R_stat_Time_based_data
Surya
2023-11-15
I am importing the libraries needed to run these notes.
library(tidyverse)## Warning: package 'dplyr' was built under R version 4.3.2## Warning: package 'lubridate' was built under R version 4.3.2## ── Attaching core tidyverse packages ──────────────────────── tidyverse 2.0.0 ──
## ✔ dplyr 1.1.3 ✔ readr 2.1.4
## ✔ forcats 1.0.0 ✔ stringr 1.5.0
## ✔ ggplot2 3.4.3 ✔ tibble 3.2.1
## ✔ lubridate 1.9.3 ✔ tidyr 1.3.0
## ✔ purrr 1.0.2
## ── Conflicts ────────────────────────────────────────── tidyverse_conflicts() ──
## ✖ dplyr::filter() masks stats::filter()
## ✖ dplyr::lag() masks stats::lag()
## ℹ Use the conflicted package (<http://conflicted.r-lib.org/>) to force all conflicts to become errorslibrary(readr)
library(tsibble)## Warning: package 'tsibble' was built under R version 4.3.2##
## Attaching package: 'tsibble'
##
## The following object is masked from 'package:lubridate':
##
## interval
##
## The following objects are masked from 'package:base':
##
## intersect, setdiff, unionlibrary(forecast)## Warning: package 'forecast' was built under R version 4.3.2## Registered S3 method overwritten by 'quantmod':
## method from
## as.zoo.data.frame zoolibrary(slider)## Warning: package 'slider' was built under R version 4.3.2my_data_3 <- read_delim("C:/Users/Surya CST/Documents/CSV_files/Bundy_Shoe_Shop.csv",delim=",",show_col_types = FALSE)## New names:
## • `` -> `...2`
## • `` -> `...3`
## • `` -> `...4`
## • `` -> `...5`
## • `` -> `...6`
## • `` -> `...7`
## • `` -> `...8`
## • `` -> `...9`
## • `` -> `...10`
## • `` -> `...11`
## • `` -> `...12`
## • `` -> `...13`
## • `` -> `...14`## Warning: One or more parsing issues, call `problems()` on your data frame for details,
## e.g.:
## dat <- vroom(...)
## problems(dat)# Print the modified data frame
head(my_data_3)## # A tibble: 6 × 14
## Inferential statistics…¹ ...2 ...3 ...4 ...5 ...6 ...7 ...8 ...9 ...10
## <chr> <chr> <chr> <dbl> <chr> <chr> <dbl> <chr> <dbl> <chr>
## 1 Al Bundy's shoe shop <NA> <NA> NA <NA> <NA> NA <NA> NA <NA>
## 2 <NA> <NA> <NA> NA <NA> <NA> NA <NA> NA <NA>
## 3 InvoiceNo Date Coun… NA Shop Gend… NA Size… NA "Uni…
## 4 52389 1/1/… Unit… 2152 UK2 Male 11 44 10.5 "$15…
## 5 52390 1/1/… Unit… 2230 US15 Male 11.5 44-45 11 "$19…
## 6 52391 1/1/… Cana… 2160 CAN7 Male 9.5 42-43 9 "$14…
## # ℹ abbreviated name: ¹​`Inferential statistics. Confidence intervals`
## # ℹ 4 more variables: ...11 <chr>, ...12 <dbl>, ...13 <dbl>, ...14 <chr>Cleaning my dataset
I am renaming my titles from{X1,X2} to {Invoice,Date},,etc to make the date more simple and clear.
new_names <- c("InvoiceNo",'Date', "Country", "ProductID",'Shop','Gender','Size(US)','Size (Europe)', 'Size (UK)','UnitPrice','Discount', 'Year','Month','SalePrice')
# Assign the new column names to the data frame
colnames(my_data_3) <- new_names
# Verify that the column names have been changed
colnames(my_data_3)## [1] "InvoiceNo" "Date" "Country" "ProductID"
## [5] "Shop" "Gender" "Size(US)" "Size (Europe)"
## [9] "Size (UK)" "UnitPrice" "Discount" "Year"
## [13] "Month" "SalePrice"I am removing the first 3 rows to remove null values and un-necessary titles for my data set
my_data_3 <- my_data_3[-c(1:3), ]
# Print the modified data frame
print(my_data_3)## # A tibble: 14,967 × 14
## InvoiceNo Date Country ProductID Shop Gender `Size(US)` `Size (Europe)`
## <chr> <chr> <chr> <dbl> <chr> <chr> <dbl> <chr>
## 1 52389 1/1/2014 United … 2152 UK2 Male 11 44
## 2 52390 1/1/2014 United … 2230 US15 Male 11.5 44-45
## 3 52391 1/1/2014 Canada 2160 CAN7 Male 9.5 42-43
## 4 52392 1/1/2014 United … 2234 US6 Female 9.5 40
## 5 52393 1/1/2014 United … 2222 UK4 Female 9 39-40
## 6 52394 1/1/2014 United … 2173 US15 Male 10.5 43-44
## 7 52395 1/2/2014 Germany 2200 GER2 Female 9 39-40
## 8 52396 1/2/2014 Canada 2238 CAN5 Male 10 43
## 9 52397 1/2/2014 United … 2191 US13 Male 10.5 43-44
## 10 52398 1/2/2014 United … 2237 UK1 Female 9 39-40
## # ℹ 14,957 more rows
## # ℹ 6 more variables: `Size (UK)` <dbl>, UnitPrice <chr>, Discount <chr>,
## # Year <dbl>, Month <dbl>, SalePrice <chr>my_data_3$SalePrice <- gsub("\\$", "", my_data_3$SalePrice)
my_data_3$SalePrice <- as.numeric(my_data_3$SalePrice)
class(my_data_3$SalePrice)## [1] "numeric"# removing $ for Unit Price
my_data_3$UnitPrice <- gsub("\\$", "", my_data_3$UnitPrice)
my_data_3$UnitPrice <- as.numeric(my_data_3$UnitPrice)
# Remove '%' from the Discount column
my_data_3$Discount <- gsub("%", "", my_data_3$Discount)
my_data_3$Discount <- as.numeric(my_data_3$Discount)
head(my_data_3$Discount)## [1] 0 20 20 0 0 0class(my_data_3$UnitPrice)## [1] "numeric"class(my_data_3$Discount)## [1] "numeric"1) Selection of date column
I have selected ‘date’ column in my dataset. It refers to when the customer bought the shoe.
2) Plotting response variable over time.
My response variable is SalePrice (price of shoe at which customers buy)
ggplot(my_data_3, aes(x = Date, y = SalePrice)) +
geom_line() +
labs(title = "Sale Price Over Time",
x = "Date",
y = "Sale Price ($)")
.
3)Creating a tsibble object.
my_tsibble <- tibble(
Date = my_data_3$Date,
SalePrice = my_data_3$SalePrice
)
print(my_tsibble)## # A tibble: 14,967 × 2
## Date SalePrice
## <chr> <dbl>
## 1 1/1/2014 159
## 2 1/1/2014 159.
## 3 1/1/2014 119.
## 4 1/1/2014 159
## 5 1/1/2014 159
## 6 1/1/2014 159
## 7 1/2/2014 179
## 8 1/2/2014 169
## 9 1/2/2014 139
## 10 1/2/2014 149
## # ℹ 14,957 more rowsFrom the above plotting between SalePrice($) vs Date, We can conclude that Sale of the shoes changes frequently as per the date, but the variations seems to be consistent.
