diff --git a/isleOfWight/cleaningFeederData.Rmd b/isleOfWight/cleaningFeederData.Rmd
index a07786ef260987b189b0dcac42ea5fb8a3f4a748..d0cc295f10b49a9f41f19ff5fc77ae29731a5949 100644
--- a/isleOfWight/cleaningFeederData.Rmd
+++ b/isleOfWight/cleaningFeederData.Rmd
@@ -1,5 +1,5 @@
---
-title: 'Cleaning Feeder Data'
+title: 'Cleaning Electricity Substation Feeder Data'
subtitle: 'Code and notes'
author: "Ben Anderson (b.anderson@soton.ac.uk), [SERG, Energy & Climate Change](http://www.energy.soton.ac.uk/), University of Southampton"
date: 'Last run at: `r Sys.time()`'
@@ -26,7 +26,7 @@ always_allow_html: yes
bibliography: '`r path.expand("~/bibliography.bib")`'
---
-```{r setup, include=FALSE}
+```{r setup}
# Knitr setup ----
knitr::opts_chunk$set(echo = TRUE)
knitr::opts_chunk$set(warning = FALSE) # for final tidy run
@@ -78,7 +78,9 @@ addSeason <- function(dt,dateVar,h){
# Intro
-We have some feeder data. There seem to be NAs and missing time stamps. We want to select the 'best' (i.e most complete) days within a day-of-the-week/season/year sampling frame.
+We have some electricity substation feeder data. There seem to be NAs and missing time stamps. We want to select the 'best' (i.e most complete) days within a day-of-the-week/season/year sampling frame.
+
+Code used to generate this report: https://git.soton.ac.uk/ba1e12/spatialec/-/blob/master/isleOfWight/cleaningFeederData.Rmd
# Data prep
@@ -134,6 +136,8 @@ ggplot2::ggplot(dt, aes(x = kW)) +
```
+Is that what we expect to see?
+
Demand profiles of kW by season and feeder and day of the week...
```{r kwProfiles}
@@ -155,13 +159,18 @@ ggplot2::ggplot(dt, aes(x = rDate, y = rTime, fill = kW)) +
geom_tile() +
facet_grid(sub_region ~ .) +
scale_fill_viridis_c() +
- labs(caption = "All kW values by feeder, time (y) and date (x)")
+ labs(caption = paste0("All kW values by feeder, time (y) and date (x)",
+ "\nGrey (blank) regions = completely missing dateTimes")
+ )
```
-oooh.
+oooh. That's not good.
+
+Try aggregating to hours...
+
+First the mean kw:
-Try aggregating...
```{r aggVis}
dt[, rHour := lubridate::hour(rDateTime)]
plotDT <- dt[, .(mean_kW = mean(kW),
@@ -171,13 +180,25 @@ ggplot2::ggplot(plotDT, aes(x = rDate, y = rHour, fill = mean_kW)) +
scale_fill_viridis_c() +
facet_grid(sub_region ~ .) +
labs(caption = "Mean kW per hour")
+```
+
+Now the number of observations per hour. The cleaned data is at 15 minutes so we should expect up to 4 observations per hour. How close do we get?
+```{r aggVisN}
ggplot2::ggplot(plotDT, aes(x = rDate, y = rHour, fill = nObs)) +
geom_tile() +
scale_fill_viridis_c() +
facet_grid(sub_region ~ .) +
- labs(caption = "Number of obs per hour")
+ labs(caption = paste0("Number of obs per hour (should be 4)",
+ "\nGrey (blank) regions = completely missing dateTimes")
+ )
+```
+Well one of them hits the 4 per hour most of the time. But what about the evenings? And what about the other feeders???
+
+There is a suspicion that as mean kw goes up so do the number of observations per hour...
+
+```{r aggVisBox}
ggplot2::ggplot(plotDT, aes(x = nObs, y = mean_kW, group = nObs)) +
geom_boxplot() +
facet_grid(.~sub_region) +
@@ -185,24 +206,31 @@ ggplot2::ggplot(plotDT, aes(x = nObs, y = mean_kW, group = nObs)) +
```
+Hmm. Maybe...
+
# Which days have the 'least' missing?
This is quite tricky as we may have completely missing dateTimes. But we can test for this by counting the number of observations per dateTime and then seeing if the dateTimes are contiguous.
