0519e-07   2.5518e-02
47099  6.419769         1.3673e-10   3.3170e-05
47196  6.670657         2.5520e-11   6.1911e-06
47521  5.197623         2.0202e-07   4.9008e-02
47636  5.717293         1.0836e-08   2.6288e-03
50107  6.419769         1.3673e-10   3.3170e-05
50419  5.264444         1.4073e-07   3.4141e-02
50520  6.696133         2.1447e-11   5.2030e-06
50533  5.691800         1.2585e-08   3.0531e-03
50534  6.845630         7.6320e-12   1.8515e-06
50535  6.001158         1.9619e-09   4.7595e-04
50536  5.683534         1.3209e-08   3.2044e-03
50619  7.038969         1.9418e-12   4.7107e-07
50922  6.744032         1.5439e-11   3.7455e-06
50978  6.066894         1.3060e-09   3.1683e-04
51044  5.251130         1.5130e-07   3.6704e-02
51058  5.270497         1.3617e-07   3.3034e-02
51125  5.263828         1.4121e-07   3.4256e-02
51129  5.264444         1.4073e-07   3.4141e-02
51248  5.855421         4.7641e-09   1.1558e-03
51331  6.569083         5.0728e-11   1.2306e-05
51332  5.604676         2.0887e-08   5.0671e-03
51388  6.066894         1.3060e-09   3.1683e-04
51399  6.612054         3.7981e-11   9.2139e-06
51441  6.529421         6.6154e-11   1.6049e-05
51465  6.529421         6.6154e-11   1.6049e-05
51494  6.612054         3.7981e-11   9.2139e-06
51520  6.237650         4.4492e-10   1.0794e-04
51555  6.612054         3.7981e-11   9.2139e-06
51640  5.594526         2.2146e-08   5.3726e-03
51825  5.235425         1.6474e-07   3.9966e-02
51900  5.264444         1.4073e-07   3.4141e-02
51966  6.066894         1.3060e-09   3.1683e-04
52335  5.339128         9.3478e-08   2.2677e-02
52480  5.391228         7.0043e-08   1.6992e-02
52710  5.328810         9.8946e-08   2.4004e-02
52721  5.604676         2.0887e-08   5.0671e-03
52874  5.243145         1.5799e-07   3.8329e-02
53063  5.311345         1.0891e-07   2.6422e-02
53130  5.348509         8.8762e-08   2.1533e-02
53391  5.991124         2.0869e-09   5.0627e-04
53409  6.612054         3.7981e-11   9.2139e-06
53493  5.556827         2.7501e-08   6.6716e-03
53668  5.275680         1.3238e-07   3.2114e-02
55041  6.182879         6.3043e-10   1.5294e-04
55332  6.586573         4.5101e-11   1.0941e-05
55562  6.180898         6.3839e-10   1.5487e-04
55682  6.945295         3.7861e-12   9.1850e-07
56359  7.051951         1.7689e-12   4.2914e-07
56574  6.882491         5.8957e-12   1.4303e-06
56667  7.078384         1.4624e-12   3.5477e-07
57257  5.354488         8.5877e-08   2.0833e-02
58120  6.609399         3.8668e-11   9.3806e-06
58130  6.695296         2.1570e-11   5.2328e-06
58222  6.612054         3.7981e-11   9.2139e-06
58417  5.264444         1.4073e-07   3.4141e-02
58836  6.609399         3.8668e-11   9.3806e-06
58890  7.027988         2.1008e-12   5.0965e-07
59086  5.229960         1.6969e-07   4.1165e-02
59113  6.026807         1.6747e-09   4.0627e-04
59270  6.335678         2.3671e-10   5.7425e-05
59318  6.419769         1.3673e-10   3.3170e-05
59682  7.091379         1.3314e-12   3.2300e-07
60089  5.423201         5.8597e-08   1.4215e-02
60345  6.686751         2.2867e-11   5.5474e-06
60455  6.066894         1.3060e-09   3.1683e-04
60728  5.364074         8.1440e-08   1.9757e-02
60950  5.867746         4.4233e-09   1.0731e-03
60998  5.264444         1.4073e-07   3.4141e-02
61167  5.215301         1.8367e-07   4.4557e-02
61198  5.604676         2.0887e-08   5.0671e-03
61252  5.443627         5.2257e-08   1.2677e-02
61803  6.586904         4.5000e-11   1.0917e-05
61952  5.694442         1.2392e-08   3.0062e-03
62682  5.695262         1.2332e-08   2.9918e-03
63842  6.001158         1.9619e-09   4.7595e-04
63981  5.431844         5.5828e-08   1.3544e-02
63991  5.683534         1.3209e-08   3.2044e-03
64315  6.713648         1.9023e-11   4.6150e-06
64400  5.604676         2.0887e-08   5.0671e-03
64521  6.755646         1.4252e-11   3.4574e-06
64565  6.174443         6.6502e-10   1.6133e-04
64601  6.335678         2.3671e-10   5.7425e-05
65274  5.793535         6.9005e-09   1.6740e-03
65348  5.991124         2.0869e-09   5.0627e-04
65401  5.284036         1.2648e-07   3.0683e-02
65588  6.674863         2.4799e-11   6.0162e-06
65657  5.604676         2.0887e-08   5.0671e-03
65879  5.226784         1.7263e-07   4.1878e-02
65997  5.396400         6.8055e-08   1.6510e-02
66232  5.431844         5.5828e-08   1.3544e-02
66312  5.480462         4.2464e-08   1.0301e-02
66411  5.272706         1.3454e-07   3.2639e-02
66471  5.220408         1.7868e-07   4.3346e-02
68139  7.113995         1.1304e-12   2.7423e-07
68313  6.916583         4.6380e-12   1.1252e-06
69127  6.132428         8.6681e-10   2.1028e-04
70618  7.183448         6.8169e-13   1.6537e-07
71386  5.358156         8.4152e-08   2.0415e-02
71567  5.891830         3.8244e-09   9.2779e-04
71675  6.899771         5.2213e-12   1.2667e-06
71777  5.328810         9.8946e-08   2.4004e-02
71972  5.604676         2.0887e-08   5.0671e-03
72011  5.264444         1.4073e-07   3.4141e-02
72333  7.123013         1.0588e-12   2.5687e-07
72515  5.431844         5.5828e-08   1.3544e-02
72569  5.417402         6.0529e-08   1.4684e-02
72581  5.552708         2.8157e-08   6.8308e-03
72680  5.664710         1.4744e-08   3.5768e-03
72821  5.604676         2.0887e-08   5.0671e-03
72826  5.604676         2.0887e-08   5.0671e-03
72849  5.604676         2.0887e-08   5.0671e-03
73026  5.263828         1.4121e-07   3.4256e-02
73233  5.328810         9.8946e-08   2.4004e-02
73741  5.480462         4.2464e-08   1.0301e-02
74101  5.604676         2.0887e-08   5.0671e-03
74266  6.612054         3.7981e-11   9.2139e-06
74311  5.226784         1.7263e-07   4.1878e-02
74368  5.264444         1.4073e-07   3.4141e-02
74497  5.423201         5.8597e-08   1.4215e-02
74828  6.612054         3.7981e-11   9.2139e-06
74927  5.604676         2.0887e-08   5.0671e-03
75001  5.304473         1.1310e-07   2.7437e-02
75038  5.604676         2.0887e-08   5.0671e-03
75073  5.604676         2.0887e-08   5.0671e-03
75246  6.066894         1.3060e-09   3.1683e-04
75294  5.604676         2.0887e-08   5.0671e-03
75398  6.612054         3.7981e-11   9.2139e-06
75419  5.604676         2.0887e-08   5.0671e-03
76127  6.393605         1.6231e-10   3.9376e-05
76943  6.419769         1.3673e-10   3.3170e-05
77488  5.935542         2.9327e-09   7.1146e-04
78412  6.586573         4.5101e-11   1.0941e-05
78783  6.586573         4.5101e-11   1.0941e-05
79168  6.335678         2.3671e-10   5.7425e-05
79202  5.264789         1.4047e-07   3.4077e-02
79271  6.321475         2.5953e-10   6.2960e-05
79706  5.396400         6.8055e-08   1.6510e-02
79769  5.328810         9.8946e-08   2.4004e-02
79834  5.396400         6.8055e-08   1.6510e-02
79990  6.788361         1.1367e-11   2.7577e-06
79991  6.200933         5.6219e-10   1.3639e-04
80001  5.604676         2.0887e-08   5.0671e-03
80185  5.252465         1.5020e-07   3.6439e-02
80628  7.099377         1.2566e-12   3.0485e-07
81274  5.431844         5.5828e-08   1.3544e-02
81323  6.066894         1.3060e-09   3.1683e-04
81742  5.604676         2.0887e-08   5.0671e-03
82353  5.408008         6.3790e-08   1.5475e-02
82454  6.438172         1.2115e-10   2.9389e-05
82658  5.574372         2.4869e-08   6.0330e-03
83487  6.335678         2.3671e-10   5.7425e-05
83775  6.546362         5.9072e-11   1.4331e-05
84817  6.335678         2.3671e-10   5.7425e-05
86331  5.604676         2.0887e-08   5.0671e-03
86341  6.612054         3.7981e-11   9.2139e-06
86502  6.832332         8.3741e-12   2.0315e-06
86504  5.861981         4.5797e-09   1.1110e-03
86641  5.243145         1.5799e-07   3.8329e-02
86645  5.348509         8.8762e-08   2.1533e-02
86702  5.304473         1.1310e-07   2.7437e-02
86880  5.604676         2.0887e-08   5.0671e-03