4)Linear regression model between date and SalePrice
linear_model <- lm(SalePrice ~ Date, data = as.data.frame(my_tsibble))
summary(linear_model)##
## Call:
## lm(formula = SalePrice ~ Date, data = as.data.frame(my_tsibble))
##
## Residuals:
## Min 1Q Median 3Q Max
## -95.450 -21.934 2.139 25.428 78.325
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 1.524e+02 1.436e+01 10.611 <2e-16 ***
## Date1/1/2015 3.329e+00 1.957e+01 0.170 0.8650
## Date1/1/2016 5.880e+00 2.130e+01 0.276 0.7825
## Date1/10/2014 -2.015e+01 2.031e+01 -0.992 0.3212
## Date1/10/2015 -6.142e+00 1.759e+01 -0.349 0.7270
## Date1/10/2016 -8.004e+00 1.599e+01 -0.500 0.6168
## Date1/11/2014 5.983e+00 2.031e+01 0.295 0.7683
## Date1/11/2015 -6.211e+00 1.854e+01 -0.335 0.7376
## Date1/11/2016 1.889e-01 1.658e+01 0.011 0.9909
## Date1/12/2014 -1.102e+01 2.130e+01 -0.517 0.6049
## Date1/12/2015 -5.871e+00 1.957e+01 -0.300 0.7642
## Date1/12/2016 4.073e+00 1.593e+01 0.256 0.7982
## Date1/13/2014 -1.386e+01 1.957e+01 -0.708 0.4790
## Date1/13/2015 5.207e+00 1.717e+01 0.303 0.7616
## Date1/13/2016 -2.245e+01 1.620e+01 -1.386 0.1659
## Date1/14/2014 1.376e+01 1.957e+01 0.703 0.4821
## Date1/14/2015 1.043e+01 1.854e+01 0.563 0.5736
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## Date11/11/2015 -1.497e+01 1.620e+01 -0.924 0.3556