```{r testDateTimes}
-dateTimesDT <- dt[, .(nFeeders = uniqueN(sub_region)), keyby = .(rDateTime, rTime, rDate, season)] # keep season
+dateTimesDT <- dt[, .(nFeeders = uniqueN(sub_region)),
+ keyby = .(rDateTime, rTime, rDate, season)] # keep season
dateTimesDT[, dtDiff := rDateTime - shift(rDateTime)] # should be 15 mins
summary(dateTimesDT)
+```
+Let's see how many unique feeders we have per dateTime. Surely we have at least one sending data each half-hour?
+
+```{r tileFeeders}
ggplot2::ggplot(dateTimesDT, aes(x = rDate, y = rTime, fill = nFeeders)) +
geom_tile() +
scale_fill_viridis_c() +
labs(caption = "Number of unique feeders in each dateTime")
```
-Well we clearly have some dateTimes where we have no data _at all_!
+No. We can clearly have some dateTimes where we have no data _at all_!
Are there time of day patterns? It looks like it...
@@ -214,6 +242,10 @@ ggplot2::ggplot(plotDT, aes(y = meanN, x = rTime, colour = season)) +
caption = "Mean n feeders by time of day")
```
+Oh yes. Why?
+
+# Summary
+
So...
I find it distinctly odd that:
@@ -221,7 +253,7 @@ I find it distinctly odd that:
* we appear to have the most feeders reporting data at 'peak' times
* we have a lot of missing dateTimes between 00:30 and 05:00
-If the monitors were set to only collect data when the power (or Wh in a given time frame) was above a given threshold then it would look like this...
+If the monitors were set to only collect data when the power (or Wh in a given time frame) was above a given threshold then it would look like this... That wouldn't happen... would it?
# Runtime
diff --git a/isleOfWight/cleaningFeederData.log b/isleOfWight/cleaningFeederData.log
index 56e3706ca40f810199acdac3e9c5cb568713e4de..071a85f2f15e864e900cca1797af06af6fe67e0a 100644
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diff --git a/isleOfWight/cleaningFeederData.pdf b/isleOfWight/cleaningFeederData.pdf
index 2505bc49de670a121c78705a5890d02f13a5dfce..0966ec4906bb01ac97c14a55900eaee27d117f94 100644
Binary files a/isleOfWight/cleaningFeederData.pdf and b/isleOfWight/cleaningFeederData.pdf differ
diff --git a/isleOfWight/cleaningFeederData.tex b/isleOfWight/cleaningFeederData.tex
index b8b6e5bd70a22d7ec32a078dfc463d6c27531859..0a253cf329d11c9fd73b2f643b67b66c2f6c1197 100644
--- a/isleOfWight/cleaningFeederData.tex
+++ b/isleOfWight/cleaningFeederData.tex
@@ -29,7 +29,7 @@
}
\usepackage{hyperref}
\hypersetup{
- pdftitle={Cleaning Feeder Data},
+ pdftitle={Cleaning Electricity Substation Feeder Data},
pdfauthor={Ben Anderson (b.anderson@soton.ac.uk), SERG, Energy \& Climate Change, University of Southampton},
pdfborder={0 0 0},
breaklinks=true}
@@ -127,11 +127,11 @@
\usepackage{makecell}
\usepackage{xcolor}
-\title{Cleaning Feeder Data}
+\title{Cleaning Electricity Substation Feeder Data}
\providecommand{\subtitle}[1]{}
\subtitle{Code and notes}
\author{Ben Anderson (\href{mailto:b.anderson@soton.ac.uk}{\nolinkurl{b.anderson@soton.ac.uk}}), \href{http://www.energy.soton.ac.uk/}{SERG, Energy \& Climate Change}, University of Southampton}
-\date{Last run at: 2020-07-07 17:25:30}
+\date{Last run at: 2020-07-07 20:24:22}