86973  5.604676         2.0887e-08   5.0671e-03
87076  6.941287         3.8951e-12   9.4494e-07
87087  5.592840         2.2362e-08   5.4250e-03
87235  5.396400         6.8055e-08   1.6510e-02
87356  5.604676         2.0887e-08   5.0671e-03
87644  6.945295         3.7861e-12   9.1850e-07
88173  5.575976         2.4641e-08   5.9777e-03
88224  5.283226         1.2704e-07   3.0819e-02
88341  5.264444         1.4073e-07   3.4141e-02
88357  5.587003         2.3127e-08   5.6104e-03
88488  5.604676         2.0887e-08   5.0671e-03
88504  6.529421         6.6154e-11   1.6049e-05
88528  5.396400         6.8055e-08   1.6510e-02
88596  5.604676         2.0887e-08   5.0671e-03
88597  5.604676         2.0887e-08   5.0671e-03
88637  5.220408         1.7868e-07   4.3346e-02
88656  6.066894         1.3060e-09   3.1683e-04
88660  5.954879         2.6062e-09   6.3225e-04
89288  6.066894         1.3060e-09   3.1683e-04
89450  5.401411         6.6181e-08   1.6055e-02
89558  5.604676         2.0887e-08   5.0671e-03
89598  5.736711         9.6647e-09   2.3446e-03
89619  5.604676         2.0887e-08   5.0671e-03
89638  5.688782         1.2810e-08   3.1075e-03
89782  5.736711         9.6647e-09   2.3446e-03
90939  6.153531         7.5894e-10   1.8412e-04
91221  6.945295         3.7861e-12   9.1850e-07
91947  6.543447         6.0236e-11   1.4613e-05
93610  5.534079         3.1319e-08   7.5978e-03
93801  6.066894         1.3060e-09   3.1683e-04
93972  5.213536         1.8543e-07   4.4984e-02
94053  5.328810         9.8946e-08   2.4004e-02
94083  5.288438         1.2347e-07   2.9954e-02
94157  5.414402         6.1552e-08   1.4932e-02
94761  5.604676         2.0887e-08   5.0671e-03
94778  5.604676         2.0887e-08   5.0671e-03
94790  6.449870         1.1216e-10   2.7208e-05
94872  6.713648         1.9023e-11   4.6150e-06
95788  5.295950         1.1850e-07   2.8748e-02
96025  5.355947         8.5186e-08   2.0666e-02
96044  5.604676         2.0887e-08   5.0671e-03
96049  6.612054         3.7981e-11   9.2139e-06
96081  5.604676         2.0887e-08   5.0671e-03
96269  5.304473         1.1310e-07   2.7437e-02
96281  6.200103         5.6517e-10   1.3711e-04
96333  5.264444         1.4073e-07   3.4141e-02
96416  5.235782         1.6442e-07   3.9889e-02
96585  5.226784         1.7263e-07   4.1878e-02
96660  5.218078         1.8094e-07   4.3895e-02
96711  5.507760         3.6379e-08   8.8255e-03
97019  6.932289         4.1511e-12   1.0070e-06
97051  7.123013         1.0588e-12   2.5687e-07
97062  7.123013         1.0588e-12   2.5687e-07
97066  6.932289         4.1511e-12   1.0070e-06
97067  6.932289         4.1511e-12   1.0070e-06
97070  6.390394         1.6576e-10   4.0212e-05
97238  5.604676         2.0887e-08   5.0671e-03
97265  6.674863         2.4799e-11   6.0162e-06
97318  5.604676         2.0887e-08   5.0671e-03
97346  5.688782         1.2810e-08   3.1075e-03
97429  5.604676         2.0887e-08   5.0671e-03
97457  6.066894         1.3060e-09   3.1683e-04
97558  6.510799         7.4897e-11   1.8170e-05
97880  7.189800         6.5072e-13   1.5786e-07
100667 5.513248         3.5263e-08   8.5546e-03
101212 5.683534         1.3209e-08   3.2044e-03
101281 6.248560         4.1494e-10   1.0066e-04
101329 6.495059         8.3160e-11   2.0174e-05
101480 6.848170         7.4977e-12   1.8189e-06
101489 5.264444         1.4073e-07   3.4141e-02
101622 5.375850         7.6292e-08   1.8508e-02
101981 5.264444         1.4073e-07   3.4141e-02
102887 5.264444         1.4073e-07   3.4141e-02
103070 5.351704         8.7209e-08   2.1156e-02
103073 5.355211         8.5534e-08   2.0750e-02
103098 5.431844         5.5828e-08   1.3544e-02
103417 6.331152         2.4376e-10   5.9135e-05
103451 5.264444         1.4073e-07   3.4141e-02
103661 5.423201         5.8597e-08   1.4215e-02
103677 5.283226         1.2704e-07   3.0819e-02
103920 5.367298         7.9998e-08   1.9407e-02
104007 5.450512         5.0274e-08   1.2196e-02
104332 5.505552         3.6838e-08   8.9368e-03
104700 6.066894         1.3060e-09   3.1683e-04
104703 5.353521         8.6337e-08   2.0945e-02
104710 6.569083         5.0728e-11   1.2306e-05
105038 6.945295         3.7861e-12   9.1850e-07
105722 6.335678         2.3671e-10   5.7425e-05
106563 6.586573         4.5101e-11   1.0941e-05
106869 7.026087         2.1296e-12   5.1663e-07
107297 5.954187         2.6173e-09   6.3493e-04
107310 5.856084         4.7452e-09   1.1512e-03
108225 6.713648         1.9023e-11   4.6150e-06
108235 6.674863         2.4799e-11   6.0162e-06
108321 5.235907         1.6431e-07   3.9861e-02
108389 5.604676         2.0887e-08   5.0671e-03
108506 5.564928         2.6254e-08   6.3690e-03
108516 5.295950         1.1850e-07   2.8748e-02
108517 5.344162         9.0918e-08   2.2056e-02
108518 5.295950         1.1850e-07   2.8748e-02
108633 5.220408         1.7868e-07   4.3346e-02
108646 5.339128         9.3478e-08   2.2677e-02
108868 5.784972         7.2613e-09   1.7616e-03
109068 6.380206         1.7717e-10   4.2980e-05
109081 5.604676         2.0887e-08   5.0671e-03
109158 6.562473         5.3029e-11   1.2864e-05
109309 6.125893         9.0314e-10   2.1910e-04
109449 5.348509         8.8762e-08   2.1533e-02
109582 5.431844         5.5828e-08   1.3544e-02
109606 5.431844         5.5828e-08   1.3544e-02
110204 5.339128         9.3478e-08   2.2677e-02
110220 6.612054         3.7981e-11   9.2139e-06
110733 5.348509         8.8762e-08   2.1533e-02
110740 5.284036         1.2648e-07   3.0683e-02
110769 5.604676         2.0887e-08   5.0671e-03
111092 6.696133         2.1447e-11   5.2030e-06
111118 5.264444         1.4073e-07   3.4141e-02
111149 5.264444         1.4073e-07   3.4141e-02
111152 5.220408         1.7868e-07   4.3346e-02
111172 5.860051         4.6332e-09   1.1240e-03
111189 5.604676         2.0887e-08   5.0671e-03
111217 5.605667         2.0768e-08   5.0382e-03
111469 5.545508         2.9341e-08   7.1179e-03
111476 6.686751         2.2867e-11   5.5474e-06
111678 5.482461         4.1987e-08   1.0186e-02
111713 5.604676         2.0887e-08   5.0671e-03
111954 7.098543         1.2642e-12   3.0669e-07
112698 7.136039         9.6326e-13   2.3368e-07
113848 7.041277         1.9099e-12   4.6333e-07
113964 5.913741         3.3487e-09   8.1238e-04
115090 5.455204         4.8964e-08   1.1879e-02
115269 6.797682         1.0656e-11   2.5851e-06
115500 5.604676         2.0887e-08   5.0671e-03
115608 5.264444         1.4073e-07   3.4141e-02
115670 6.776812         1.2314e-11   2.9872e-06
115826 6.002220         1.9491e-09   4.7285e-04
115885 5.604676         2.0887e-08   5.0671e-03
115904 5.594737         2.2119e-08   5.3660e-03
115919 6.186397         6.1653e-10   1.4957e-04
116385 6.979521         2.9694e-12   7.2037e-07
116769 5.264444         1.4073e-07   3.4141e-02
117031 5.604676         2.0887e-08   5.0671e-03
117242 5.688782         1.2810e-08   3.1075e-03
117345 6.066894         1.3060e-09   3.1683e-04
117381 5.604676         2.0887e-08   5.0671e-03
117421 5.328810         9.8946e-08   2.4004e-02
117644 6.932289         4.1511e-12   1.0070e-06
117676 6.932289         4.1511e-12   1.0070e-06
117721 6.932289         4.1511e-12   1.0070e-06
117760 6.932289         4.1511e-12   1.0070e-06
117774 5.991124         2.0869e-09   5.0627e-04
117785 6.932289         4.1511e-12   1.0070e-06
117793 6.932289         4.1511e-12   1.0070e-06
117977 5.287484         1.2412e-07   3.0110e-02
119146 6.764970         1.3364e-11   3.2420e-06
119535 6.138542         8.3411e-10   2.0235e-04
119592 6.586573         4.5101e-11   1.0941e-05
119644 5.436908         5.4265e-08   1.3164e-02
120081 6.945295         3.7861e-12   9.1850e-07
120559 6.017585         1.7729e-09   4.3010e-04
120973 6.066894         1.3060e-09   3.1683e-04