## Date11/11/2016 -1.277e+01 1.613e+01 -0.792 0.4285
## Date11/12/2014 -1.767e+01 2.031e+01 -0.870 0.3844
## Date11/12/2015 -2.703e+01 1.647e+01 -1.641 0.1009
## Date11/12/2016 -1.253e+01 1.647e+01 -0.761 0.4469
## Date11/13/2014 1.502e+01 2.031e+01 0.739 0.4597
## Date11/13/2015 -1.231e+01 1.717e+01 -0.717 0.4732
## Date11/13/2016 -1.060e+01 1.671e+01 -0.635 0.5257
## Date11/14/2014 -1.510e+01 2.031e+01 -0.743 0.4572
## Date11/14/2015 -1.344e+01 1.671e+01 -0.805 0.4211
## Date11/14/2016 -5.173e+00 1.785e+01 -0.290 0.7720
## Date11/15/2014 -6.075e+00 1.900e+01 -0.320 0.7492
## Date11/15/2015 -9.269e+00 1.736e+01 -0.534 0.5935
## Date11/15/2016 8.691e+00 1.785e+01 0.487 0.6264
## Date11/16/2014 6.820e+00 2.130e+01 0.320 0.7489
## Date11/16/2015 5.579e+00 1.717e+01 0.325 0.7452
## Date11/16/2016 6.875e-01 1.900e+01 0.036 0.9711
## Date11/17/2014 8.657e+00 1.957e+01 0.442 0.6583
## Date11/17/2015 -1.056e+01 1.736e+01 -0.608 0.5430
## Date11/17/2016 -1.138e+01 1.785e+01 -0.637 0.5238
## Date11/18/2014 -1.300e+00 2.130e+01 -0.061 0.9513
## Date11/18/2015 -5.644e+00 1.684e+01 -0.335 0.7375
## Date11/18/2016 -2.630e+00 1.817e+01 -0.145 0.8849
## Date11/19/2014 -2.547e+01 2.031e+01 -1.254 0.2099
## Date11/19/2015 -1.463e+01 1.736e+01 -0.843 0.3994
## Date11/19/2016 -1.181e+01 1.736e+01 -0.680 0.4965
## Date11/2/2014 1.126e+01 1.957e+01 0.575 0.5652
## Date11/2/2015 6.689e+00 1.658e+01 0.403 0.6867
## Date11/2/2016 -1.285e+01 1.593e+01 -0.806 0.4200
## Date11/20/2014 1.233e+01 2.031e+01 0.607 0.5437
## Date11/20/2015 -8.250e-01 1.759e+01 -0.047 0.9626
## Date11/20/2016 -1.025e+01 1.671e+01 -0.614 0.5394
## Date11/21/2014 1.063e+01 2.031e+01 0.524 0.6006
## Date11/21/2015 -1.458e+01 1.759e+01 -0.829 0.4073
## Date11/21/2016 3.567e+00 1.658e+01 0.215 0.8297
## Date11/22/2014 -3.001e+01 1.957e+01 -1.534 0.1252
## Date11/22/2015 -8.700e+00 1.638e+01 -0.531 0.5952
## Date11/22/2016 2.685e+00 1.736e+01 0.155 0.8771
## Date11/23/2014 -2.083e+01 1.957e+01 -1.064 0.2873
## Date11/23/2015 -7.507e+00 1.699e+01 -0.442 0.6587
## Date11/23/2016 -3.294e-01 1.671e+01 -0.020 0.9843
## Date11/24/2014 -7.957e+00 1.957e+01 -0.407 0.6843
## Date11/24/2015 -7.396e+00 1.613e+01 -0.459 0.6465
## Date11/24/2016 -5.182e-01 1.785e+01 -0.029 0.9768
## Date11/25/2014 -1.364e+01 2.130e+01 -0.640 0.5220
## Date11/25/2015 -1.025e+01 1.671e+01 -0.613 0.5396
## Date11/25/2016 -1.455e+01 1.759e+01 -0.827 0.4082
## Date11/26/2014 -1.990e+01 2.488e+01 -0.800 0.4237
## Date11/26/2015 -1.312e+01 1.717e+01 -0.764 0.4447
## Date11/26/2016 -1.243e+01 1.785e+01 -0.696 0.4864
## Date11/27/2014 -4.525e+00 2.271e+01 -0.199 0.8421
## Date11/27/2015 -6.323e+00 1.736e+01 -0.364 0.7157
## Date11/27/2016 -4.018e+00 1.785e+01 -0.225 0.8219
## Date11/28/2014 3.160e+01 2.271e+01 1.392 0.1641
## Date11/28/2015 -3.793e+00 1.717e+01 -0.221 0.8251
## Date11/28/2016 -1.196e+01 1.684e+01 -0.710 0.4775
## Date11/29/2014 -5.900e+00 2.271e+01 -0.260 0.7950
## Date11/29/2015 -5.108e+00 1.759e+01 -0.290 0.7715
## Date11/29/2016 -1.604e+01 1.671e+01 -0.960 0.3370
## Date11/3/2014 -2.250e+00 2.031e+01 -0.111 0.9118
## Date11/3/2015 -9.425e+00 1.684e+01 -0.560 0.5757
## Date11/3/2016 -1.884e+01 1.613e+01 -1.168 0.2428
## Date11/30/2014 -7.750e-01 2.271e+01 -0.034 0.9728
## Date11/30/2015 -2.634e+01 1.699e+01 -1.550 0.1212
## Date11/30/2016 -1.404e+01 1.671e+01 -0.840 0.4008
## Date11/4/2014 -1.319e+01 1.817e+01 -0.726 0.4678
## Date11/4/2015 4.933e+00 1.854e+01 0.266 0.7902
## Date11/4/2016 -6.483e+00 1.578e+01 -0.411 0.6812
## Date11/5/2014 -6.000e-01 1.900e+01 -0.032 0.9748
## Date11/5/2015 -2.785e+01 1.900e+01 -1.466 0.1427
## Date11/5/2016 -8.615e+00 1.638e+01 -0.526 0.5988
## Date11/6/2014 -7.950e+00 1.900e+01 -0.418 0.6756
## Date11/6/2015 -1.501e+01 1.785e+01 -0.841 0.4006
## Date11/6/2016 -1.220e+01 1.638e+01 -0.745 0.4565
## Date11/7/2014 -2.024e+01 2.130e+01 -0.950 0.3421
## Date11/7/2015 -2.129e+00 1.671e+01 -0.127 0.8986
## Date11/7/2016 -1.269e+01 1.638e+01 -0.775 0.4386
## Date11/8/2014 -2.060e+01 2.271e+01 -0.907 0.3643
## Date11/8/2015 -1.256e+01 1.736e+01 -0.723 0.4694
## Date11/8/2016 -7.763e+00 1.588e+01 -0.489 0.6249
## Date11/9/2014 -1.788e+01 2.031e+01 -0.880 0.3786
## Date11/9/2015 -1.865e+01 1.606e+01 -1.161 0.2455
## Date11/9/2016 1.210e+00 1.629e+01 0.074 0.9408
## Date12/1/2014 6.600e+00 2.271e+01 0.291 0.7713
## Date12/1/2015 3.240e+00 1.699e+01 0.191 0.8488
## Date12/1/2016 -2.360e+01 1.736e+01 -1.359 0.1741
## Date12/10/2014 -7.750e+00 1.817e+01 -0.427 0.6697
## Date12/10/2015 -8.012e+00 1.671e+01 -0.480 0.6315
## Date12/10/2016 -5.667e+00 1.699e+01 -0.333 0.7388
## Date12/11/2014 -9.240e+00 1.817e+01 -0.509 0.6110
## Date12/11/2015 4.336e+00 1.785e+01 0.243 0.8081
## Date12/11/2016 -1.384e+01 1.629e+01 -0.850 0.3955
## Date12/12/2014 -1.077e+01 1.957e+01 -0.550 0.5821
## Date12/12/2015 -3.461e+00 1.658e+01 -0.209 0.8347
## Date12/12/2016 -4.442e+00 1.759e+01 -0.253 0.8006
## Date12/13/2014 -1.936e+01 1.817e+01 -1.066 0.2866
## Date12/13/2015 4.980e+00 1.817e+01 0.274 0.7840
## Date12/13/2016 -1.337e+01 1.647e+01 -0.811 0.4171
## Date12/14/2014 -2.989e+01 1.900e+01 -1.573 0.1157
## Date12/14/2015 -4.455e+00 1.638e+01 -0.272 0.7856
## Date12/14/2016 -2.511e+01 1.671e+01 -1.503 0.1329
## Date12/15/2014 -1.990e+01 2.031e+01 -0.980 0.3272
## Date12/15/2015 -4.155e+00 1.620e+01 -0.256 0.7976
## Date12/15/2016 -4.250e-01 1.759e+01 -0.024 0.9807
## Date12/16/2014 -1.023e+01 2.271e+01 -0.450 0.6525
## Date12/16/2015 -6.205e+00 1.620e+01 -0.383 0.7018
## Date12/16/2016 -3.077e+01 1.684e+01 -1.827 0.0677 .
## Date12/17/2014 -1.444e+01 2.130e+01 -0.678 0.4979
## Date12/17/2015 3.995e+00 1.620e+01 0.247 0.8052
## Date12/17/2016 -1.685e+01 1.684e+01 -1.001 0.3171
## Date12/18/2014 7.517e+00 2.031e+01 0.370 0.7113
## Date12/18/2015 -1.183e+01 1.684e+01 -0.702 0.4826
## Date12/18/2016 -2.471e+01 1.647e+01 -1.500 0.1337
## Date12/19/2014 -1.724e+01 1.900e+01 -0.907 0.3643
## Date12/19/2015 -2.756e+01 1.736e+01 -1.587 0.1125
## Date12/19/2016 9.317e+00 1.658e+01 0.562 0.5743
## Date12/2/2014 -1.600e+01 2.130e+01 -0.751 0.4526
## Date12/2/2015 -1.911e+01 1.717e+01 -1.113 0.2655
## Date12/2/2016 9.960e+00 1.699e+01 0.586 0.5578
## Date12/20/2014 9.287e+00 1.900e+01 0.489 0.6250
## Date12/20/2015 -7.692e+00 1.736e+01 -0.443 0.6578
## Date12/20/2016 -5.850e+00 1.817e+01 -0.322 0.7474
## Date12/21/2014 -1.967e+01 1.957e+01 -1.005 0.3149
## Date12/21/2015 2.779e+00 1.647e+01 0.169 0.8660
## Date12/21/2016 6.356e+00 1.854e+01 0.343 0.7318
## Date12/22/2014 -1.774e+01 2.130e+01 -0.833 0.4050
## Date12/22/2015 -3.906e+00 1.671e+01 -0.234 0.8151
## Date12/22/2016 -8.429e+00 1.717e+01 -0.491 0.6234
## Date12/23/2014 -2.649e+01 1.785e+01 -1.484 0.1379
## Date12/23/2015 -8.433e+00 1.699e+01 -0.496 0.6197
## Date12/23/2016 -8.286e-01 1.717e+01 -0.048 0.9615
## Date12/24/2014 -1.645e+00 1.785e+01 -0.092 0.9266
## Date12/24/2015 -1.668e+01 1.759e+01 -0.948 0.3432
## Date12/24/2016 -4.268e+01 1.717e+01 -2.486 0.0129 *
## Date12/25/2014 -1.609e+01 1.817e+01 -0.886 0.3758
## Date12/25/2015 -1.775e+01 1.759e+01 -1.009 0.3129
## Date12/25/2016 -5.844e+00 1.854e+01 -0.315 0.7526
## Date12/26/2014 -2.520e+01 2.130e+01 -1.183 0.2368
## Date12/26/2015 -9.378e+00 1.854e+01 -0.506 0.6130
## Date12/26/2016 -1.438e+01 1.717e+01 -0.838 0.4023
## Date12/27/2014 -1.725e+01 2.031e+01 -0.849 0.3957
## Date12/27/2015 -1.117e+01 1.759e+01 -0.635 0.5255
## Date12/27/2016 1.636e+00 1.717e+01 0.095 0.9241
## Date12/28/2014 -4.144e+01 1.957e+01 -2.117 0.0342 *
## Date12/28/2015 5.335e+00 1.671e+01 0.319 0.7494
## Date12/28/2016 -1.622e+01 1.736e+01 -0.934 0.3501
## Date12/29/2014 1.937e+01 1.900e+01 1.020 0.3079
## Date12/29/2015 -2.003e+01 1.684e+01 -1.189 0.2344
## Date12/29/2016 -2.820e+00 1.699e+01 -0.166 0.8682
## Date12/3/2014 -7.717e+00 2.031e+01 -0.380 0.7040
## Date12/3/2015 -6.117e+00 1.759e+01 -0.348 0.7280
## Date12/3/2016 -4.423e+00 1.736e+01 -0.255 0.7989
## Date12/30/2014 -1.007e+01 1.957e+01 -0.515 0.6069
## Date12/30/2015 -2.245e+01 1.900e+01 -1.182 0.2374
## Date12/30/2016 -1.058e+01 1.684e+01 -0.628 0.5301
## Date12/31/2014 -3.173e+01 1.759e+01 -1.804 0.0713 .