\begin{document}
\maketitle
@@ -140,10 +140,102 @@
\setcounter{tocdepth}{2}
\tableofcontents
}
+\begin{Shaded}
+\begin{Highlighting}[]
+\CommentTok{# Knitr setup ----}
+\NormalTok{knitr}\OperatorTok{::}\NormalTok{opts_chunk}\OperatorTok{$}\KeywordTok{set}\NormalTok{(}\DataTypeTok{echo =} \OtherTok{TRUE}\NormalTok{)}
+\NormalTok{knitr}\OperatorTok{::}\NormalTok{opts_chunk}\OperatorTok{$}\KeywordTok{set}\NormalTok{(}\DataTypeTok{warning =} \OtherTok{FALSE}\NormalTok{) }\CommentTok{# for final tidy run}
+\NormalTok{knitr}\OperatorTok{::}\NormalTok{opts_chunk}\OperatorTok{$}\KeywordTok{set}\NormalTok{(}\DataTypeTok{message =} \OtherTok{FALSE}\NormalTok{) }\CommentTok{# for final tidy run}
+
+\CommentTok{# Set start time ----}
+\NormalTok{startTime <-}\StringTok{ }\KeywordTok{proc.time}\NormalTok{()}
+
+\CommentTok{# Libraries ----}
+
+\KeywordTok{library}\NormalTok{(data.table) }\CommentTok{# cos we like data.table (you may not in which case dplyr is fine :-)}
+\KeywordTok{library}\NormalTok{(lubridate) }\CommentTok{# for data & time manip}
+\end{Highlighting}
+\end{Shaded}
+
+\begin{verbatim}
+##
+## Attaching package: 'lubridate'
+\end{verbatim}
+
+\begin{verbatim}
+## The following objects are masked from 'package:data.table':
+##
+## hour, isoweek, mday, minute, month, quarter, second, wday, week,
+## yday, year
+\end{verbatim}
+
+\begin{verbatim}
+## The following object is masked from 'package:base':
+##
+## date
+\end{verbatim}
+
+\begin{Shaded}
+\begin{Highlighting}[]
+\KeywordTok{library}\NormalTok{(hms) }\CommentTok{# for hh:mm:ss if we need it}
+\end{Highlighting}
+\end{Shaded}
+
+\begin{verbatim}
+##
+## Attaching package: 'hms'
+\end{verbatim}
+
+\begin{verbatim}
+## The following object is masked from 'package:lubridate':
+##
+## hms
+\end{verbatim}
+
+\begin{Shaded}
+\begin{Highlighting}[]
+\KeywordTok{library}\NormalTok{(ggplot2) }\CommentTok{# fancy plots}
+\KeywordTok{library}\NormalTok{(kableExtra) }\CommentTok{# for extra kable}
+\KeywordTok{library}\NormalTok{(skimr) }\CommentTok{# for skim (data description)}
+
+\CommentTok{# Parameters ----}
+\NormalTok{dFile <-}\StringTok{ "~/Dropbox/Ben_IOW_SS.csv"} \CommentTok{# edit for your set up}
+
+\CommentTok{# Functions ----}
+
+\CommentTok{# set season}
+\NormalTok{addSeason <-}\StringTok{ }\ControlFlowTok{function}\NormalTok{(dt,dateVar,h)\{}
+ \CommentTok{# h = hemisphere (N or S)}
+ \CommentTok{# dateVar is a date that lubridate can convert to months}
+\NormalTok{ dt <-}\StringTok{ }\NormalTok{dt[, tmpM }\OperatorTok{:}\ErrorTok{=}\StringTok{ }\NormalTok{lubridate}\OperatorTok{::}\KeywordTok{month}\NormalTok{(}\KeywordTok{get}\NormalTok{(dateVar))] }\CommentTok{# sets 1 (Jan) - 12 (Dec). May already exist but we can't rely on it}
+ \ControlFlowTok{if}\NormalTok{(h }\OperatorTok{==}\StringTok{ "S"}\NormalTok{)\{}
+\NormalTok{ dt <-}\StringTok{ }\NormalTok{dt[, season }\OperatorTok{:}\ErrorTok{=}\StringTok{ "Summer"}\NormalTok{] }\CommentTok{# easiest to set the default to be the one that bridges years}