121018 5.679267         1.3543e-08   3.2854e-03
121022 5.767583         8.0514e-09   1.9532e-03
121099 5.235425         1.6474e-07   3.9966e-02
121242 5.683534         1.3209e-08   3.2044e-03
121362 5.263828         1.4121e-07   3.4256e-02
121480 6.696133         2.1447e-11   5.2030e-06
121726 5.213634         1.8533e-07   4.4960e-02
121788 6.932289         4.1511e-12   1.0070e-06
121828 7.016322         2.2838e-12   5.5403e-07
121838 7.016322         2.2838e-12   5.5403e-07
121912 6.389207         1.6705e-10   4.0525e-05
121991 7.016322         2.2838e-12   5.5403e-07
122160 6.066894         1.3060e-09   3.1683e-04
122326 5.991124         2.0869e-09   5.0627e-04
122327 5.263828         1.4121e-07   3.4256e-02
122411 5.621148         1.8990e-08   4.6069e-03
123027 5.281875         1.2798e-07   3.1047e-02
123600 5.348509         8.8762e-08   2.1533e-02
123632 5.348509         8.8762e-08   2.1533e-02
124003 5.220408         1.7868e-07   4.3346e-02
124011 5.412877         6.2079e-08   1.5060e-02
124433 5.315700         1.0634e-07   2.5798e-02
125832 5.472942         4.4306e-08   1.0748e-02
126203 5.645918         1.6449e-08   3.9903e-03
126792 6.546362         5.9072e-11   1.4331e-05
126804 6.992738         2.7026e-12   6.5565e-07
126982 6.550721         5.7374e-11   1.3919e-05
127036 6.586573         4.5101e-11   1.0941e-05
128066 6.889519         5.6117e-12   1.3614e-06
129933 6.557508         5.4824e-11   1.3300e-05
129941 5.806722         6.3787e-09   1.5474e-03
129958 6.001158         1.9619e-09   4.7595e-04
130103 5.264444         1.4073e-07   3.4141e-02
130136 6.001158         1.9619e-09   4.7595e-04
130264 5.604676         2.0887e-08   5.0671e-03
130334 5.604676         2.0887e-08   5.0671e-03
130417 6.001158         1.9619e-09   4.7595e-04
130441 6.612054         3.7981e-11   9.2139e-06
130476 5.213634         1.8533e-07   4.4960e-02
130554 5.264444         1.4073e-07   3.4141e-02
130665 5.604676         2.0887e-08   5.0671e-03
130711 5.487756         4.0748e-08   9.8852e-03
130764 5.485523         4.1266e-08   1.0011e-02
130815 5.604676         2.0887e-08   5.0671e-03
131001 7.029371         2.0801e-12   5.0462e-07
131308 6.419769         1.3673e-10   3.3170e-05
131659 5.693950         1.2428e-08   3.0149e-03
131913 5.604676         2.0887e-08   5.0671e-03
132045 5.243145         1.5799e-07   3.8329e-02
132062 6.119639         9.3930e-10   2.2787e-04
132322 6.066894         1.3060e-09   3.1683e-04
132707 5.604676         2.0887e-08   5.0671e-03
132918 6.066894         1.3060e-09   3.1683e-04
132933 5.549520         2.8675e-08   6.9565e-03
134376 5.541139         3.0082e-08   7.2978e-03
134410 7.078384         1.4624e-12   3.5477e-07
134842 6.393295         1.6264e-10   3.9456e-05
135716 5.969025         2.3900e-09   5.7981e-04
136918 5.306496         1.1185e-07   2.7134e-02
137389 7.000659         2.5542e-12   6.1963e-07
137721 5.264444         1.4073e-07   3.4141e-02
137891 5.691800         1.2585e-08   3.0531e-03
137929 6.215542         5.1231e-10   1.2428e-04
137938 5.375850         7.6292e-08   1.8508e-02
137974 6.881162         5.9509e-12   1.4437e-06
137975 5.747267         9.0806e-09   2.2029e-03
138299 5.767583         8.0514e-09   1.9532e-03
138470 6.395711         1.6009e-10   3.8837e-05
138472 6.932289         4.1511e-12   1.0070e-06
138481 6.200215         5.6476e-10   1.3701e-04
138523 7.123013         1.0588e-12   2.5687e-07
138526 7.016322         2.2838e-12   5.5403e-07
138585 5.226784         1.7263e-07   4.1878e-02
138605 5.604676         2.0887e-08   5.0671e-03
138864 6.612054         3.7981e-11   9.2139e-06
138868 5.451631         4.9958e-08   1.2120e-02
138871 6.248560         4.1494e-10   1.0066e-04
140309 5.213634         1.8533e-07   4.4960e-02
140354 5.604676         2.0887e-08   5.0671e-03
140565 5.229999         1.6965e-07   4.1157e-02
140628 5.383021         7.3314e-08   1.7786e-02
140878 6.095185         1.0947e-09   2.6558e-04
141044 5.604676         2.0887e-08   5.0671e-03
141161 5.604676         2.0887e-08   5.0671e-03
142209 6.586573         4.5101e-11   1.0941e-05
143934 7.087497         1.3693e-12   3.3218e-07
145869 6.713648         1.9023e-11   4.6150e-06
146157 5.348509         8.8762e-08   2.1533e-02
146416 6.619961         3.6004e-11   8.7343e-06
146623 6.066894         1.3060e-09   3.1683e-04
146680 6.674863         2.4799e-11   6.0162e-06
146703 6.248560         4.1494e-10   1.0066e-04
146803 5.352709         8.6725e-08   2.1039e-02
147087 5.607745         2.0520e-08   4.9781e-03
147095 5.226784         1.7263e-07   4.1878e-02
147099 5.226784         1.7263e-07   4.1878e-02
147130 6.001158         1.9619e-09   4.7595e-04
147140 5.683534         1.3209e-08   3.2044e-03
147145 5.315348         1.0655e-07   2.5848e-02
147164 5.683534         1.3209e-08   3.2044e-03
147542 5.688782         1.2810e-08   3.1075e-03
147611 6.239652         4.3927e-10   1.0656e-04
147656 5.604676         2.0887e-08   5.0671e-03
147733 5.243145         1.5799e-07   3.8329e-02
148124 5.604676         2.0887e-08   5.0671e-03
148184 5.217403         1.8160e-07   4.4055e-02
148258 5.342432         9.1790e-08   2.2268e-02
148327 6.612054         3.7981e-11   9.2139e-06
148425 5.339128         9.3478e-08   2.2677e-02
148743 6.332647         2.4141e-10   5.8565e-05
148835 5.264444         1.4073e-07   3.4141e-02
148964 6.612054         3.7981e-11   9.2139e-06
148971 5.604676         2.0887e-08   5.0671e-03
149100 6.612054         3.7981e-11   9.2139e-06
149519 6.041121         1.5327e-09   3.7182e-04
151085 6.335678         2.3671e-10   5.7425e-05
151323 6.768071         1.3081e-11   3.1733e-06
152319 6.966568         3.2559e-12   7.8986e-07
152634 6.395129         1.6070e-10   3.8986e-05
152641 5.969963         2.3763e-09   5.7649e-04
153020 6.122823         9.2072e-10   2.2336e-04
153524 6.387995         1.6838e-10   4.0847e-05
153818 6.335678         2.3671e-10   5.7425e-05
154284 5.604676         2.0887e-08   5.0671e-03
154357 5.251130         1.5130e-07   3.6704e-02
154451 6.713648         1.9023e-11   4.6150e-06
154533 6.026807         1.6747e-09   4.0627e-04
154609 6.085208         1.1651e-09   2.8266e-04
154760 5.213536         1.8543e-07   4.4984e-02
154923 6.529421         6.6154e-11   1.6049e-05
154932 5.423201         5.8597e-08   1.4215e-02
155149 5.455522         4.8877e-08   1.1857e-02
155464 6.569083         5.0728e-11   1.2306e-05
155474 6.612054         3.7981e-11   9.2139e-06
155478 5.616829         1.9471e-08   4.7235e-03
155713 5.535363         3.1090e-08   7.5424e-03
155849 5.303043         1.1399e-07   2.7653e-02
156448 6.335678         2.3671e-10   5.7425e-05
156639 6.569083         5.0728e-11   1.2306e-05
156717 5.507760         3.6379e-08   8.8255e-03
156770 5.505685         3.6811e-08   8.9301e-03
156870 5.423201         5.8597e-08   1.4215e-02
156954 5.489663         4.0310e-08   9.7791e-03
157472 5.604676         2.0887e-08   5.0671e-03
157558 5.226784         1.7263e-07   4.1878e-02
157740 5.300372         1.1567e-07   2.8060e-02
158013 6.066894         1.3060e-09   3.1683e-04
158041 6.248560         4.1494e-10   1.0066e-04
158223 6.586573         4.5101e-11   1.0941e-05
158291 5.604676         2.0887e-08   5.0671e-03
158328 6.248560         4.1494e-10   1.0066e-04
159500 5.823377         5.7743e-09   1.4008e-03
159623 6.012631         1.8280e-09   4.4345e-04
160173 7.189800         6.5072e-13   1.5786e-07
160233 7.078384         1.4624e-12   3.5477e-07
161301 7.189800         6.5072e-13   1.5786e-07
162024 5.455522         4.8877e-08   1.1857e-02
162095 5.604676         2.0887e-08   5.0671e-03
162499 5.604676         2.0887e-08   5.0671e-03
162875 5.504917         3.6972e-08   8.9691e-03
163149 5.604676         2.0887e-08   5.0671e-03