## Date12/31/2015 -9.300e+00 1.854e+01 -0.502 0.6160
## Date12/31/2016 -1.298e+01 1.736e+01 -0.748 0.4546
## Date12/4/2014 -7.029e+00 1.957e+01 -0.359 0.7195
## Date12/4/2015 -1.154e+00 1.736e+01 -0.066 0.9470
## Date12/4/2016 -1.747e+01 1.684e+01 -1.037 0.2996
## Date12/5/2014 -2.417e+00 2.031e+01 -0.119 0.9053
## Date12/5/2015 -8.400e+00 1.717e+01 -0.489 0.6246
## Date12/5/2016 8.636e-01 1.785e+01 0.048 0.9614
## Date12/6/2014 -1.108e+01 2.271e+01 -0.488 0.6258
## Date12/6/2015 -2.464e+01 1.671e+01 -1.475 0.1403
## Date12/6/2016 1.623e+01 1.759e+01 0.923 0.3561
## Date12/7/2014 5.000e-02 2.271e+01 0.002 0.9982
## Date12/7/2015 1.753e+00 1.647e+01 0.106 0.9153
## Date12/7/2016 -1.547e+00 1.699e+01 -0.091 0.9275
## Date12/8/2014 -2.272e+01 2.031e+01 -1.118 0.2634
## Date12/8/2015 -2.907e+00 1.699e+01 -0.171 0.8642
## Date12/8/2016 1.710e+00 1.629e+01 0.105 0.9164
## Date12/9/2014 -8.764e+00 1.785e+01 -0.491 0.6235
## Date12/9/2015 -1.083e+00 1.759e+01 -0.062 0.9509
## Date12/9/2016 -1.611e+01 1.588e+01 -1.015 0.3103
## Date2/1/2014 2.008e+01 1.854e+01 1.083 0.2789
## Date2/1/2015 -7.594e+00 1.684e+01 -0.451 0.6521
## Date2/1/2016 2.405e+00 1.647e+01 0.146 0.8839
## Date2/10/2014 -2.014e+00 1.957e+01 -0.103 0.9180
## Date2/10/2015 -1.081e+01 1.785e+01 -0.605 0.5449
## Date2/10/2016 -2.471e+01 1.647e+01 -1.500 0.1337
## Date2/11/2014 -1.569e+01 1.854e+01 -0.846 0.3975
## Date2/11/2015 -4.549e+01 1.900e+01 -2.394 0.0167 *
## Date2/11/2016 -2.143e+01 1.699e+01 -1.261 0.2072
## Date2/12/2014 -7.600e+00 2.031e+01 -0.374 0.7083
## Date2/12/2015 -1.573e+01 1.817e+01 -0.866 0.3866
## Date2/12/2016 -1.226e+01 1.658e+01 -0.739 0.4599
## Date2/13/2014 -3.607e+01 1.957e+01 -1.843 0.0654 .
## Date2/13/2015 -1.822e+01 1.736e+01 -1.049 0.2942
## Date2/13/2016 -8.325e+00 1.684e+01 -0.494 0.6211
## Date2/14/2014 9.500e-01 2.031e+01 0.047 0.9627
## Date2/14/2015 -1.664e+01 1.759e+01 -0.946 0.3441
## Date2/14/2016 -8.456e+00 1.658e+01 -0.510 0.6102
## Date2/15/2014 -1.404e+01 1.957e+01 -0.717 0.4731
## Date2/15/2015 -7.100e+00 1.785e+01 -0.398 0.6909
## Date2/15/2016 -1.281e+01 1.658e+01 -0.773 0.4398
## Date2/16/2014 7.000e-01 1.854e+01 0.038 0.9699
## Date2/16/2015 -8.367e+00 1.759e+01 -0.476 0.6343
## Date2/16/2016 5.453e+00 1.647e+01 0.331 0.7407
## Date2/17/2014 -3.491e+01 1.785e+01 -1.955 0.0506 .
## Date2/17/2015 -3.220e+00 1.817e+01 -0.177 0.8593
## Date2/17/2016 -1.066e+01 1.684e+01 -0.633 0.5269
## Date2/18/2014 -9.650e+00 1.817e+01 -0.531 0.5953
## Date2/18/2015 -2.197e+01 1.785e+01 -1.231 0.2185
## Date2/18/2016 -9.311e+00 1.647e+01 -0.565 0.5720
## Date2/19/2014 -1.304e+01 1.854e+01 -0.704 0.4817
## Date2/19/2015 7.536e+00 1.717e+01 0.439 0.6607
## Date2/19/2016 3.825e+00 1.638e+01 0.234 0.8153
## Date2/2/2014 5.211e+00 1.854e+01 0.281 0.7787
## Date2/2/2015 3.700e+00 1.736e+01 0.213 0.8313
## Date2/2/2016 -2.035e+01 1.658e+01 -1.227 0.2198
## Date2/20/2014 -9.267e+00 2.031e+01 -0.456 0.6482
## Date2/20/2015 -1.573e+01 1.817e+01 -0.866 0.3866
## Date2/20/2016 -1.791e+01 1.647e+01 -1.087 0.2771
## Date2/21/2014 8.571e-01 1.957e+01 0.044 0.9651
## Date2/21/2015 -8.923e-01 1.736e+01 -0.051 0.9590
## Date2/21/2016 4.048e-01 1.629e+01 0.025 0.9802
## Date2/22/2014 5.983e+00 2.031e+01 0.295 0.7683
## Date2/22/2015 -1.058e+00 1.759e+01 -0.060 0.9520
## Date2/22/2016 -1.383e+01 1.629e+01 -0.849 0.3958
## Date2/23/2014 -1.409e+01 1.957e+01 -0.720 0.4717
## Date2/23/2015 6.662e+00 1.900e+01 0.351 0.7258
## Date2/23/2016 -1.459e+01 1.647e+01 -0.886 0.3757
## Date2/24/2014 -1.806e+01 2.130e+01 -0.848 0.3966
## Date2/24/2015 -6.456e+00 1.854e+01 -0.348 0.7277
## Date2/24/2016 -1.036e+01 1.620e+01 -0.639 0.5226
## Date2/25/2014 -6.317e+00 2.031e+01 -0.311 0.7558
## Date2/25/2015 1.983e+00 2.031e+01 0.098 0.9222
## Date2/25/2016 -4.550e+00 1.684e+01 -0.270 0.7870
## Date2/26/2014 -3.644e+01 2.130e+01 -1.711 0.0872 .
## Date2/26/2015 -1.162e+01 1.854e+01 -0.627 0.5308
## Date2/26/2016 -4.286e-01 1.629e+01 -0.026 0.9790
## Date2/27/2014 -1.668e+01 1.854e+01 -0.899 0.3684
## Date2/27/2015 -1.230e+01 1.854e+01 -0.663 0.5071
## Date2/27/2016 -1.303e+01 1.629e+01 -0.800 0.4235
## Date2/28/2014 -1.006e+01 1.817e+01 -0.554 0.5798
## Date2/28/2015 -9.660e+00 1.817e+01 -0.532 0.5949
## Date2/28/2016 -2.015e+01 1.620e+01 -1.244 0.2137
## Date2/29/2016 -5.089e+00 1.658e+01 -0.307 0.7590
## Date2/3/2014 1.037e+00 1.900e+01 0.055 0.9565
## Date2/3/2015 -1.769e+01 1.671e+01 -1.059 0.2895
## Date2/3/2016 -2.563e+01 1.588e+01 -1.614 0.1065
## Date2/4/2014 3.133e+00 1.854e+01 0.169 0.8658
## Date2/4/2015 -9.717e+00 1.759e+01 -0.552 0.5807
## Date2/4/2016 -1.279e+01 1.629e+01 -0.785 0.4322
## Date2/5/2014 -4.286e-01 1.957e+01 -0.022 0.9825
## Date2/5/2015 -6.667e-02 2.031e+01 -0.003 0.9974
## Date2/5/2016 -2.447e+01 1.638e+01 -1.494 0.1351
## Date2/6/2014 -1.520e+00 2.130e+01 -0.071 0.9431
## Date2/6/2015 8.375e+00 1.900e+01 0.441 0.6594
## Date2/6/2016 -1.122e+01 1.671e+01 -0.671 0.5019
## Date2/7/2014 -4.100e+00 2.271e+01 -0.181 0.8567
## Date2/7/2015 -1.189e+01 1.736e+01 -0.685 0.4934
## Date2/7/2016 2.271e+00 1.717e+01 0.132 0.8947
## Date2/8/2014 2.515e+01 2.271e+01 1.108 0.2681
## Date2/8/2015 -8.192e+00 1.759e+01 -0.466 0.6414
## Date2/8/2016 -7.787e+00 1.699e+01 -0.458 0.6468
## Date2/9/2014 -5.429e-01 1.957e+01 -0.028 0.9779
## Date2/9/2015 -1.601e+01 1.736e+01 -0.922 0.3566
## Date2/9/2016 -4.460e+00 1.638e+01 -0.272 0.7853
## Date3/1/2014 -1.676e+01 1.817e+01 -0.923 0.3563
## Date3/1/2015 -1.864e+01 1.854e+01 -1.006 0.3146
## Date3/1/2016 -1.795e+01 1.736e+01 -1.034 0.3013
## Date3/10/2014 -3.545e+01 2.031e+01 -1.745 0.0809 .
## Date3/10/2015 6.447e+00 1.699e+01 0.379 0.7044
## Date3/10/2016 3.462e-02 1.593e+01 0.002 0.9983
## Date3/11/2014 2.260e+01 2.130e+01 1.061 0.2887
## Date3/11/2015 -3.271e+00 1.671e+01 -0.196 0.8448
## Date3/11/2016 -1.544e+00 1.658e+01 -0.093 0.9258
## Date3/12/2014 -3.986e+00 1.957e+01 -0.204 0.8386
## Date3/12/2015 -1.970e+01 2.031e+01 -0.970 0.3321
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## Date3/14/2015 -1.107e+01 1.817e+01 -0.609 0.5423
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## Date3/27/2015 -3.700e+01 2.031e+01 -1.822 0.0685 .
## Date3/27/2016 -9.539e+00 1.658e+01 -0.575 0.5652
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## Date3/5/2015 1.829e+00 1.957e+01 0.093 0.9256
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## Date3/8/2015 -9.643e+00 1.717e+01 -0.562 0.5743
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## Date4/10/2015 -1.259e+01 1.854e+01 -0.679 0.4972
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## Date4/12/2015 -1.143e+01 1.717e+01 -0.666 0.5056
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## Date4/13/2015 -6.182e+00 1.671e+01 -0.370 0.7113
## Date4/13/2016 -1.942e+01 1.613e+01 -1.204 0.2286
## Date4/14/2014 8.758e+00 1.759e+01 0.498 0.6186
## Date4/14/2015 -6.600e+00 1.785e+01 -0.370 0.7116
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## Date4/15/2015 -1.934e+01 2.130e+01 -0.908 0.3640
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## Date4/16/2015 -3.436e+00 1.785e+01 -0.192 0.8474
## Date4/16/2016 -7.429e-01 1.717e+01 -0.043 0.9655
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## Date4/17/2015 -1.529e+01 1.699e+01 -0.900 0.3682
## Date4/17/2016 3.706e+00 1.684e+01 0.220 0.8258
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## Date4/18/2015 -6.679e+00 1.717e+01 -0.389 0.6972
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## Date4/19/2014 -8.956e+00 1.854e+01 -0.483 0.6291
## Date4/19/2015 -1.918e+01 1.736e+01 -1.105 0.2692
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## Date4/2/2014 1.348e+01 1.785e+01 0.755 0.4502
## Date4/2/2015 -1.980e+01 1.759e+01 -1.126 0.2603
## Date4/2/2016 -4.500e+00 1.647e+01 -0.273 0.7847
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## Date4/20/2015 -2.549e+01 1.957e+01 -1.302 0.1929
## Date4/20/2016 -8.739e+00 1.569e+01 -0.557 0.5776
## Date4/21/2014 7.060e+00 2.130e+01 0.331 0.7403
## Date4/21/2015 -2.438e-01 1.684e+01 -0.014 0.9885
## Date4/21/2016 -1.586e+00 1.717e+01 -0.092 0.9264
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## Date4/22/2015 5.860e+00 2.130e+01 0.275 0.7833
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## Date4/23/2015 1.291e+01 1.900e+01 0.680 0.4967