+\NormalTok{ dt <-}\StringTok{ }\NormalTok{dt[tmpM }\OperatorTok{>=}\StringTok{ }\DecValTok{3} \OperatorTok{&}\StringTok{ }\NormalTok{tmpM }\OperatorTok{<=}\StringTok{ }\DecValTok{5}\NormalTok{, season }\OperatorTok{:}\ErrorTok{=}\StringTok{ "Autumn"}\NormalTok{]}
+\NormalTok{ dt <-}\StringTok{ }\NormalTok{dt[tmpM }\OperatorTok{>=}\StringTok{ }\DecValTok{6} \OperatorTok{&}\StringTok{ }\NormalTok{tmpM }\OperatorTok{<=}\StringTok{ }\DecValTok{8}\NormalTok{ , season }\OperatorTok{:}\ErrorTok{=}\StringTok{ "Winter"}\NormalTok{]}
+\NormalTok{ dt <-}\StringTok{ }\NormalTok{dt[tmpM }\OperatorTok{>=}\StringTok{ }\DecValTok{9} \OperatorTok{&}\StringTok{ }\NormalTok{tmpM }\OperatorTok{<=}\StringTok{ }\DecValTok{11}\NormalTok{, season }\OperatorTok{:}\ErrorTok{=}\StringTok{ "Spring"}\NormalTok{]}
+ \CommentTok{# re-order to make sense}
+\NormalTok{ dt <-}\StringTok{ }\NormalTok{dt[, season }\OperatorTok{:}\ErrorTok{=}\StringTok{ }\KeywordTok{factor}\NormalTok{(season, }\DataTypeTok{levels =} \KeywordTok{c}\NormalTok{(}\StringTok{"Spring"}\NormalTok{, }\StringTok{"Summer"}\NormalTok{, }\StringTok{"Autumn"}\NormalTok{, }\StringTok{"Winter"}\NormalTok{))]}
+\NormalTok{ \}}
+ \ControlFlowTok{if}\NormalTok{(h }\OperatorTok{==}\StringTok{ "N"}\NormalTok{)\{}
+\NormalTok{ dt <-}\StringTok{ }\NormalTok{dt[, season }\OperatorTok{:}\ErrorTok{=}\StringTok{ "Winter"}\NormalTok{] }\CommentTok{# easiest to set the default to be the one that bridges years}
+\NormalTok{ dt <-}\StringTok{ }\NormalTok{dt[tmpM }\OperatorTok{>=}\StringTok{ }\DecValTok{3} \OperatorTok{&}\StringTok{ }\NormalTok{tmpM }\OperatorTok{<=}\StringTok{ }\DecValTok{5}\NormalTok{, season }\OperatorTok{:}\ErrorTok{=}\StringTok{ "Spring"}\NormalTok{]}
+\NormalTok{ dt <-}\StringTok{ }\NormalTok{dt[tmpM }\OperatorTok{>=}\StringTok{ }\DecValTok{6} \OperatorTok{&}\StringTok{ }\NormalTok{tmpM }\OperatorTok{<=}\StringTok{ }\DecValTok{8}\NormalTok{ , season }\OperatorTok{:}\ErrorTok{=}\StringTok{ "Summer"}\NormalTok{]}
+\NormalTok{ dt <-}\StringTok{ }\NormalTok{dt[tmpM }\OperatorTok{>=}\StringTok{ }\DecValTok{9} \OperatorTok{&}\StringTok{ }\NormalTok{tmpM }\OperatorTok{<=}\StringTok{ }\DecValTok{11}\NormalTok{, season }\OperatorTok{:}\ErrorTok{=}\StringTok{ "Autumn"}\NormalTok{]}
+ \CommentTok{# re-order to make sense}
+\NormalTok{ dt <-}\StringTok{ }\NormalTok{dt[, season }\OperatorTok{:}\ErrorTok{=}\StringTok{ }\KeywordTok{factor}\NormalTok{(season, }\DataTypeTok{levels =} \KeywordTok{c}\NormalTok{(}\StringTok{"Spring"}\NormalTok{, }\StringTok{"Summer"}\NormalTok{, }\StringTok{"Autumn"}\NormalTok{, }\StringTok{"Winter"}\NormalTok{))]}
+\NormalTok{ \}}
+\NormalTok{ dt}\OperatorTok{$}\NormalTok{tmpM <-}\StringTok{ }\OtherTok{NULL}
+ \KeywordTok{return}\NormalTok{(dt)}
+\NormalTok{\}}
+\end{Highlighting}
+\end{Shaded}
+
\hypertarget{intro}{%
\section{Intro}\label{intro}}
-We have some feeder data. There seem to be NAs and missing time stamps. We want to select the `best' (i.e most complete) days within a day-of-the-week/season/year sampling frame.
+We have some electricity substation feeder data. There seem to be NAs and missing time stamps. We want to select the `best' (i.e most complete) days within a day-of-the-week/season/year sampling frame.