163161 5.624787         1.8594e-08   4.5108e-03
163315 5.604676         2.0887e-08   5.0671e-03
163499 6.872405         6.3280e-12   1.5351e-06
163540 6.845630         7.6320e-12   1.8515e-06
163756 6.945295         3.7861e-12   9.1850e-07
164122 6.726260         1.7446e-11   4.2324e-06
164315 6.335678         2.3671e-10   5.7425e-05
164636 5.861710         4.5872e-09   1.1128e-03
164723 5.264444         1.4073e-07   3.4141e-02
165077 5.604676         2.0887e-08   5.0671e-03
165108 6.066894         1.3060e-09   3.1683e-04
165132 5.264444         1.4073e-07   3.4141e-02
165138 5.604676         2.0887e-08   5.0671e-03
165143 6.612054         3.7981e-11   9.2139e-06
165149 5.220408         1.7868e-07   4.3346e-02
165163 5.264444         1.4073e-07   3.4141e-02
165463 5.383021         7.3314e-08   1.7786e-02
165468 5.423201         5.8597e-08   1.4215e-02
165761 5.254165         1.4882e-07   3.6104e-02
167178 6.945295         3.7861e-12   9.1850e-07
167739 5.348337         8.8846e-08   2.1554e-02
168046 6.670657         2.5520e-11   6.1911e-06
169448 7.091379         1.3314e-12   3.2300e-07
170310 7.091379         1.3314e-12   3.2300e-07
170371 6.134094         8.5778e-10   2.0809e-04
170409 5.220901         1.7820e-07   4.3231e-02
170496 6.001158         1.9619e-09   4.7595e-04
170555 6.845630         7.6320e-12   1.8515e-06
170558 6.872405         6.3280e-12   1.5351e-06
171162 5.604676         2.0887e-08   5.0671e-03
172435 5.348509         8.8762e-08   2.1533e-02
172456 5.529081         3.2224e-08   7.8175e-03
172663 5.264444         1.4073e-07   3.4141e-02
172665 5.431844         5.5828e-08   1.3544e-02
172749 5.348509         8.8762e-08   2.1533e-02
173432 5.264444         1.4073e-07   3.4141e-02
173650 5.264444         1.4073e-07   3.4141e-02
173710 5.335192         9.5529e-08   2.3175e-02
173728 5.507760         3.6379e-08   8.8255e-03
173739 5.604676         2.0887e-08   5.0671e-03
176400 6.993922         2.6799e-12   6.5014e-07
177688 6.770339         1.2877e-11   3.1239e-06
179185 5.683534         1.3209e-08   3.2044e-03
179335 5.389843         7.0585e-08   1.7123e-02
179385 5.339128         9.3478e-08   2.2677e-02
179630 6.150986         7.7122e-10   1.8710e-04
179855 5.604676         2.0887e-08   5.0671e-03
179866 5.264444         1.4073e-07   3.4141e-02
179874 5.584125         2.3513e-08   5.7042e-03
180145 6.419769         1.3673e-10   3.3170e-05
180194 5.305421         1.1251e-07   2.7295e-02
180204 6.066894         1.3060e-09   3.1683e-04
180218 6.788361         1.1367e-11   2.7577e-06
180268 6.001158         1.9619e-09   4.7595e-04
180279 6.619961         3.6004e-11   8.7343e-06
180309 6.026807         1.6747e-09   4.0627e-04
180388 6.264067         3.7569e-10   9.1141e-05
180856 5.371570         7.8125e-08   1.8953e-02
180947 5.264444         1.4073e-07   3.4141e-02
181017 5.396400         6.8055e-08   1.6510e-02
181039 5.339128         9.3478e-08   2.2677e-02
181089 5.604676         2.0887e-08   5.0671e-03
181224 5.604676         2.0887e-08   5.0671e-03
181596 5.604676         2.0887e-08   5.0671e-03
181895 5.604676         2.0887e-08   5.0671e-03
181898 5.604676         2.0887e-08   5.0671e-03
181981 5.604676         2.0887e-08   5.0671e-03
182136 6.066894         1.3060e-09   3.1683e-04
182245 5.604676         2.0887e-08   5.0671e-03
182333 6.335678         2.3671e-10   5.7425e-05
182398 5.775246         7.6934e-09   1.8664e-03
182835 6.342230         2.2686e-10   5.5035e-05
183048 6.395910         1.5988e-10   3.8787e-05
183052 5.213162         1.8580e-07   4.5074e-02
183668 5.695832         1.2291e-08   2.9818e-03
184705 6.132428         8.6681e-10   2.1028e-04
185037 6.573113         4.9373e-11   1.1978e-05
185511 5.655453         1.5561e-08   3.7750e-03
186553 5.574414         2.4863e-08   6.0316e-03
186655 5.296978         1.1784e-07   2.8587e-02
186717 6.066894         1.3060e-09   3.1683e-04
186732 5.423201         5.8597e-08   1.4215e-02
186827 5.215772         1.8320e-07   4.4444e-02
186847 5.220408         1.7868e-07   4.3346e-02
187039 5.431844         5.5828e-08   1.3544e-02
187345 5.328810         9.8946e-08   2.4004e-02
187360 5.297698         1.1737e-07   2.8474e-02
187626 5.604676         2.0887e-08   5.0671e-03
187940 7.113995         1.1304e-12   2.7423e-07
188134 5.683534         1.3209e-08   3.2044e-03
188201 5.604676         2.0887e-08   5.0671e-03
188247 5.604676         2.0887e-08   5.0671e-03
188258 5.609879         2.0269e-08   4.9171e-03
188329 6.612054         3.7981e-11   9.2139e-06
188448 5.254105         1.4887e-07   3.6115e-02
188558 5.374581         7.6832e-08   1.8639e-02
188574 5.408008         6.3790e-08   1.5475e-02
189138 5.604676         2.0887e-08   5.0671e-03
189253 5.264444         1.4073e-07   3.4141e-02
189254 5.226784         1.7263e-07   4.1878e-02
189703 6.106998         1.0168e-09   2.4666e-04
189768 6.612054         3.7981e-11   9.2139e-06
189882 6.400971         1.5467e-10   3.7523e-05
189909 6.066894         1.3060e-09   3.1683e-04
189932 5.361776         8.2483e-08   2.0010e-02
189943 6.612054         3.7981e-11   9.2139e-06
189959 5.604676         2.0887e-08   5.0671e-03
190149 5.404509         6.5047e-08   1.5780e-02
190436 5.454172         4.9249e-08   1.1948e-02
191318 5.767583         8.0514e-09   1.9532e-03
191925 6.634806         3.2561e-11   7.8991e-06
193785 7.136039         9.6326e-13   2.3368e-07
193813 5.383157         7.3258e-08   1.7772e-02
193850 5.932979         2.9789e-09   7.2266e-04
193889 6.276571         3.4670e-10   8.4108e-05
193938 6.586573         4.5101e-11   1.0941e-05
194148 6.579095         4.7428e-11   1.1506e-05
194278 5.291487         1.2143e-07   2.9459e-02
194424 5.604676         2.0887e-08   5.0671e-03
194548 5.264444         1.4073e-07   3.4141e-02
194688 6.397527         1.5820e-10   3.8378e-05
194692 6.932289         4.1511e-12   1.0070e-06
194701 6.797682         1.0656e-11   2.5851e-06
194742 7.016322         2.2838e-12   5.5403e-07
194886 6.945295         3.7861e-12   9.1850e-07
195275 5.550047         2.8589e-08   6.9355e-03
195705 5.558726         2.7204e-08   6.5995e-03
195706 6.026807         1.6747e-09   4.0627e-04
195764 5.607745         2.0520e-08   4.9781e-03
195793 6.695296         2.1570e-11   5.2328e-06
196472 5.348509         8.8762e-08   2.1533e-02
196723 5.507760         3.6379e-08   8.8255e-03
196782 5.202504         1.9678e-07   4.7738e-02
196895 5.507760         3.6379e-08   8.8255e-03
197004 5.584125         2.3513e-08   5.7042e-03
197099 5.235425         1.6474e-07   3.9966e-02
197720 5.220408         1.7868e-07   4.3346e-02
198684 7.113995         1.1304e-12   2.7423e-07
199430 6.882491         5.8957e-12   1.4303e-06
199441 6.586573         4.5101e-11   1.0941e-05
199514 6.882491         5.8957e-12   1.4303e-06
200156 6.586573         4.5101e-11   1.0941e-05
201428 5.812207         6.1731e-09   1.4976e-03
201869 5.683534         1.3209e-08   3.2044e-03
201913 5.199987         1.9946e-07   4.8389e-02
202081 5.399032         6.7064e-08   1.6269e-02
202128 6.001158         1.9619e-09   4.7595e-04
202315 5.604676         2.0887e-08   5.0671e-03
202449 5.328456         9.9139e-08   2.4051e-02
202498 5.231629         1.6816e-07   4.0795e-02
202547 5.683534         1.3209e-08   3.2044e-03
202676 6.529421         6.6154e-11   1.6049e-05
202802 5.607745         2.0520e-08   4.9781e-03
203042 6.335678         2.3671e-10   5.7425e-05
203062 5.756678         8.5888e-09   2.0836e-03
203360 6.112563         9.8192e-10   2.3821e-04
203361 5.558726         2.7204e-08   6.5995e-03
203366 6.632452         3.3084e-11   8.0261e-06
203372 5.607745         2.0520e-08   4.9781e-03
203459 6.243850         4.2763e-10   1.0374e-04
203600 6.132428         8.6681e-10   2.1028e-04