## Date4/23/2016 -1.613e+01 1.638e+01 -0.985 0.3248
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## Date4/24/2015 -5.180e+00 2.130e+01 -0.243 0.8079
## Date4/24/2016 -1.329e+01 1.638e+01 -0.811 0.4172
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## Date4/25/2015 8.375e+00 1.900e+01 0.441 0.6594
## Date4/25/2016 -1.605e+01 1.620e+01 -0.991 0.3219
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## Date4/26/2015 -2.703e+01 1.817e+01 -1.488 0.1368
## Date4/26/2016 -1.460e+01 1.638e+01 -0.891 0.3728
## Date4/27/2014 6.667e-01 1.854e+01 0.036 0.9713
## Date4/27/2015 -1.294e+01 1.759e+01 -0.736 0.4619
## Date4/27/2016 -6.625e+00 1.638e+01 -0.405 0.6858
## Date4/28/2014 -1.538e+01 1.817e+01 -0.847 0.3972
## Date4/28/2015 -1.925e+01 1.736e+01 -1.108 0.2677
## Date4/28/2016 4.169e+00 1.684e+01 0.248 0.8045
## Date4/29/2014 1.833e+00 2.031e+01 0.090 0.9281
## Date4/29/2015 -3.500e+00 1.854e+01 -0.189 0.8503
## Date4/29/2016 -1.703e+01 1.671e+01 -1.019 0.3080
## Date4/3/2014 1.018e+01 1.854e+01 0.549 0.5831
## Date4/3/2015 -6.278e+00 1.854e+01 -0.339 0.7349
## Date4/3/2016 -1.689e+01 1.638e+01 -1.031 0.3024
## Date4/30/2014 -1.721e+01 1.854e+01 -0.928 0.3533
## Date4/30/2015 -1.273e+01 1.900e+01 -0.670 0.5030
## Date4/30/2016 -6.625e+00 1.638e+01 -0.405 0.6858
## Date4/4/2014 -2.100e-01 1.817e+01 -0.012 0.9908
## Date4/4/2015 -9.470e+00 1.817e+01 -0.521 0.6022
## Date4/4/2016 -1.509e+00 1.620e+01 -0.093 0.9258
## Date4/5/2014 -3.268e+01 2.031e+01 -1.609 0.1076
## Date4/5/2015 4.009e+00 1.785e+01 0.225 0.8223
## Date4/5/2016 -2.123e+01 1.647e+01 -1.288 0.1976
## Date4/6/2014 1.598e+01 2.031e+01 0.787 0.4313
## Date4/6/2015 -1.319e+01 1.699e+01 -0.776 0.4378
## Date4/6/2016 -8.720e-01 1.599e+01 -0.055 0.9565
## Date4/7/2014 -1.962e+01 2.130e+01 -0.921 0.3571
## Date4/7/2015 -1.926e+01 1.717e+01 -1.122 0.2620
## Date4/7/2016 -1.088e+01 1.620e+01 -0.672 0.5018
## Date4/8/2014 -2.802e+01 2.130e+01 -1.315 0.1884
## Date4/8/2015 -2.321e+01 1.900e+01 -1.222 0.2218
## Date4/8/2016 -1.546e+01 1.606e+01 -0.963 0.3356
## Date4/9/2014 8.755e+00 1.785e+01 0.490 0.6239
## Date4/9/2015 -7.846e-01 1.736e+01 -0.045 0.9640
## Date4/9/2016 -1.109e+01 1.684e+01 -0.659 0.5101
## Date5/1/2014 -2.200e+00 1.957e+01 -0.112 0.9105
## Date5/1/2015 -7.610e+00 1.817e+01 -0.419 0.6753
## Date5/1/2016 -1.168e+01 1.629e+01 -0.717 0.4734
## Date5/10/2014 -6.167e-01 1.759e+01 -0.035 0.9720
## Date5/10/2015 -8.350e+00 1.759e+01 -0.475 0.6350
## Date5/10/2016 -1.576e+01 1.638e+01 -0.962 0.3360
## Date5/11/2014 -2.918e+01 1.785e+01 -1.634 0.1022
## Date5/11/2015 -6.355e+00 1.638e+01 -0.388 0.6980
## Date5/11/2016 -3.964e+00 1.620e+01 -0.245 0.8067
## Date5/12/2014 -7.530e+00 1.817e+01 -0.414 0.6785
## Date5/12/2015 -1.530e+01 1.684e+01 -0.908 0.3636
## Date5/12/2016 -1.302e+01 1.606e+01 -0.811 0.4174
## Date5/13/2014 -3.252e+01 2.031e+01 -1.601 0.1094
## Date5/13/2015 6.107e+00 1.717e+01 0.356 0.7220
## Date5/13/2016 -3.348e+00 1.599e+01 -0.209 0.8342
## Date5/14/2014 -2.029e+00 1.957e+01 -0.104 0.9175
## Date5/14/2015 2.600e+00 1.759e+01 0.148 0.8825
## Date5/14/2016 -8.043e+00 1.717e+01 -0.469 0.6394
## Date5/15/2014 -1.390e+01 1.957e+01 -0.710 0.4776
## Date5/15/2015 -1.676e+01 1.854e+01 -0.904 0.3662
## Date5/15/2016 1.433e+00 1.606e+01 0.089 0.9289
## Date5/16/2014 -2.701e+01 1.957e+01 -1.380 0.1675
## Date5/16/2015 -1.011e+01 1.736e+01 -0.582 0.5605
## Date5/16/2016 1.427e+00 1.620e+01 0.088 0.9298
## Date5/17/2014 8.350e+00 2.031e+01 0.411 0.6810
## Date5/17/2015 6.900e-01 1.817e+01 0.038 0.9697
## Date5/17/2016 -9.700e+00 1.578e+01 -0.615 0.5387
## Date5/18/2014 -5.944e+00 1.854e+01 -0.321 0.7485
## Date5/18/2015 -2.889e-01 1.658e+01 -0.017 0.9861
## Date5/18/2016 -1.063e+01 1.599e+01 -0.665 0.5064
## Date5/19/2014 -1.838e+01 1.900e+01 -0.967 0.3335
## Date5/19/2015 -5.906e+00 1.684e+01 -0.351 0.7258
## Date5/19/2016 7.512e+00 1.684e+01 0.446 0.6555
## Date5/2/2014 -1.244e+01 1.900e+01 -0.655 0.5127
## Date5/2/2015 3.956e+00 1.854e+01 0.213 0.8311
## Date5/2/2016 -2.133e+01 1.613e+01 -1.323 0.1860
## Date5/20/2014 -6.063e+00 1.900e+01 -0.319 0.7497
## Date5/20/2015 -1.104e+01 1.817e+01 -0.608 0.5434
## Date5/20/2016 -1.033e+01 1.638e+01 -0.631 0.5282
## Date5/21/2014 -3.229e+00 1.957e+01 -0.165 0.8690
## Date5/21/2015 5.073e+00 1.785e+01 0.284 0.7763
## Date5/21/2016 -3.771e+00 1.717e+01 -0.220 0.8261
## Date5/22/2014 -4.633e+00 2.031e+01 -0.228 0.8196
## Date5/22/2015 -6.738e+00 1.900e+01 -0.355 0.7229
## Date5/22/2016 -5.521e+00 1.647e+01 -0.335 0.7375
## Date5/23/2014 -1.294e+01 1.957e+01 -0.661 0.5084
## Date5/23/2015 -1.268e+01 1.759e+01 -0.721 0.4709
## Date5/23/2016 -3.572e+00 1.658e+01 -0.215 0.8295
## Date5/24/2014 2.712e+01 2.271e+01 1.194 0.2323
## Date5/24/2015 1.041e+01 1.900e+01 0.548 0.5837
## Date5/24/2016 -2.574e+00 1.647e+01 -0.156 0.8759
## Date5/25/2014 -5.428e+01 2.271e+01 -2.390 0.0169 *
## Date5/25/2015 8.025e+00 1.759e+01 0.456 0.6482
## Date5/25/2016 -7.279e+00 1.647e+01 -0.442 0.6586
## Date5/26/2014 -4.429e-01 1.957e+01 -0.023 0.9819
## Date5/26/2015 -1.214e+01 1.957e+01 -0.620 0.5350
## Date5/26/2016 -6.720e+00 1.599e+01 -0.420 0.6744
## Date5/27/2014 1.582e+01 1.900e+01 0.833 0.4049
## Date5/27/2015 -1.693e+01 1.699e+01 -0.996 0.3190
## Date5/27/2016 -4.033e+00 1.629e+01 -0.248 0.8044
## Date5/28/2014 -2.143e+01 1.900e+01 -1.128 0.2595
## Date5/28/2015 -3.106e+00 1.658e+01 -0.187 0.8515
## Date5/28/2016 -9.055e+00 1.638e+01 -0.553 0.5803
## Date5/29/2014 -1.945e+01 2.271e+01 -0.857 0.3917
## Date5/29/2015 2.667e+00 1.699e+01 0.157 0.8753
## Date5/29/2016 -1.461e+01 1.658e+01 -0.881 0.3785
## Date5/3/2014 -3.213e+00 1.900e+01 -0.169 0.8657
## Date5/3/2015 -9.829e+00 1.717e+01 -0.573 0.5670
## Date5/3/2016 -1.358e+01 1.684e+01 -0.806 0.4202
## Date5/30/2014 6.344e+00 1.854e+01 0.342 0.7322
## Date5/30/2015 1.286e-01 1.717e+01 0.007 0.9940
## Date5/30/2016 -7.750e+00 1.638e+01 -0.473 0.6360
## Date5/31/2014 5.167e+00 1.854e+01 0.279 0.7805
## Date5/31/2015 -1.863e+01 1.759e+01 -1.059 0.2897
## Date5/31/2016 -1.271e+01 1.647e+01 -0.772 0.4404
## Date5/4/2014 -2.356e+01 1.785e+01 -1.320 0.1869
## Date5/4/2015 -5.325e+00 1.900e+01 -0.280 0.7793
## Date5/4/2016 3.440e+00 1.699e+01 0.202 0.8396
## Date5/5/2014 -3.933e+00 1.854e+01 -0.212 0.8320
## Date5/5/2015 -8.782e+00 1.785e+01 -0.492 0.6228
## Date5/5/2016 -1.242e+01 1.658e+01 -0.749 0.4538
## Date5/6/2014 -8.714e+00 1.957e+01 -0.445 0.6562
## Date5/6/2015 -2.236e+01 1.817e+01 -1.231 0.2184
## Date5/6/2016 -1.628e+01 1.606e+01 -1.014 0.3107
## Date5/7/2014 4.671e+00 1.957e+01 0.239 0.8114
## Date5/7/2015 -1.118e+01 1.671e+01 -0.669 0.5033
## Date5/7/2016 -4.655e+00 1.638e+01 -0.284 0.7762
## Date5/8/2014 -1.571e+01 1.900e+01 -0.827 0.4082
## Date5/8/2015 -2.994e+00 1.684e+01 -0.178 0.8589
## Date5/8/2016 -1.449e+01 1.671e+01 -0.868 0.3856
## Date5/9/2014 -1.147e+01 1.854e+01 -0.618 0.5363
## Date5/9/2015 -2.188e+01 1.736e+01 -1.260 0.2077
## Date5/9/2016 -2.210e+01 1.717e+01 -1.287 0.1980
## Date6/1/2014 -4.645e+00 1.785e+01 -0.260 0.7947
## Date6/1/2015 5.582e+00 1.785e+01 0.313 0.7546
## Date6/1/2016 -1.107e+01 1.606e+01 -0.689 0.4907
## Date6/10/2014 -2.206e+01 1.957e+01 -1.127 0.2598
## Date6/10/2015 2.912e+00 1.684e+01 0.173 0.8627
## Date6/10/2016 4.082e+00 1.620e+01 0.252 0.8011
## Date6/11/2014 -1.808e+01 2.031e+01 -0.890 0.3733
## Date6/11/2015 -1.524e+01 1.684e+01 -0.905 0.3654
## Date6/11/2016 -1.803e+01 1.620e+01 -1.113 0.2659
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## Date6/12/2015 -1.435e+01 1.736e+01 -0.827 0.4084
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## Date6/13/2015 -3.700e+00 1.658e+01 -0.223 0.8235
## Date6/13/2016 -5.040e+00 1.599e+01 -0.315 0.7527
## Date6/14/2014 -1.881e+01 1.817e+01 -1.035 0.3005
## Date6/14/2015 -1.468e+00 1.647e+01 -0.089 0.9290
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## Date6/17/2015 -1.444e+01 1.620e+01 -0.891 0.3730
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## Date6/18/2015 -1.243e+01 1.629e+01 -0.763 0.4452
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## Date6/19/2015 -5.971e+00 1.629e+01 -0.367 0.7139
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## Date6/2/2014 -1.544e+01 2.130e+01 -0.725 0.4686