+
+Code used to generate this report: \url{https://git.soton.ac.uk/ba1e12/spatialec/-/blob/master/isleOfWight/cleaningFeederData.Rmd}
\hypertarget{data-prep}{%
\section{Data prep}\label{data-prep}}
@@ -292,6 +384,8 @@ Histograms of kW by season and feeder\ldots{}
\includegraphics{cleaningFeederData_files/figure-latex/histo-1.pdf}
+Is that what we expect to see?
+
Demand profiles of kW by season and feeder and day of the week\ldots{}
\begin{Shaded}
@@ -318,15 +412,19 @@ Can we see missing data?
\StringTok{ }\KeywordTok{geom_tile}\NormalTok{() }\OperatorTok{+}
\StringTok{ }\KeywordTok{facet_grid}\NormalTok{(sub_region }\OperatorTok{~}\StringTok{ }\NormalTok{.) }\OperatorTok{+}
\StringTok{ }\KeywordTok{scale_fill_viridis_c}\NormalTok{() }\OperatorTok{+}
-\StringTok{ }\KeywordTok{labs}\NormalTok{(}\DataTypeTok{caption =} \StringTok{"All kW values by feeder, time (y) and date (x)"}\NormalTok{)}
+\StringTok{ }\KeywordTok{labs}\NormalTok{(}\DataTypeTok{caption =} \KeywordTok{paste0}\NormalTok{(}\StringTok{"All kW values by feeder, time (y) and date (x)"}\NormalTok{,}
+ \StringTok{"}\CharTok{\textbackslash{}n}\StringTok{Grey (blank) regions = completely missing dateTimes"}\NormalTok{)}
+\NormalTok{ )}
\end{Highlighting}
\end{Shaded}
\includegraphics{cleaningFeederData_files/figure-latex/missingVis-1.pdf}
-oooh.
+oooh. That's not good.
+
+Try aggregating to hours\ldots{}
-Try aggregating\ldots{}
+First the mean kw:
\begin{Shaded}
\begin{Highlighting}[]
@@ -343,17 +441,25 @@ Try aggregating\ldots{}
\includegraphics{cleaningFeederData_files/figure-latex/aggVis-1.pdf}
+Now the number of observations per hour. The cleaned data is at 15 minutes so we should expect up to 4 observations per hour. How close do we get?
+
\begin{Shaded}
\begin{Highlighting}[]
\NormalTok{ggplot2}\OperatorTok{::}\KeywordTok{ggplot}\NormalTok{(plotDT, }\KeywordTok{aes}\NormalTok{(}\DataTypeTok{x =}\NormalTok{ rDate, }\DataTypeTok{y =}\NormalTok{ rHour, }\DataTypeTok{fill =}\NormalTok{ nObs)) }\OperatorTok{+}
\StringTok{ }\KeywordTok{geom_tile}\NormalTok{() }\OperatorTok{+}
\StringTok{ }\KeywordTok{scale_fill_viridis_c}\NormalTok{() }\OperatorTok{+}
\StringTok{ }\KeywordTok{facet_grid}\NormalTok{(sub_region }\OperatorTok{~}\StringTok{ }\NormalTok{.) }\OperatorTok{+}
-\StringTok{ }\KeywordTok{labs}\NormalTok{(}\DataTypeTok{caption =} \StringTok{"Number of obs per hour"}\NormalTok{)}
+\StringTok{ }\KeywordTok{labs}\NormalTok{(}\DataTypeTok{caption =} \KeywordTok{paste0}\NormalTok{(}\StringTok{"Number of obs per hour (should be 4)"}\NormalTok{,}
+ \StringTok{"}\CharTok{\textbackslash{}n}\StringTok{Grey (blank) regions = completely missing dateTimes"}\NormalTok{)}
+\NormalTok{ )}
\end{Highlighting}
\end{Shaded}
-\includegraphics{cleaningFeederData_files/figure-latex/aggVis-2.pdf}
+\includegraphics{cleaningFeederData_files/figure-latex/aggVisN-1.pdf}
+
+Well one of them hits the 4 per hour most of the time. But what about the evenings? And what about the other feeders???