203744 6.335678         2.3671e-10   5.7425e-05
203802 6.413539         1.4244e-10   3.4555e-05
203877 7.189800         6.5072e-13   1.5786e-07
203961 6.274058         3.5235e-10   8.5478e-05
203980 5.220408         1.7868e-07   4.3346e-02
203987 5.604676         2.0887e-08   5.0671e-03
203990 6.612054         3.7981e-11   9.2139e-06
203991 6.612054         3.7981e-11   9.2139e-06
204014 6.144851         8.0162e-10   1.9447e-04
204322 5.383021         7.3314e-08   1.7786e-02
204384 5.236165         1.6408e-07   3.9806e-02
204480 6.562473         5.3029e-11   1.2864e-05
204699 6.612054         3.7981e-11   9.2139e-06
204946 5.824275         5.7433e-09   1.3933e-03
204985 5.747060         9.0917e-09   2.2056e-03
205367 6.529421         6.6154e-11   1.6049e-05
205370 6.066894         1.3060e-09   3.1683e-04
205400 5.246888         1.5482e-07   3.7558e-02
205936 6.586573         4.5101e-11   1.0941e-05
206326 6.882491         5.8957e-12   1.4303e-06
206523 6.945295         3.7861e-12   9.1850e-07
207362 7.078384         1.4624e-12   3.5477e-07
209467 6.632452         3.3084e-11   8.0261e-06
209549 5.643249         1.6706e-08   4.0527e-03
209550 5.683534         1.3209e-08   3.2044e-03
209693 5.312157         1.0843e-07   2.6305e-02
209703 6.788361         1.1367e-11   2.7577e-06
209749 5.311345         1.0891e-07   2.6422e-02
210881 6.832332         8.3741e-12   2.0315e-06
211038 5.448587         5.0821e-08   1.2329e-02
211628 5.604676         2.0887e-08   5.0671e-03
211677 5.328810         9.8946e-08   2.4004e-02
211714 5.604676         2.0887e-08   5.0671e-03
211747 5.339128         9.3478e-08   2.2677e-02
211980 5.348509         8.8762e-08   2.1533e-02
211985 6.248560         4.1494e-10   1.0066e-04
212089 5.348509         8.8762e-08   2.1533e-02
212213 5.450512         5.0274e-08   1.2196e-02
212301 5.348509         8.8762e-08   2.1533e-02
212613 5.604676         2.0887e-08   5.0671e-03
212622 5.339128         9.3478e-08   2.2677e-02
212723 5.322969         1.0218e-07   2.4788e-02
212894 5.264444         1.4073e-07   3.4141e-02
212925 5.348509         8.8762e-08   2.1533e-02
212954 5.489663         4.0310e-08   9.7791e-03
213225 5.604676         2.0887e-08   5.0671e-03
213275 6.066894         1.3060e-09   3.1683e-04
213364 5.604676         2.0887e-08   5.0671e-03
213373 5.925387         3.1198e-09   7.5685e-04
213571 6.498550         8.1254e-11   1.9712e-05
214141 6.335678         2.3671e-10   5.7425e-05
215785 6.335678         2.3671e-10   5.7425e-05
216164 6.060494         1.3590e-09   3.2969e-04
216253 6.236648         4.4778e-10   1.0863e-04
217311 5.711760         1.1194e-08   2.7157e-03
217347 5.339128         9.3478e-08   2.2677e-02
217454 5.284036         1.2648e-07   3.0683e-02
217584 6.001158         1.9619e-09   4.7595e-04
217599 5.794957         6.8423e-09   1.6599e-03
217607 6.762523         1.3591e-11   3.2972e-06
217611 5.264444         1.4073e-07   3.4141e-02
217618 5.683534         1.3209e-08   3.2044e-03
217713 5.213536         1.8543e-07   4.4984e-02
217851 5.339128         9.3478e-08   2.2677e-02
218394 5.604676         2.0887e-08   5.0671e-03
218490 5.604676         2.0887e-08   5.0671e-03
218510 5.656435         1.5472e-08   3.7535e-03
218547 6.686751         2.2867e-11   5.5474e-06
218573 5.424533         5.8162e-08   1.4110e-02
219131 6.808124         9.9108e-12   2.4043e-06
219278 7.008628         2.4129e-12   5.8536e-07
219414 5.408008         6.3790e-08   1.5475e-02
219423 5.226784         1.7263e-07   4.1878e-02
219430 5.295950         1.1850e-07   2.8748e-02
219503 6.612054         3.7981e-11   9.2139e-06
219594 6.066894         1.3060e-09   3.1683e-04
219631 5.423201         5.8597e-08   1.4215e-02
219812 5.431844         5.5828e-08   1.3544e-02
219813 5.328810         9.8946e-08   2.4004e-02
219859 5.383021         7.3314e-08   1.7786e-02
219872 5.803340         6.5087e-09   1.5790e-03
219912 5.264444         1.4073e-07   3.4141e-02
219990 5.431844         5.5828e-08   1.3544e-02
219997 5.604676         2.0887e-08   5.0671e-03
220038 5.264444         1.4073e-07   3.4141e-02
220168 5.367298         7.9998e-08   1.9407e-02
220169 5.367298         7.9998e-08   1.9407e-02
220484 5.604676         2.0887e-08   5.0671e-03
220556 5.383021         7.3314e-08   1.7786e-02
220715 5.401411         6.6181e-08   1.6055e-02
220870 5.604676         2.0887e-08   5.0671e-03
221087 5.339128         9.3478e-08   2.2677e-02
221167 5.604676         2.0887e-08   5.0671e-03
222674 6.546362         5.9072e-11   1.4331e-05
222694 6.877230         6.1174e-12   1.4841e-06
224111 6.149339         7.7927e-10   1.8905e-04
224424 6.296898         3.0418e-10   7.3792e-05
224484 6.945295         3.7861e-12   9.1850e-07
224485 6.335678         2.3671e-10   5.7425e-05
224501 7.136039         9.6326e-13   2.3368e-07
225581 6.132428         8.6681e-10   2.1028e-04
226135 5.264444         1.4073e-07   3.4141e-02
226235 5.604676         2.0887e-08   5.0671e-03
226247 6.112563         9.8192e-10   2.3821e-04
226386 5.607745         2.0520e-08   4.9781e-03
226408 6.716487         1.8657e-11   4.5260e-06
226653 5.383021         7.3314e-08   1.7786e-02
226657 6.932289         4.1511e-12   1.0070e-06
226674 7.016322         2.2838e-12   5.5403e-07
226759 5.264444         1.4073e-07   3.4141e-02
226858 5.683534         1.3209e-08   3.2044e-03
226859 6.001158         1.9619e-09   4.7595e-04
226861 6.248560         4.1494e-10   1.0066e-04
226865 5.604676         2.0887e-08   5.0671e-03
227299 5.604676         2.0887e-08   5.0671e-03
227425 6.693946         2.1770e-11   5.2813e-06
228086 5.416978         6.0672e-08   1.4719e-02
228118 5.639869         1.7037e-08   4.1330e-03
228213 5.432711         5.5557e-08   1.3478e-02
228293 5.235425         1.6474e-07   3.9966e-02
228478 5.348509         8.8762e-08   2.1533e-02
228539 5.634690         1.7557e-08   4.2592e-03
228814 5.304473         1.1310e-07   2.7437e-02
229808 6.496371         8.2439e-11   1.9999e-05
229833 6.529421         6.6154e-11   1.6049e-05
229867 6.419966         1.3655e-10   3.3128e-05
229952 6.043826         1.5072e-09   3.6564e-04
230037 5.918027         3.2626e-09   7.9150e-04
230038 5.736711         9.6647e-09   2.3446e-03
230081 6.248560         4.1494e-10   1.0066e-04
230489 6.276571         3.4670e-10   8.4108e-05
230795 7.189800         6.5072e-13   1.5786e-07
233090 6.335658         2.3674e-10   5.7433e-05
233962 6.412536         1.4338e-10   3.4783e-05
234445 6.695296         2.1570e-11   5.2328e-06
234446 6.713648         1.9023e-11   4.6150e-06
234527 6.001158         1.9619e-09   4.7595e-04
234609 5.199987         1.9946e-07   4.8389e-02
234828 5.328810         9.8946e-08   2.4004e-02
234902 6.066894         1.3060e-09   3.1683e-04
234918 5.604676         2.0887e-08   5.0671e-03
234984 6.095185         1.0947e-09   2.6558e-04
235347 5.604676         2.0887e-08   5.0671e-03
235372 6.066894         1.3060e-09   3.1683e-04
236368 6.953808         3.5645e-12   8.6473e-07
236553 5.368858         7.9309e-08   1.9240e-02
236630 5.733752         9.8349e-09   2.3859e-03
236697 5.795814         6.8074e-09   1.6514e-03
237279 5.336274         9.4961e-08   2.3037e-02
237281 5.826003         5.6842e-09   1.3790e-03
237683 5.302204         1.1451e-07   2.7780e-02
238239 5.604676         2.0887e-08   5.0671e-03
238247 5.604676         2.0887e-08   5.0671e-03
238449 5.466040         4.6065e-08   1.1175e-02
239324 5.714732         1.1001e-08   2.6687e-03
240799 6.757034         1.4116e-11   3.4245e-06
240829 6.335678         2.3671e-10   5.7425e-05
240866 6.452165         1.1047e-10   2.6799e-05
241123 5.898179         3.6802e-09   8.9280e-04
241647 5.251824         1.5073e-07   3.6566e-02
241781 5.430199         5.6345e-08   1.3669e-02