## Date6/2/2015 3.950e+00 1.684e+01 0.235 0.8146
## Date6/2/2016 -1.335e+01 1.647e+01 -0.810 0.4178
## Date6/20/2014 9.110e+00 1.817e+01 0.501 0.6161
## Date6/20/2015 -1.346e+01 1.717e+01 -0.784 0.4328
## Date6/20/2016 -5.107e+00 1.588e+01 -0.322 0.7477
## Date6/21/2014 1.818e-02 1.785e+01 0.001 0.9992
## Date6/21/2015 4.664e+00 1.785e+01 0.261 0.7939
## Date6/21/2016 -5.008e+00 1.599e+01 -0.313 0.7542
## Date6/22/2014 8.012e+00 1.900e+01 0.422 0.6732
## Date6/22/2015 -2.788e+00 1.684e+01 -0.166 0.8685
## Date6/22/2016 -1.389e+01 1.583e+01 -0.878 0.3800
## Date6/23/2014 1.949e+01 1.957e+01 0.996 0.3195
## Date6/23/2015 -2.187e+00 1.699e+01 -0.129 0.8976
## Date6/23/2016 -3.508e+00 1.599e+01 -0.219 0.8264
## Date6/24/2014 -1.266e+01 1.900e+01 -0.666 0.5051
## Date6/24/2015 -5.167e-01 1.658e+01 -0.031 0.9751
## Date6/24/2016 -1.162e+01 1.573e+01 -0.739 0.4600
## Date6/25/2014 9.857e-01 1.957e+01 0.050 0.9598
## Date6/25/2015 8.833e-01 1.658e+01 0.053 0.9575
## Date6/25/2016 -1.302e+01 1.606e+01 -0.811 0.4176
## Date6/26/2014 2.384e+01 2.130e+01 1.119 0.2631
## Date6/26/2015 5.007e+00 1.717e+01 0.292 0.7705
## Date6/26/2016 -5.517e+00 1.606e+01 -0.344 0.7312
## Date6/27/2014 -3.147e+01 1.957e+01 -1.608 0.1079
## Date6/27/2015 -2.466e+01 1.854e+01 -1.330 0.1836
## Date6/27/2016 -4.957e+00 1.613e+01 -0.307 0.7586
## Date6/28/2014 -1.114e+01 1.957e+01 -0.569 0.5691
## Date6/28/2015 -1.585e+01 1.759e+01 -0.901 0.3676
## Date6/28/2016 -1.626e+01 1.620e+01 -1.003 0.3156
## Date6/29/2014 -2.205e+01 1.900e+01 -1.161 0.2458
## Date6/29/2015 -4.229e+00 1.671e+01 -0.253 0.8001
## Date6/29/2016 -2.114e+00 1.629e+01 -0.130 0.8967
## Date6/3/2014 -1.336e+01 1.957e+01 -0.682 0.4950
## Date6/3/2015 -4.339e+00 1.658e+01 -0.262 0.7936
## Date6/3/2016 -1.313e+01 1.593e+01 -0.824 0.4099
## Date6/30/2014 6.480e+00 2.130e+01 0.304 0.7610
## Date6/30/2015 7.593e+00 1.699e+01 0.447 0.6550
## Date6/30/2016 -2.145e+01 1.593e+01 -1.346 0.1782
## Date6/4/2014 5.143e+00 1.957e+01 0.263 0.7927
## Date6/4/2015 -1.402e+01 1.647e+01 -0.851 0.3949
## Date6/4/2016 -1.546e+01 1.599e+01 -0.967 0.3337
## Date6/5/2014 -6.829e+00 1.957e+01 -0.349 0.7272
## Date6/5/2015 -5.285e+00 1.736e+01 -0.304 0.7609
## Date6/5/2016 -3.889e+00 1.588e+01 -0.245 0.8065
## Date6/6/2014 7.550e+00 2.031e+01 0.372 0.7101
## Date6/6/2015 4.686e+00 1.717e+01 0.273 0.7849
## Date6/6/2016 -1.509e+01 1.717e+01 -0.879 0.3795
## Date6/7/2014 3.160e+00 2.130e+01 0.148 0.8821
## Date6/7/2015 -3.400e+00 1.759e+01 -0.193 0.8467
## Date6/7/2016 -1.838e+00 1.736e+01 -0.106 0.9157
## Date6/8/2014 -1.150e+00 2.031e+01 -0.057 0.9548
## Date6/8/2015 6.680e+00 1.817e+01 0.368 0.7131
## Date6/8/2016 -6.686e+00 1.629e+01 -0.411 0.6814
## Date6/9/2014 -9.500e-01 2.031e+01 -0.047 0.9627
## Date6/9/2015 -1.287e+01 1.671e+01 -0.770 0.4411
## Date6/9/2016 -1.283e+01 1.638e+01 -0.783 0.4335
## Date7/1/2014 5.060e+00 2.130e+01 0.238 0.8122
## Date7/1/2015 -2.850e+00 1.658e+01 -0.172 0.8636
## Date7/1/2016 -1.093e+01 1.629e+01 -0.671 0.5020
## Date7/10/2014 3.111e+00 1.854e+01 0.168 0.8667
## Date7/10/2015 -9.400e+00 1.717e+01 -0.548 0.5840
## Date7/10/2016 -5.410e+00 1.573e+01 -0.344 0.7310
## Date7/11/2014 -2.818e+00 1.785e+01 -0.158 0.8746
## Date7/11/2015 -5.944e+00 1.684e+01 -0.353 0.7241
## Date7/11/2016 -3.505e+00 1.620e+01 -0.216 0.8288
## Date7/12/2014 6.100e-01 1.817e+01 0.034 0.9732
## Date7/12/2015 -1.388e+01 1.736e+01 -0.800 0.4239
## Date7/12/2016 8.148e+00 1.599e+01 0.509 0.6104
## Date7/13/2014 -1.711e+01 1.957e+01 -0.874 0.3819
## Date7/13/2015 -1.300e+00 1.900e+01 -0.068 0.9454
## Date7/13/2016 3.447e+00 1.573e+01 0.219 0.8266
## Date7/14/2014 -8.167e-01 2.031e+01 -0.040 0.9679
## Date7/14/2015 -6.207e+00 1.699e+01 -0.365 0.7149
## Date7/14/2016 -1.855e+01 1.638e+01 -1.133 0.2573
## Date7/15/2014 -2.887e+01 1.957e+01 -1.475 0.1402
## Date7/15/2015 -2.109e+01 1.699e+01 -1.241 0.2145
## Date7/15/2016 -2.056e+01 1.671e+01 -1.231 0.2185
## Date7/16/2014 -3.403e+01 1.957e+01 -1.739 0.0821 .
## Date7/16/2015 9.025e+00 1.900e+01 0.475 0.6348
## Date7/16/2016 -4.610e+00 1.638e+01 -0.282 0.7783
## Date7/17/2014 -2.460e+01 2.130e+01 -1.155 0.2482
## Date7/17/2015 -6.153e+00 1.671e+01 -0.368 0.7126
## Date7/17/2016 -2.392e+00 1.759e+01 -0.136 0.8918
## Date7/18/2014 -7.000e+00 2.130e+01 -0.329 0.7425
## Date7/18/2015 -1.082e+01 1.699e+01 -0.637 0.5243
## Date7/18/2016 2.194e+00 1.658e+01 0.132 0.8947
## Date7/19/2014 -2.985e+01 2.031e+01 -1.470 0.1417
## Date7/19/2015 -1.119e+01 1.817e+01 -0.616 0.5379
## Date7/19/2016 -7.761e+00 1.613e+01 -0.481 0.6304
## Date7/2/2014 1.072e+01 2.271e+01 0.472 0.6367
## Date7/2/2015 -2.400e+01 1.717e+01 -1.398 0.1621
## Date7/2/2016 -1.957e+01 1.613e+01 -1.214 0.2249
## Date7/20/2014 1.089e+01 1.957e+01 0.556 0.5781
## Date7/20/2015 -1.333e+00 1.699e+01 -0.078 0.9375
## Date7/20/2016 -1.646e+01 1.613e+01 -1.020 0.3075
## Date7/21/2014 -1.377e+01 2.031e+01 -0.678 0.4979
## Date7/21/2015 -1.765e+01 1.736e+01 -1.017 0.3093
## Date7/21/2016 -7.741e+00 1.620e+01 -0.478 0.6328
## Date7/22/2014 6.983e+00 2.031e+01 0.344 0.7310
## Date7/22/2015 -1.507e+01 1.759e+01 -0.857 0.3917
## Date7/22/2016 -7.097e+00 1.569e+01 -0.452 0.6511
## Date7/23/2014 -1.870e+01 2.271e+01 -0.823 0.4102
## Date7/23/2015 -1.427e+01 1.658e+01 -0.861 0.3895
## Date7/23/2016 -1.965e+01 1.599e+01 -1.229 0.2192
## Date7/24/2014 1.891e+01 1.957e+01 0.966 0.3339
## Date7/24/2015 1.437e+00 1.684e+01 0.085 0.9320
## Date7/24/2016 -1.441e+01 1.593e+01 -0.904 0.3658
## Date7/25/2014 -6.175e+00 1.900e+01 -0.325 0.7452
## Date7/25/2015 4.562e+00 1.736e+01 0.263 0.7928
## Date7/25/2016 -6.644e+00 1.588e+01 -0.418 0.6756
## Date7/26/2014 -1.603e+01 1.817e+01 -0.882 0.3776
## Date7/26/2015 -2.823e+00 1.736e+01 -0.163 0.8708
## Date7/26/2016 -6.796e+00 1.613e+01 -0.421 0.6735
## Date7/27/2014 -1.010e+01 1.957e+01 -0.516 0.6058
## Date7/27/2015 -1.917e+01 1.759e+01 -1.090 0.2759
## Date7/27/2016 1.445e+00 1.620e+01 0.089 0.9289
## Date7/28/2014 -2.701e+01 1.900e+01 -1.422 0.1551
## Date7/28/2015 -7.218e+00 1.671e+01 -0.432 0.6657
## Date7/28/2016 -1.373e+01 1.647e+01 -0.833 0.4048
## Date7/29/2014 -2.519e+01 1.957e+01 -1.287 0.1982
## Date7/29/2015 -4.818e+00 1.671e+01 -0.288 0.7731
## Date7/29/2016 -2.720e+01 1.599e+01 -1.701 0.0890 .
