# Run this code block to load the Tidyverse package
.libPaths(new = "~/Rlibs")
library(tidyverse)
# The dataset is in the file "MDWASHDC_JAN1995_DEC2016.csv"
dc.temps<-read.csv("MDWASHDC_JAN1995_DEC2016.csv")
head(dc.temps)
Lab Task 1¶
The code below generates a summary statistics (mean(), median(), min(), max(), and sd()) report of the average temperature grouped by month using the summarise() function.
by_month<-group_by(dc.temps,month)
temps.table<-summarise(by_month,
mean=mean(t.avg), max=max(t.avg),min=min(t.avg),med=median(t.avg), sd=sd(t.avg))
temps.table
Lab Task 2¶
The code below plots the Probability Mass Function (PMF) histogram of the average daily temperatures in the full dataset for each month of the year using the geom_histogram() and ggplot() functions. It uses the facet_wrap() function to create this as a 12 panel plot.
all.months.temps<-ggplot(dc.temps) +
geom_histogram(mapping = aes(x =t.avg, y = ..density..),
binwidth = 1, fill = "cyan3", color = "cyan4") + facet_wrap(~month)
ggsave("all.months.temps.png", plot = all.months.temps, device="png", scale=1, width=5, height=4)
all.months.temps
Lab Task 3¶
The code below creates the normal distribution model for the month of June (all years) using the summary statistics computed in task 1 by generating the Probability Density Function (PDF). It then stores the computed values of the model in a new two-column tibble named jun.model.
dc.temps.june<-filter(dc.temps,month==6)
jun.pdf<-dnorm(x = dc.temps.june$t.avg, mean =74.23167, sd = 14.716578)
jun.model<-tibble(temps=dc.temps.june$t.avg,PDF=jun.pdf)
Lab Task 4¶
The code below creates a new plot containing the average daily temperature PMF histogram and the normal distribution model for June (all years). Note whether or not the model visually agrees with the histogram.
jun.ggplot<-ggplot(data=dc.temps.june) + geom_histogram(binwidth = .5, mapping = aes(x=t.avg), alpha=.5)
data.ggplot.full <- ggplot_build(jun.ggplot)
data.ggplot.table <- data.ggplot.full$data[[1]]
histogram.table <- tibble(x = data.ggplot.table$x, density = data.ggplot.table$density, frequency = data.ggplot.table$count)
mean.june<-mean(dc.temps.june$t.avg)
sd.june<-sd(dc.temps.june$t.avg)
options(repr.plot.width = 6, repr.plot.height = 4)
data.ggplot.june<-ggplot(data=histogram.table) + geom_col(mapping = aes(x=x, y=density), alpha=.5) + stat_function(fun=dnorm, args=list(mean=mean.june,sd=sd.june), color= "red")
ggsave("data.ggplot.june.png", plot = data.ggplot.june, device="png", scale=1, width=5, height=4)
data.ggplot.june
Lab Task 5¶
The code below creates a qqplot for the average temperature distribution in June. A theoretical line is computed and included for comparison.
# Find the 1st and 3rd quartiles (0.25 and 0.75 percentiles)
qq_y <- quantile(dc.temps.june$t.avg, c(0.25, 0.75))
# Find the matching normal values on the x-axis
qq_x <- qnorm(c(0.25, 0.75))
# Compute line slope
qq_slope <- diff(qq_y) / diff(qq_x)
# Compute line intercept
qq_int <- qq_y[1] - qq_slope * qq_x[1]
qqplot.june<-ggplot(dc.temps.june) +
geom_qq(aes(sample = t.avg), color = "cyan3") +
geom_abline(intercept = qq_int, slope = qq_slope, color = "black")
ggsave("qqplot.june.png", plot = qqplot.june, device="png", scale=1, width=5, height=4)
qqplot.june
Lab Task 6¶
The code below creates a 12 panel series of qqplots (without theoretical lines) for each month (all years) using facet_wrap(). Note whether the trend for June applies to the other months.
all.months.qqplot<-ggplot(dc.temps) + geom_qq(aes(sample = t.avg), color = "cyan3") + facet_wrap(~month)
ggsave("all.months.qqplot.png",plot = all.months.qqplot, device="png", scale=1, width=5, height=4)
all.months.qqplot
Lab Task 7¶
The normal distribution model is used to compute the temperature of the 0.10 percentile for the month of June (all years) using the qnorm() function.
# The top 90% of temperatures are the temperatures in the 10th percentile or higher
june.mean =74.23167
june.sd = 14.716578
june.p10 <- qnorm(p = 0.10, mean = june.mean, sd = june.sd)
june.p10
Lab Task 8¶
The normal distribution model is used to compute the percentile of the temperature 83◦F for the month of June (all years) using the pnorm() function.
pnorm(q = 83, mean = june.mean, sd = june.sd)
Key Questions¶
For the month of June, what is the probability that any given day will have a temperature of 83◦F or higher? The code below uses the pnorm() function to find this probability.
How cold are the coldest 10% of days? The qnorm() function is used to find this average temperature of the 10% coldest days.
pnorm(83, mean=june.mean, sd=june.sd, lower.tail=FALSE)
qnorm(0.1, mean=june.mean, sd=june.sd)
Report the mean for the month of March with a 68% and a 95% confidence interval.
ci.95<- 2* june.sd
cat("The 95% confidence interval for the unfiltered dataset is ", june.mean, "+-",ci.95,"\n")
cat("The 68% confidence interval for the unfiltered dataset is ", june.mean, "+-",june.sd)
june.mean+ci.95
june.mean-ci.95
june.mean+june.sd
june.mean-june.sd