[1] 231177     16

plot of chunk unnamed-chunk-12

Removing Outliers

After removing outliers, same model gave an adjusted R square of 41.67%


Call:
lm(formula = fulldata.or$Sales.New ~ fulldata.or$Fridge.Volume + 
    fulldata.or$TownClass + fulldata.or$RE_new + fulldata.or$State + 
    fulldata.or$TownClass * fulldata.or$Fridge.Volume + fulldata.or$RE_new * 
    fulldata.or$Fridge.Volume)

Residuals:
    Min      1Q  Median      3Q     Max 
-249831  -21445   -9691    9490  440669 

Coefficients:
                                                                             Estimate
(Intercept)                                                                 19811.840
fulldata.or$Fridge.Volume                                                     391.852
fulldata.or$TownClassGOLD                                                    2891.806
fulldata.or$TownClassSilver                                                 -6215.705
fulldata.or$TownClassSILVER                                                  -425.663
fulldata.or$TownClassTITANIUM                                                9910.971
fulldata.or$RE_newCHEMIST                                                   12180.896
fulldata.or$RE_newFOOD STORE                                               104353.855
fulldata.or$RE_newHIGH END GROCER                                           94418.538
fulldata.or$RE_newLOW END GROCER                                             -969.380
fulldata.or$StateGujarat                                                    -4416.225
fulldata.or$StateMadhya Pradesh                                             -5717.344
fulldata.or$StateMaharashtra                                                 1972.207
fulldata.or$Fridge.Volume:fulldata.or$TownClassGOLD                            53.519
fulldata.or$Fridge.Volume:fulldata.or$TownClassSilver                         -85.377
fulldata.or$Fridge.Volume:fulldata.or$TownClassSILVER                          35.607
fulldata.or$Fridge.Volume:fulldata.or$TownClassTITANIUM                         2.754
fulldata.or$Fridge.Volume:fulldata.or$RE_newCHEMIST                          -186.412
fulldata.or$Fridge.Volume:fulldata.or$RE_newFOOD STORE                        -86.806
fulldata.or$Fridge.Volume:fulldata.or$RE_newHIGH END GROCER                  -175.396
fulldata.or$Fridge.Volume:fulldata.or$RE_newLOW END GROCER                   -278.578
                                                                           Std. Error
(Intercept)                                                                   977.369
fulldata.or$Fridge.Volume                                                       8.522
fulldata.or$TownClassGOLD                                                     550.067
fulldata.or$TownClassSilver                                                  1823.039
fulldata.or$TownClassSILVER                                                   578.256
fulldata.or$TownClassTITANIUM                                                 505.467
fulldata.or$RE_newCHEMIST                                                     614.223
fulldata.or$RE_newFOOD STORE                                                  994.906
fulldata.or$RE_newHIGH END GROCER                                             825.331
fulldata.or$RE_newLOW END GROCER                                              503.294
fulldata.or$StateGujarat                                                      785.119
fulldata.or$StateMadhya Pradesh                                               798.565
fulldata.or$StateMaharashtra                                                  757.900
fulldata.or$Fridge.Volume:fulldata.or$TownClassGOLD                             7.808
fulldata.or$Fridge.Volume:fulldata.or$TownClassSilver                          19.030
fulldata.or$Fridge.Volume:fulldata.or$TownClassSILVER                           8.513
fulldata.or$Fridge.Volume:fulldata.or$TownClassTITANIUM                         7.376
fulldata.or$Fridge.Volume:fulldata.or$RE_newCHEMIST                             5.766
fulldata.or$Fridge.Volume:fulldata.or$RE_newFOOD STORE                          6.386
fulldata.or$Fridge.Volume:fulldata.or$RE_newHIGH END GROCER                     6.128
fulldata.or$Fridge.Volume:fulldata.or$RE_newLOW END GROCER                      5.200
                                                                           t value
(Intercept)                                                                 20.271
fulldata.or$Fridge.Volume                                                   45.983
fulldata.or$TownClassGOLD                                                    5.257
fulldata.or$TownClassSilver                                                 -3.410
fulldata.or$TownClassSILVER                                                 -0.736
fulldata.or$TownClassTITANIUM                                               19.608
fulldata.or$RE_newCHEMIST                                                   19.831
fulldata.or$RE_newFOOD STORE                                               104.888
fulldata.or$RE_newHIGH END GROCER                                          114.401
fulldata.or$RE_newLOW END GROCER                                            -1.926
fulldata.or$StateGujarat                                                    -5.625
fulldata.or$StateMadhya Pradesh                                             -7.160
fulldata.or$StateMaharashtra                                                 2.602
fulldata.or$Fridge.Volume:fulldata.or$TownClassGOLD                          6.854
fulldata.or$Fridge.Volume:fulldata.or$TownClassSilver                       -4.486
fulldata.or$Fridge.Volume:fulldata.or$TownClassSILVER                        4.183
fulldata.or$Fridge.Volume:fulldata.or$TownClassTITANIUM                      0.373
fulldata.or$Fridge.Volume:fulldata.or$RE_newCHEMIST                        -32.331
fulldata.or$Fridge.Volume:fulldata.or$RE_newFOOD STORE                     -13.592
fulldata.or$Fridge.Volume:fulldata.or$RE_newHIGH END GROCER                -28.621
fulldata.or$Fridge.Volume:fulldata.or$RE_newLOW END GROCER                 -53.574
                                                                           Pr(>|t|)
(Intercept)                                                                 < 2e-16
fulldata.or$Fridge.Volume                                                   < 2e-16
fulldata.or$TownClassGOLD                                                  1.46e-07
fulldata.or$TownClassSilver                                                0.000651
fulldata.or$TownClassSILVER                                                0.461661
fulldata.or$TownClassTITANIUM                                               < 2e-16
fulldata.or$RE_newCHEMIST                                                   < 2e-16
fulldata.or$RE_newFOOD STORE                                                < 2e-16
fulldata.or$RE_newHIGH END GROCER                                           < 2e-16
fulldata.or$RE_newLOW END GROCER                                           0.054097
fulldata.or$StateGujarat                                                   1.86e-08
fulldata.or$StateMadhya Pradesh                                            8.12e-13
fulldata.or$StateMaharashtra                                               0.009263
fulldata.or$Fridge.Volume:fulldata.or$TownClassGOLD                        7.20e-12
fulldata.or$Fridge.Volume:fulldata.or$TownClassSilver                      7.25e-06
fulldata.or$Fridge.Volume:fulldata.or$TownClassSILVER                      2.88e-05
fulldata.or$Fridge.Volume:fulldata.or$TownClassTITANIUM                    0.708825
fulldata.or$Fridge.Volume:fulldata.or$RE_newCHEMIST                         < 2e-16
fulldata.or$Fridge.Volume:fulldata.or$RE_newFOOD STORE                      < 2e-16
fulldata.or$Fridge.Volume:fulldata.or$RE_newHIGH END GROCER                 < 2e-16
fulldata.or$Fridge.Volume:fulldata.or$RE_newLOW END GROCER                  < 2e-16

(Intercept)                                                                ***
fulldata.or$Fridge.Volume                                                  ***
fulldata.or$TownClassGOLD                                                  ***
fulldata.or$TownClassSilver                                                ***
fulldata.or$TownClassSILVER                                                   
fulldata.or$TownClassTITANIUM                                              ***
fulldata.or$RE_newCHEMIST                                                  ***
fulldata.or$RE_newFOOD STORE                                               ***
fulldata.or$RE_newHIGH END GROCER                                          ***
fulldata.or$RE_newLOW END GROCER                                           .  
fulldata.or$StateGujarat                                                   ***
fulldata.or$StateMadhya Pradesh                                            ***
fulldata.or$StateMaharashtra                                               ** 
fulldata.or$Fridge.Volume:fulldata.or$TownClassGOLD                        ***
fulldata.or$Fridge.Volume:fulldata.or$TownClassSilver                      ***
fulldata.or$Fridge.Volume:fulldata.or$TownClassSILVER                      ***
fulldata.or$Fridge.Volume:fulldata.or$TownClassTITANIUM                       
fulldata.or$Fridge.Volume:fulldata.or$RE_newCHEMIST                        ***
fulldata.or$Fridge.Volume:fulldata.or$RE_newFOOD STORE                     ***
fulldata.or$Fridge.Volume:fulldata.or$RE_newHIGH END GROCER                ***
fulldata.or$Fridge.Volume:fulldata.or$RE_newLOW END GROCER                 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Residual standard error: 61770 on 231156 degrees of freedom
Multiple R-squared:  0.3894,    Adjusted R-squared:  0.3894 
F-statistic:  7372 on 20 and 231156 DF,  p-value: < 2.2e-16

Checking Linearity

** 1. Model does not seem to be linear visually **

plot of chunk unnamed-chunk-14

Checking Normality

** Data seems to be deviating from the normality at the extreme points ** plot of chunk unnamed-chunk-15

Testing for NonLiearity

** From Anderson Test and Shapiro- wilks Test it was found that Residuals are not following a normal distribution since p <.05 **


    Anderson-Darling normality test

data:  fulldata.or$Sales.New
A = 30989, p-value < 2.2e-16

BoxCox Transformation

Lambda Value is 0, so log transform was taken on Sales.New

Box-Cox Transformation

231177 data points used to estimate Lambda

Input data summary:
   Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
   1000    7376   19600   48345   50975  454670 

Largest/Smallest: 455 
Sample Skewness: 3.28 

Estimated Lambda: 0 
With fudge factor, Lambda = 0 will be used for transformations

Running regression after transformation


Call:
lm(formula = fulldata.or$Sales.New.Log ~ fulldata.or$Fridge.Volume + 
    fulldata.or$TownClass + fulldata.or$RE_new + fulldata.or$State + 
    fulldata.or$TownClass * fulldata.or$Fridge.Volume + fulldata.or$RE_new * 
    fulldata.or$Fridge.Volume)

Residuals:
    Min      1Q  Median      3Q     Max 
-5.2360 -0.7625  0.0884  0.8304  3.7950 