## Date7/3/2014 1.848e+01 2.130e+01 0.868 0.3857
## Date7/3/2015 -2.049e+01 1.699e+01 -1.206 0.2279
## Date7/3/2016 -1.034e+01 1.583e+01 -0.653 0.5137
## Date7/30/2014 -1.433e+01 1.785e+01 -0.802 0.4223
## Date7/30/2015 -1.012e+00 1.671e+01 -0.061 0.9517
## Date7/30/2016 -2.290e+00 1.578e+01 -0.145 0.8846
## Date7/31/2014 -2.132e+01 1.854e+01 -1.150 0.2502
## Date7/31/2015 1.100e-01 1.638e+01 0.007 0.9946
## Date7/31/2016 -1.846e+01 1.606e+01 -1.150 0.2503
## Date7/4/2014 -1.082e+01 2.031e+01 -0.533 0.5944
## Date7/4/2015 -1.284e+01 1.684e+01 -0.762 0.4459
## Date7/4/2016 -8.208e+00 1.599e+01 -0.513 0.6078
## Date7/5/2014 -1.354e+01 1.957e+01 -0.692 0.4890
## Date7/5/2015 -1.563e+01 1.736e+01 -0.900 0.3680
## Date7/5/2016 -1.029e+01 1.573e+01 -0.654 0.5131
## Date7/6/2014 1.833e-01 2.031e+01 0.009 0.9928
## Date7/6/2015 -9.686e+00 1.717e+01 -0.564 0.5726
## Date7/6/2016 -2.368e+01 1.620e+01 -1.462 0.1439
## Date7/7/2014 -3.643e+00 1.957e+01 -0.186 0.8524
## Date7/7/2015 -5.612e+00 1.671e+01 -0.336 0.7369
## Date7/7/2016 1.026e+00 1.613e+01 0.064 0.9493
## Date7/8/2014 8.887e+00 1.900e+01 0.468 0.6399
## Date7/8/2015 -1.890e+01 1.759e+01 -1.074 0.2826
## Date7/8/2016 -7.748e+00 1.569e+01 -0.494 0.6214
## Date7/9/2014 3.500e-01 1.900e+01 0.018 0.9853
## Date7/9/2015 -9.380e+00 1.638e+01 -0.573 0.5668
## Date7/9/2016 -1.720e-01 1.599e+01 -0.011 0.9914
## Date8/1/2014 5.556e+00 1.854e+01 0.300 0.7645
## Date8/1/2015 -4.931e+00 1.684e+01 -0.293 0.7697
## Date8/1/2016 -1.349e+01 1.620e+01 -0.832 0.4052
## Date8/10/2014 -1.869e+01 1.854e+01 -1.008 0.3135
## Date8/10/2015 -1.027e+01 1.699e+01 -0.604 0.5458
## Date8/10/2016 -4.569e+00 1.578e+01 -0.290 0.7721
## Date8/11/2014 -8.400e+00 2.271e+01 -0.370 0.7115
## Date8/11/2015 -3.150e+00 1.684e+01 -0.187 0.8516
## Date8/11/2016 -1.862e+01 1.583e+01 -1.176 0.2395
## Date8/12/2014 -2.030e+01 2.130e+01 -0.953 0.3406
## Date8/12/2015 -8.238e+00 1.736e+01 -0.474 0.6352
## Date8/12/2016 -6.376e+00 1.629e+01 -0.392 0.6954
## Date8/13/2014 -6.811e+00 1.854e+01 -0.367 0.7134
## Date8/13/2015 3.227e+00 1.620e+01 0.199 0.8421
## Date8/13/2016 -2.767e+00 1.658e+01 -0.167 0.8675
## Date8/14/2014 -2.067e+01 1.854e+01 -1.115 0.2650
## Date8/14/2015 -1.602e+01 1.658e+01 -0.966 0.3340
## Date8/14/2016 -5.083e+00 1.613e+01 -0.315 0.7526
## Date8/15/2014 -1.599e+01 1.817e+01 -0.880 0.3788
## Date8/15/2015 -2.536e+01 1.671e+01 -1.518 0.1290
## Date8/15/2016 -1.196e+01 1.613e+01 -0.741 0.4585
## Date8/16/2014 -4.244e+00 1.854e+01 -0.229 0.8189
## Date8/16/2015 -5.708e+00 1.759e+01 -0.325 0.7455
## Date8/16/2016 -1.426e+01 1.599e+01 -0.892 0.3726
## Date8/17/2014 1.878e+00 1.854e+01 0.101 0.9193
## Date8/17/2015 -1.692e+00 1.736e+01 -0.097 0.9224
## Date8/17/2016 -1.747e+01 1.620e+01 -1.078 0.2810
## Date8/18/2014 4.360e+00 1.817e+01 0.240 0.8103
## Date8/18/2015 4.546e+00 1.736e+01 0.262 0.7935
## Date8/18/2016 -3.517e+00 1.613e+01 -0.218 0.8273
## Date8/19/2014 2.160e+01 2.031e+01 1.063 0.2876
## Date8/19/2015 -1.298e+01 1.759e+01 -0.738 0.4605
## Date8/19/2016 -9.840e+00 1.638e+01 -0.601 0.5479
## Date8/2/2014 -1.400e-01 2.130e+01 -0.007 0.9948
## Date8/2/2015 3.743e+00 1.717e+01 0.218 0.8274
## Date8/2/2016 -1.288e+01 1.638e+01 -0.787 0.4316
## Date8/20/2014 1.024e+01 1.957e+01 0.523 0.6007
## Date8/20/2015 4.457e+00 1.717e+01 0.260 0.7951
## Date8/20/2016 -1.248e+01 1.613e+01 -0.774 0.4391
## Date8/21/2014 -2.123e+01 2.271e+01 -0.935 0.3500
## Date8/21/2015 -3.429e+00 1.717e+01 -0.200 0.8417
## Date8/21/2016 -8.667e+00 1.629e+01 -0.532 0.5946
## Date8/22/2014 -2.641e+01 1.900e+01 -1.390 0.1645
## Date8/22/2015 4.321e+00 1.717e+01 0.252 0.8012
## Date8/22/2016 -7.970e+00 1.613e+01 -0.494 0.6212
## Date8/23/2014 -1.614e+01 1.817e+01 -0.888 0.3743
## Date8/23/2015 -1.021e+01 1.785e+01 -0.572 0.5675
## Date8/23/2016 -7.118e+00 1.620e+01 -0.439 0.6604
## Date8/24/2014 -1.407e+01 1.817e+01 -0.774 0.4387
## Date8/24/2015 2.973e+00 1.699e+01 0.175 0.8611
## Date8/24/2016 -1.325e+01 1.593e+01 -0.832 0.4057
## Date8/25/2014 2.686e+00 1.957e+01 0.137 0.8909
## Date8/25/2015 -7.206e+00 1.658e+01 -0.434 0.6639
## Date8/25/2016 -3.182e+00 1.583e+01 -0.201 0.8406
## Date8/26/2014 -3.113e+01 2.271e+01 -1.371 0.1705
## Date8/26/2015 -6.583e+00 1.759e+01 -0.374 0.7082
## Date8/26/2016 -1.473e+01 1.565e+01 -0.941 0.3466
## Date8/27/2014 -8.117e+00 2.031e+01 -0.400 0.6894
## Date8/27/2015 -3.773e+00 1.699e+01 -0.222 0.8243
## Date8/27/2016 -1.435e+01 1.599e+01 -0.897 0.3697
## Date8/28/2014 -5.444e-01 1.854e+01 -0.029 0.9766
## Date8/28/2015 -5.000e+00 1.684e+01 -0.297 0.7666
## Date8/28/2016 -3.806e+00 1.658e+01 -0.229 0.8185
## Date8/29/2014 -1.252e+01 1.854e+01 -0.675 0.4995
## Date8/29/2015 3.900e+00 1.699e+01 0.229 0.8185
## Date8/29/2016 -1.323e+01 1.620e+01 -0.816 0.4143
## Date8/3/2014 3.660e+00 2.130e+01 0.172 0.8636
## Date8/3/2015 -1.826e+01 1.684e+01 -1.084 0.2784
## Date8/3/2016 4.350e+00 1.658e+01 0.262 0.7931
## Date8/30/2014 -1.176e+01 1.817e+01 -0.647 0.5174
## Date8/30/2015 4.150e+00 1.684e+01 0.246 0.8054
## Date8/30/2016 -1.376e+01 1.684e+01 -0.817 0.4138
## Date8/31/2014 -1.647e+01 1.957e+01 -0.842 0.4000
## Date8/31/2015 -1.906e+01 1.785e+01 -1.068 0.2857
## Date8/31/2016 -1.176e+01 1.593e+01 -0.738 0.4604
## Date8/4/2014 -3.054e+01 1.900e+01 -1.607 0.1080
## Date8/4/2015 -8.100e+00 1.759e+01 -0.460 0.6452
## Date8/4/2016 -2.315e+01 1.620e+01 -1.429 0.1531
## Date8/5/2014 -3.616e+01 1.900e+01 -1.903 0.0570 .
## Date8/5/2015 9.800e-01 1.817e+01 0.054 0.9570
## Date8/5/2016 -4.100e+00 1.606e+01 -0.255 0.7985
## Date8/6/2014 -3.393e+01 1.957e+01 -1.734 0.0830 .