+
+There is a suspicion that as mean kw goes up so do the number of observations per hour\ldots{}
\begin{Shaded}
\begin{Highlighting}[]
@@ -364,7 +470,9 @@ Try aggregating\ldots{}
\end{Highlighting}
\end{Shaded}
-\includegraphics{cleaningFeederData_files/figure-latex/aggVis-3.pdf}
+\includegraphics{cleaningFeederData_files/figure-latex/aggVisBox-1.pdf}
+
+Hmm. Maybe\ldots{}
\hypertarget{which-days-have-the-least-missing}{%
\section{Which days have the `least' missing?}\label{which-days-have-the-least-missing}}
@@ -373,7 +481,8 @@ This is quite tricky as we may have completely missing dateTimes. But we can tes
\begin{Shaded}
\begin{Highlighting}[]
-\NormalTok{dateTimesDT <-}\StringTok{ }\NormalTok{dt[, .(}\DataTypeTok{nFeeders =} \KeywordTok{uniqueN}\NormalTok{(sub_region)), keyby =}\StringTok{ }\NormalTok{.(rDateTime, rTime, rDate, season)] }\CommentTok{# keep season}
+\NormalTok{dateTimesDT <-}\StringTok{ }\NormalTok{dt[, .(}\DataTypeTok{nFeeders =} \KeywordTok{uniqueN}\NormalTok{(sub_region)), }
+\NormalTok{ keyby =}\StringTok{ }\NormalTok{.(rDateTime, rTime, rDate, season)] }\CommentTok{# keep season}
\NormalTok{dateTimesDT[, dtDiff }\OperatorTok{:}\ErrorTok{=}\StringTok{ }\NormalTok{rDateTime }\OperatorTok{-}\StringTok{ }\KeywordTok{shift}\NormalTok{(rDateTime)] }\CommentTok{# should be 15 mins}
@@ -398,6 +507,8 @@ This is quite tricky as we may have completely missing dateTimes. But we can tes
## Max. :5.000
\end{verbatim}
+Let's see how many unique feeders we have per dateTime. Surely we have at least one sending data each half-hour?
+
\begin{Shaded}
\begin{Highlighting}[]
\NormalTok{ggplot2}\OperatorTok{::}\KeywordTok{ggplot}\NormalTok{(dateTimesDT, }\KeywordTok{aes}\NormalTok{(}\DataTypeTok{x =}\NormalTok{ rDate, }\DataTypeTok{y =}\NormalTok{ rTime, }\DataTypeTok{fill =}\NormalTok{ nFeeders)) }\OperatorTok{+}
@@ -407,9 +518,9 @@ This is quite tricky as we may have completely missing dateTimes. But we can tes
\end{Highlighting}
\end{Shaded}
-\includegraphics{cleaningFeederData_files/figure-latex/testDateTimes-1.pdf}
+\includegraphics{cleaningFeederData_files/figure-latex/tileFeeders-1.pdf}
-Well we clearly have some dateTimes where we have no data \emph{at all}!
+No.~We can clearly have some dateTimes where we have no data \emph{at all}!
Are there time of day patterns? It looks like it\ldots{}
@@ -425,6 +536,11 @@ Are there time of day patterns? It looks like it\ldots{}
\includegraphics{cleaningFeederData_files/figure-latex/missingProfiles-1.pdf}
+Oh yes. Why?
+
+\hypertarget{summary}{%
+\section{Summary}\label{summary}}
+
So\ldots{}
I find it distinctly odd that:
@@ -437,12 +553,12 @@ I find it distinctly odd that:
we have a lot of missing dateTimes between 00:30 and 05:00
\end{itemize}
-If the monitors were set to only collect data when the power (or Wh in a given time frame) was above a given threshold then it would look like this\ldots{}
+If the monitors were set to only collect data when the power (or Wh in a given time frame) was above a given threshold then it would look like this\ldots{} That wouldn't happen\ldots{} would it?
\hypertarget{runtime}{%
\section{Runtime}\label{runtime}}
-Analysis completed in 15.32 seconds ( 0.26 minutes) using \href{https://cran.r-project.org/package=knitr}{knitr} in \href{http://www.rstudio.com}{RStudio} with R version 3.6.3 (2020-02-29) running on x86\_64-apple-darwin15.6.0.
+Analysis completed in 16.92 seconds ( 0.28 minutes) using \href{https://cran.r-project.org/package=knitr}{knitr} in \href{http://www.rstudio.com}{RStudio} with R version 3.6.3 (2020-02-29) running on x86\_64-apple-darwin15.6.0.
\hypertarget{r-environment}{%
\section{R environment}\label{r-environment}}
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