Coefficients:
                                                                             Estimate
(Intercept)                                                                 9.412e+00
fulldata.or$Fridge.Volume                                                   6.458e-03
fulldata.or$TownClassGOLD                                                  -3.299e-02
fulldata.or$TownClassSilver                                                -2.507e-02
fulldata.or$TownClassSILVER                                                -1.458e-01
fulldata.or$TownClassTITANIUM                                               1.299e-01
fulldata.or$RE_newCHEMIST                                                   3.311e-01
fulldata.or$RE_newFOOD STORE                                                1.798e+00
fulldata.or$RE_newHIGH END GROCER                                           1.881e+00
fulldata.or$RE_newLOW END GROCER                                            4.109e-02
fulldata.or$StateGujarat                                                   -7.451e-02
fulldata.or$StateMadhya Pradesh                                            -1.033e-01
fulldata.or$StateMaharashtra                                                6.443e-02
fulldata.or$Fridge.Volume:fulldata.or$TownClassGOLD                        -7.948e-05
fulldata.or$Fridge.Volume:fulldata.or$TownClassSilver                      -2.256e-03
fulldata.or$Fridge.Volume:fulldata.or$TownClassSILVER                       2.423e-04
fulldata.or$Fridge.Volume:fulldata.or$TownClassTITANIUM                    -1.391e-03
fulldata.or$Fridge.Volume:fulldata.or$RE_newCHEMIST                        -1.399e-03
fulldata.or$Fridge.Volume:fulldata.or$RE_newFOOD STORE                     -3.661e-03
fulldata.or$Fridge.Volume:fulldata.or$RE_newHIGH END GROCER                -4.401e-03
fulldata.or$Fridge.Volume:fulldata.or$RE_newLOW END GROCER                 -1.752e-03
                                                                           Std. Error
(Intercept)                                                                 1.790e-02
fulldata.or$Fridge.Volume                                                   1.561e-04
fulldata.or$TownClassGOLD                                                   1.008e-02
fulldata.or$TownClassSilver                                                 3.339e-02
fulldata.or$TownClassSILVER                                                 1.059e-02
fulldata.or$TownClassTITANIUM                                               9.259e-03
fulldata.or$RE_newCHEMIST                                                   1.125e-02
fulldata.or$RE_newFOOD STORE                                                1.822e-02
fulldata.or$RE_newHIGH END GROCER                                           1.512e-02
fulldata.or$RE_newLOW END GROCER                                            9.219e-03
fulldata.or$StateGujarat                                                    1.438e-02
fulldata.or$StateMadhya Pradesh                                             1.463e-02
fulldata.or$StateMaharashtra                                                1.388e-02
fulldata.or$Fridge.Volume:fulldata.or$TownClassGOLD                         1.430e-04
fulldata.or$Fridge.Volume:fulldata.or$TownClassSilver                       3.486e-04
fulldata.or$Fridge.Volume:fulldata.or$TownClassSILVER                       1.559e-04
fulldata.or$Fridge.Volume:fulldata.or$TownClassTITANIUM                     1.351e-04
fulldata.or$Fridge.Volume:fulldata.or$RE_newCHEMIST                         1.056e-04
fulldata.or$Fridge.Volume:fulldata.or$RE_newFOOD STORE                      1.170e-04
fulldata.or$Fridge.Volume:fulldata.or$RE_newHIGH END GROCER                 1.123e-04
fulldata.or$Fridge.Volume:fulldata.or$RE_newLOW END GROCER                  9.525e-05
                                                                           t value
(Intercept)                                                                525.710
fulldata.or$Fridge.Volume                                                   41.374
fulldata.or$TownClassGOLD                                                   -3.274
fulldata.or$TownClassSilver                                                 -0.751
fulldata.or$TownClassSILVER                                                -13.769
fulldata.or$TownClassTITANIUM                                               14.026
fulldata.or$RE_newCHEMIST                                                   29.427
fulldata.or$RE_newFOOD STORE                                                98.667
fulldata.or$RE_newHIGH END GROCER                                          124.405
fulldata.or$RE_newLOW END GROCER                                             4.458
fulldata.or$StateGujarat                                                    -5.181
fulldata.or$StateMadhya Pradesh                                             -7.064
fulldata.or$StateMaharashtra                                                 4.641
fulldata.or$Fridge.Volume:fulldata.or$TownClassGOLD                         -0.556
fulldata.or$Fridge.Volume:fulldata.or$TownClassSilver                       -6.473
fulldata.or$Fridge.Volume:fulldata.or$TownClassSILVER                        1.554
fulldata.or$Fridge.Volume:fulldata.or$TownClassTITANIUM                    -10.297
fulldata.or$Fridge.Volume:fulldata.or$RE_newCHEMIST                        -13.243
fulldata.or$Fridge.Volume:fulldata.or$RE_newFOOD STORE                     -31.293
fulldata.or$Fridge.Volume:fulldata.or$RE_newHIGH END GROCER                -39.205
fulldata.or$Fridge.Volume:fulldata.or$RE_newLOW END GROCER                 -18.393
                                                                           Pr(>|t|)
(Intercept)                                                                 < 2e-16
fulldata.or$Fridge.Volume                                                   < 2e-16
fulldata.or$TownClassGOLD                                                   0.00106
fulldata.or$TownClassSilver                                                 0.45279
fulldata.or$TownClassSILVER                                                 < 2e-16
fulldata.or$TownClassTITANIUM                                               < 2e-16
fulldata.or$RE_newCHEMIST                                                   < 2e-16
fulldata.or$RE_newFOOD STORE                                                < 2e-16
fulldata.or$RE_newHIGH END GROCER                                           < 2e-16
fulldata.or$RE_newLOW END GROCER                                           8.29e-06
fulldata.or$StateGujarat                                                   2.21e-07
fulldata.or$StateMadhya Pradesh                                            1.62e-12
fulldata.or$StateMaharashtra                                               3.46e-06
fulldata.or$Fridge.Volume:fulldata.or$TownClassGOLD                         0.57840
fulldata.or$Fridge.Volume:fulldata.or$TownClassSilver                      9.61e-11
fulldata.or$Fridge.Volume:fulldata.or$TownClassSILVER                       0.12026
fulldata.or$Fridge.Volume:fulldata.or$TownClassTITANIUM                     < 2e-16
fulldata.or$Fridge.Volume:fulldata.or$RE_newCHEMIST                         < 2e-16
fulldata.or$Fridge.Volume:fulldata.or$RE_newFOOD STORE                      < 2e-16
fulldata.or$Fridge.Volume:fulldata.or$RE_newHIGH END GROCER                 < 2e-16
fulldata.or$Fridge.Volume:fulldata.or$RE_newLOW END GROCER                  < 2e-16

(Intercept)                                                                ***
fulldata.or$Fridge.Volume                                                  ***
fulldata.or$TownClassGOLD                                                  ** 
fulldata.or$TownClassSilver                                                   
fulldata.or$TownClassSILVER                                                ***
fulldata.or$TownClassTITANIUM                                              ***
fulldata.or$RE_newCHEMIST                                                  ***
fulldata.or$RE_newFOOD STORE                                               ***
fulldata.or$RE_newHIGH END GROCER                                          ***
fulldata.or$RE_newLOW END GROCER                                           ***
fulldata.or$StateGujarat                                                   ***
fulldata.or$StateMadhya Pradesh                                            ***
fulldata.or$StateMaharashtra                                               ***
fulldata.or$Fridge.Volume:fulldata.or$TownClassGOLD                           
fulldata.or$Fridge.Volume:fulldata.or$TownClassSilver                      ***
fulldata.or$Fridge.Volume:fulldata.or$TownClassSILVER                         
fulldata.or$Fridge.Volume:fulldata.or$TownClassTITANIUM                    ***
fulldata.or$Fridge.Volume:fulldata.or$RE_newCHEMIST                        ***
fulldata.or$Fridge.Volume:fulldata.or$RE_newFOOD STORE                     ***
fulldata.or$Fridge.Volume:fulldata.or$RE_newHIGH END GROCER                ***
fulldata.or$Fridge.Volume:fulldata.or$RE_newLOW END GROCER                 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Residual standard error: 1.131 on 231156 degrees of freedom
Multiple R-squared:  0.2932,    Adjusted R-squared:  0.2932 
F-statistic:  4795 on 20 and 231156 DF,  p-value: < 2.2e-16

Checking Linearity

The normality has been solved, however linearity still remains an issue, due to which the adjusted R square has gone down to 29.2.

Anderson Test plot of chunk unnamed-chunk-19


    Anderson-Darling normality test

data:  fulldata.or$Sales.New.Log
A = 225.88, p-value < 2.2e-16

Model does not seem to be linear visually

Checking Normality

plot of chunk unnamed-chunk-20 Data seems to be deviating from the normality at the extreme points

Running Regression 

fit6 <- lm(fulldata.or$Sales.New.Log ~ fulldata.or$Fridge.Volume + fulldata.or$RE_new + fulldata.or$State + fulldata.or$Has.Fridge*fulldata.or$TownClass)
summary(fit6)


Call:
lm(formula = fulldata.or$Sales.New.Log ~ fulldata.or$Fridge.Volume + 
    fulldata.or$RE_new + fulldata.or$State + fulldata.or$Has.Fridge * 
    fulldata.or$TownClass)

Residuals:
    Min      1Q  Median      3Q     Max 
-4.8504 -0.6060  0.0525  0.6542  4.0409 