## Date8/6/2015 -1.921e+01 1.817e+01 -1.057 0.2903
## Date8/6/2016 -1.439e+01 1.620e+01 -0.888 0.3746
## Date8/7/2014 -1.415e+01 2.031e+01 -0.697 0.4860
## Date8/7/2015 -2.547e+01 1.699e+01 -1.499 0.1339
## Date8/7/2016 -1.949e+01 1.671e+01 -1.167 0.2434
## Date8/8/2014 -2.909e+01 1.785e+01 -1.629 0.1033
## Date8/8/2015 -2.477e+01 1.684e+01 -1.471 0.1414
## Date8/8/2016 -2.139e+00 1.658e+01 -0.129 0.8974
## Date8/9/2014 -7.782e+00 1.785e+01 -0.436 0.6630
## Date8/9/2015 -1.782e+01 1.699e+01 -1.049 0.2944
## Date8/9/2016 2.759e-01 1.578e+01 0.017 0.9861
## Date9/1/2014 -6.057e+00 1.957e+01 -0.309 0.7570
## Date9/1/2015 -3.353e+00 1.699e+01 -0.197 0.8436
## Date9/1/2016 -3.776e+00 1.671e+01 -0.226 0.8212
## Date9/10/2014 7.400e-01 2.130e+01 0.035 0.9723
## Date9/10/2015 -2.067e+01 1.717e+01 -1.204 0.2285
## Date9/10/2016 -1.913e+01 1.620e+01 -1.181 0.2378
## Date9/11/2014 8.267e+00 2.031e+01 0.407 0.6840
## Date9/11/2015 4.080e+00 1.699e+01 0.240 0.8103
## Date9/11/2016 -1.186e+01 1.620e+01 -0.732 0.4641
## Date9/12/2014 -2.156e+01 1.900e+01 -1.135 0.2564
## Date9/12/2015 -1.045e+01 1.736e+01 -0.602 0.5474
## Date9/12/2016 -4.487e+00 1.569e+01 -0.286 0.7749
## Date9/13/2014 -4.250e-01 1.900e+01 -0.022 0.9822
## Date9/13/2015 -3.145e+00 1.638e+01 -0.192 0.8477
## Date9/13/2016 -3.117e+01 1.613e+01 -1.933 0.0533 .
## Date9/14/2014 -1.557e+01 1.957e+01 -0.796 0.4263
## Date9/14/2015 -1.969e+00 1.684e+01 -0.117 0.9069
## Date9/14/2016 -6.808e+00 1.606e+01 -0.424 0.6716
## Date9/15/2014 -2.072e+01 2.031e+01 -1.020 0.3078
## Date9/15/2015 -5.507e+00 1.717e+01 -0.321 0.7484
## Date9/15/2016 9.119e+00 1.629e+01 0.560 0.5755
## Date9/16/2014 -1.207e+01 2.031e+01 -0.594 0.5525
## Date9/16/2015 -3.347e+00 1.671e+01 -0.200 0.8412
## Date9/16/2016 -1.825e+00 1.684e+01 -0.108 0.9137
## Date9/17/2014 -1.152e+01 2.130e+01 -0.541 0.5887
## Date9/17/2015 9.455e-01 1.785e+01 0.053 0.9578
## Date9/17/2016 -9.625e+00 1.606e+01 -0.599 0.5489
## Date9/18/2014 -2.710e+01 2.488e+01 -1.089 0.2760
## Date9/18/2015 -2.289e+00 1.854e+01 -0.123 0.9018
## Date9/18/2016 -1.051e+01 1.569e+01 -0.670 0.5029
## Date9/19/2014 -2.100e+00 2.130e+01 -0.099 0.9215
## Date9/19/2015 -1.487e+01 1.736e+01 -0.856 0.3918
## Date9/19/2016 -2.419e+00 1.593e+01 -0.152 0.8793
## Date9/2/2014 -9.657e+00 1.957e+01 -0.493 0.6217
## Date9/2/2015 -2.334e+01 1.671e+01 -1.397 0.1625
## Date9/2/2016 -1.033e+01 1.658e+01 -0.623 0.5335
## Date9/20/2014 1.314e+00 1.957e+01 0.067 0.9465
## Date9/20/2015 -1.268e+01 1.671e+01 -0.759 0.4478
## Date9/20/2016 -1.512e+01 1.647e+01 -0.918 0.3589
## Date9/21/2014 -2.347e+01 1.785e+01 -1.315 0.1886
## Date9/21/2015 2.080e+00 1.817e+01 0.114 0.9088
## Date9/21/2016 -2.046e+01 1.606e+01 -1.274 0.2026
## Date9/22/2014 3.615e-01 1.736e+01 0.021 0.9834
## Date9/22/2015 -9.233e+00 1.699e+01 -0.543 0.5869
## Date9/22/2016 -3.390e+00 1.638e+01 -0.207 0.8360
## Date9/23/2014 -1.245e+01 1.759e+01 -0.708 0.4791
## Date9/23/2015 -7.581e+00 1.684e+01 -0.450 0.6526
## Date9/23/2016 -6.333e+00 1.699e+01 -0.373 0.7094
## Date9/24/2014 -2.579e+01 1.817e+01 -1.420 0.1557
## Date9/24/2015 5.000e-02 1.717e+01 0.003 0.9977
## Date9/24/2016 -7.219e+00 1.684e+01 -0.429 0.6682
## Date9/25/2014 -5.267e+00 2.031e+01 -0.259 0.7954
## Date9/25/2015 -1.753e+01 1.854e+01 -0.946 0.3444
## Date9/25/2016 5.980e+00 1.599e+01 0.374 0.7085
## Date9/26/2014 -2.181e+01 1.957e+01 -1.115 0.2651
## Date9/26/2015 -1.132e+00 1.620e+01 -0.070 0.9443
## Date9/26/2016 -1.662e+01 1.629e+01 -1.021 0.3075
## Date9/27/2014 -3.605e+01 1.736e+01 -2.076 0.0379 *
## Date9/27/2015 -1.741e+01 1.638e+01 -1.063 0.2879
## Date9/27/2016 -6.489e+00 1.588e+01 -0.409 0.6828
## Date9/28/2014 -4.462e+00 1.736e+01 -0.257 0.7972
## Date9/28/2015 -9.363e+00 1.684e+01 -0.556 0.5783
## Date9/28/2016 7.945e+00 1.569e+01 0.506 0.6126
## Date9/29/2014 -1.395e+01 1.785e+01 -0.782 0.4345
## Date9/29/2015 -1.031e+01 1.658e+01 -0.622 0.5341
## Date9/29/2016 -6.892e+00 1.599e+01 -0.431 0.6665
## Date9/3/2014 -2.561e+01 1.957e+01 -1.309 0.1907
## Date9/3/2015 -8.350e+00 1.817e+01 -0.460 0.6458
## Date9/3/2016 -3.723e+00 1.620e+01 -0.230 0.8183
## Date9/30/2014 1.546e+01 2.130e+01 0.726 0.4680
## Date9/30/2015 2.508e+00 1.759e+01 0.143 0.8866
## Date9/30/2016 -8.704e+00 1.613e+01 -0.540 0.5894
## Date9/4/2014 -8.227e+00 1.785e+01 -0.461 0.6450
## Date9/4/2015 -8.454e+00 1.736e+01 -0.487 0.6263
## Date9/4/2016 -1.273e+01 1.613e+01 -0.789 0.4301
## Date9/5/2014 9.011e+00 1.854e+01 0.486 0.6270
## Date9/5/2015 -5.554e+00 1.736e+01 -0.320 0.7491
## Date9/5/2016 -1.188e+00 1.599e+01 -0.074 0.9408
## Date9/6/2014 -6.144e+00 1.854e+01 -0.331 0.7404
## Date9/6/2015 -1.454e+01 1.759e+01 -0.827 0.4084
## Date9/6/2016 -1.697e+01 1.606e+01 -1.057 0.2906
## Date9/7/2014 -9.255e+00 1.785e+01 -0.518 0.6042
## Date9/7/2015 -6.963e+00 1.647e+01 -0.423 0.6725
## Date9/7/2016 -3.238e-01 1.629e+01 -0.020 0.9841
## Date9/8/2014 -6.364e+00 1.785e+01 -0.356 0.7215
## Date9/8/2015 -7.820e+00 1.699e+01 -0.460 0.6454
## Date9/8/2016 -1.294e+01 1.593e+01 -0.812 0.4166
## Date9/9/2014 4.273e-01 1.785e+01 0.024 0.9809
## Date9/9/2015 1.029e+01 1.699e+01 0.605 0.5450
## Date9/9/2016 -1.218e+01 1.599e+01 -0.761 0.4465
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 35.18 on 13871 degrees of freedom
## Multiple R-squared: 0.07321, Adjusted R-squared: 5.293e-05
## F-statistic: 1.001 on 1095 and 13871 DF, p-value: 0.48854.b) Interpretation on trends
The linear regression analysis suggests that there is no significant linear trend in SalePrice(\() over time. The coefficient for the Date variable is not statistically significant, indicating that there is no strong evidence of a relationship between the date and the sale prices. The model explains only a very small proportion of the variance in SalePrice(\)) (low R-squared), suggesting that other factors not included in the model may influence sale prices.
5) Smoothing the time series.
my_tsibble <- my_tsibble %>%
mutate(Smoothed_SalePrice = slide_dbl(SalePrice, mean, .before = 5, .after = 5, complete = TRUE))
ggplot(my_tsibble, aes(x = Date)) +
geom_line(aes(y = SalePrice, color = "Original")) +
geom_line(aes(y = Smoothed_SalePrice, color = "Smoothed"), linetype = "dashed") +
labs(title = "Original and Smoothed Time Series",
y = "SalePrice",
color = "Legend") +
theme_minimal()
my_ts <- ts(my_tsibble$SalePrice, frequency = 12) # Assuming monthly data
# Plot ACF and PACF
par(mfrow = c(2, 1))
# ACF plot
acf(my_ts, main = "Autocorrelation Function (ACF)")
# PACF plot
pacf(my_ts, main = "Partial Autocorrelation Function (PACF)")