Coefficients:
                                                        Estimate
(Intercept)                                            9.361e+00
fulldata.or$Fridge.Volume                             -1.110e-04
fulldata.or$RE_newCHEMIST                              1.858e-01
fulldata.or$RE_newFOOD STORE                           1.088e+00
fulldata.or$RE_newHIGH END GROCER                      1.010e+00
fulldata.or$RE_newLOW END GROCER                      -7.636e-02
fulldata.or$StateGujarat                              -2.470e-02
fulldata.or$StateMadhya Pradesh                       -1.370e-01
fulldata.or$StateMaharashtra                           1.269e-02
fulldata.or$Has.Fridge1                                1.126e+00
fulldata.or$TownClassGOLD                             -2.737e-01
fulldata.or$TownClassSilver                            4.447e-02
fulldata.or$TownClassSILVER                           -2.412e-01
fulldata.or$TownClassTITANIUM                         -1.713e-01
fulldata.or$Has.Fridge1:fulldata.or$TownClassGOLD      3.729e-01
fulldata.or$Has.Fridge1:fulldata.or$TownClassSilver   -3.355e-01
fulldata.or$Has.Fridge1:fulldata.or$TownClassSILVER    3.159e-01
fulldata.or$Has.Fridge1:fulldata.or$TownClassTITANIUM  3.566e-01
                                                      Std. Error t value
(Intercept)                                            1.567e-02 597.223
fulldata.or$Fridge.Volume                              2.632e-05  -4.215
fulldata.or$RE_newCHEMIST                              8.918e-03  20.840
fulldata.or$RE_newFOOD STORE                           1.161e-02  93.724
fulldata.or$RE_newHIGH END GROCER                      1.061e-02  95.180
fulldata.or$RE_newLOW END GROCER                       7.402e-03 -10.315
fulldata.or$StateGujarat                               1.242e-02  -1.988
fulldata.or$StateMadhya Pradesh                        1.264e-02 -10.846
fulldata.or$StateMaharashtra                           1.199e-02   1.058
fulldata.or$Has.Fridge1                                1.539e-02  73.116
fulldata.or$TownClassGOLD                              1.000e-02 -27.360
fulldata.or$TownClassSilver                            3.353e-02   1.326
fulldata.or$TownClassSILVER                            1.027e-02 -23.484
fulldata.or$TownClassTITANIUM                          9.091e-03 -18.845
fulldata.or$Has.Fridge1:fulldata.or$TownClassGOLD      1.752e-02  21.290
fulldata.or$Has.Fridge1:fulldata.or$TownClassSilver    5.409e-02  -6.202
fulldata.or$Has.Fridge1:fulldata.or$TownClassSILVER    1.886e-02  16.747
fulldata.or$Has.Fridge1:fulldata.or$TownClassTITANIUM  1.634e-02  21.824
                                                      Pr(>|t|)    
(Intercept)                                            < 2e-16 ***
fulldata.or$Fridge.Volume                             2.49e-05 ***
fulldata.or$RE_newCHEMIST                              < 2e-16 ***
fulldata.or$RE_newFOOD STORE                           < 2e-16 ***
fulldata.or$RE_newHIGH END GROCER                      < 2e-16 ***
fulldata.or$RE_newLOW END GROCER                       < 2e-16 ***
fulldata.or$StateGujarat                                0.0468 *  
fulldata.or$StateMadhya Pradesh                        < 2e-16 ***
fulldata.or$StateMaharashtra                            0.2899    
fulldata.or$Has.Fridge1                                < 2e-16 ***
fulldata.or$TownClassGOLD                              < 2e-16 ***
fulldata.or$TownClassSilver                             0.1848    
fulldata.or$TownClassSILVER                            < 2e-16 ***
fulldata.or$TownClassTITANIUM                          < 2e-16 ***
fulldata.or$Has.Fridge1:fulldata.or$TownClassGOLD      < 2e-16 ***
fulldata.or$Has.Fridge1:fulldata.or$TownClassSilver   5.59e-10 ***
fulldata.or$Has.Fridge1:fulldata.or$TownClassSILVER    < 2e-16 ***
fulldata.or$Has.Fridge1:fulldata.or$TownClassTITANIUM  < 2e-16 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Residual standard error: 0.9779 on 231159 degrees of freedom
Multiple R-squared:  0.4721,    Adjusted R-squared:  0.4721 
F-statistic: 1.216e+04 on 17 and 231159 DF,  p-value: < 2.2e-16

Results

fulldata.or$Has.Fridge*fulldata.or$RE_new - w/0 47.29

fulldata.or$Has.Fridge*fulldata.or$State - w/o 47.29

fulldata.or$Has.Fridge*fulldata.or$TownClass - w/o all interaction 28

all FridgeVol interactions - 28

fulldata.or$Fridge.Volume:fulldata.or$State w/o - 29.2

fulldata.or$Fridge.Volume*fulldata.or$RE_new w/o - 28.2

Step function for finding the best model


Call:
lm(formula = fulldata.or$Sales.New.Log ~ fulldata.or$Fridge.Volume + 
    fulldata.or$RE_new + fulldata.or$State + fulldata.or$Has.Fridge * 
    fulldata.or$TownClass)

Residuals:
    Min      1Q  Median      3Q     Max 
-4.8504 -0.6060  0.0525  0.6542  4.0409 

Coefficients:
                                                        Estimate
(Intercept)                                            9.361e+00
fulldata.or$Fridge.Volume                             -1.110e-04
fulldata.or$RE_newCHEMIST                              1.858e-01
fulldata.or$RE_newFOOD STORE                           1.088e+00
fulldata.or$RE_newHIGH END GROCER                      1.010e+00
fulldata.or$RE_newLOW END GROCER                      -7.636e-02
fulldata.or$StateGujarat                              -2.470e-02
fulldata.or$StateMadhya Pradesh                       -1.370e-01
fulldata.or$StateMaharashtra                           1.269e-02
fulldata.or$Has.Fridge1                                1.126e+00
fulldata.or$TownClassGOLD                             -2.737e-01
fulldata.or$TownClassSilver                            4.447e-02
fulldata.or$TownClassSILVER                           -2.412e-01
fulldata.or$TownClassTITANIUM                         -1.713e-01
fulldata.or$Has.Fridge1:fulldata.or$TownClassGOLD      3.729e-01
fulldata.or$Has.Fridge1:fulldata.or$TownClassSilver   -3.355e-01
fulldata.or$Has.Fridge1:fulldata.or$TownClassSILVER    3.159e-01
fulldata.or$Has.Fridge1:fulldata.or$TownClassTITANIUM  3.566e-01
                                                      Std. Error t value
(Intercept)                                            1.567e-02 597.223
fulldata.or$Fridge.Volume                              2.632e-05  -4.215
fulldata.or$RE_newCHEMIST                              8.918e-03  20.840
fulldata.or$RE_newFOOD STORE                           1.161e-02  93.724
fulldata.or$RE_newHIGH END GROCER                      1.061e-02  95.180
fulldata.or$RE_newLOW END GROCER                       7.402e-03 -10.315
fulldata.or$StateGujarat                               1.242e-02  -1.988
fulldata.or$StateMadhya Pradesh                        1.264e-02 -10.846
fulldata.or$StateMaharashtra                           1.199e-02   1.058
fulldata.or$Has.Fridge1                                1.539e-02  73.116
fulldata.or$TownClassGOLD                              1.000e-02 -27.360
fulldata.or$TownClassSilver                            3.353e-02   1.326
fulldata.or$TownClassSILVER                            1.027e-02 -23.484
fulldata.or$TownClassTITANIUM                          9.091e-03 -18.845
fulldata.or$Has.Fridge1:fulldata.or$TownClassGOLD      1.752e-02  21.290
fulldata.or$Has.Fridge1:fulldata.or$TownClassSilver    5.409e-02  -6.202
fulldata.or$Has.Fridge1:fulldata.or$TownClassSILVER    1.886e-02  16.747
fulldata.or$Has.Fridge1:fulldata.or$TownClassTITANIUM  1.634e-02  21.824
                                                      Pr(>|t|)    
(Intercept)                                            < 2e-16 ***
fulldata.or$Fridge.Volume                             2.49e-05 ***
fulldata.or$RE_newCHEMIST                              < 2e-16 ***
fulldata.or$RE_newFOOD STORE                           < 2e-16 ***
fulldata.or$RE_newHIGH END GROCER                      < 2e-16 ***
fulldata.or$RE_newLOW END GROCER                       < 2e-16 ***
fulldata.or$StateGujarat                                0.0468 *  
fulldata.or$StateMadhya Pradesh                        < 2e-16 ***
fulldata.or$StateMaharashtra                            0.2899    
fulldata.or$Has.Fridge1                                < 2e-16 ***
fulldata.or$TownClassGOLD                              < 2e-16 ***
fulldata.or$TownClassSilver                             0.1848    
fulldata.or$TownClassSILVER                            < 2e-16 ***
fulldata.or$TownClassTITANIUM                          < 2e-16 ***
fulldata.or$Has.Fridge1:fulldata.or$TownClassGOLD      < 2e-16 ***
fulldata.or$Has.Fridge1:fulldata.or$TownClassSilver   5.59e-10 ***
fulldata.or$Has.Fridge1:fulldata.or$TownClassSILVER    < 2e-16 ***
fulldata.or$Has.Fridge1:fulldata.or$TownClassTITANIUM  < 2e-16 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Residual standard error: 0.9779 on 231159 degrees of freedom
Multiple R-squared:  0.4721,    Adjusted R-squared:  0.4721 
F-statistic: 1.216e+04 on 17 and 231159 DF,  p-value: < 2.2e-16

Checking for Multicollinearity

                                                  GVIF Df GVIF^(1/(2*Df))
fulldata.or$Fridge.Volume                     1.535902  1        1.239315
fulldata.or$RE_new                            1.297861  4        1.033127
fulldata.or$State                             1.208073  3        1.032006
fulldata.or$Has.Fridge                       14.144193  1        3.760877
fulldata.or$TownClass                         7.665911  4        1.289943
fulldata.or$Has.Fridge:fulldata.or$TownClass 71.817818  4        1.706196

Does not have multicollinearity

Checking Linearity

plot of chunk unnamed-chunk-24

Model seems to be linear visually compared to the previous model

Checking Normality

plot of chunk unnamed-chunk-25

The residual errors of the model are now normally distributed in comparison to our previous model

Checking heteroskedasticity

a1<-bptest(fit6)
a1


    studentized Breusch-Pagan test

data:  fit6
BP = 10156, df = 17, p-value < 2.2e-16

b1<-ncvTest(fit6)
b1

Non-constant Variance Score Test 
Variance formula: ~ fitted.values 
Chisquare = 241.809, Df = 1, p = < 2.22e-16

Data has heteroskedasticity

One-Way ANOVA

Error in eval(bysub, x, parent.frame()) : 
  object 'Has.Fridge.Factor' not found