ANLY 512 - Problem Set 1
Basic Visualization Process
Ashwin Mendhi
2020-08-09
Directions
During ANLY 512 we will be studying the theory and practice of data visualization. We will be using R and the packages within R to assemble data and construct many different types of visualizations. We begin by studying some of the theoretical aspects of visualization. To do that we must appreciate the basic steps in the process of making a visualization.
The objective of this assignment is to introduce you to R markdown and to complete and explain basic plots before moving on to more complicated ways to graph data.
A couple of tips, remember that there may be preprocessing involved in your graphics so you may have to do summaries or calculations to prepare, those should be included in your work.
To ensure accuracy pay close attention to axes and labels, you will be evaluated based on the accuracy and expository nature of your graphics. Make sure your axis labels are easy to understand and are comprised of full words with units if necessary.
The final product of your homework (this file) should include a short summary of each graphic.
To submit this homework you will create the document in Rstudio, using the knitr package (button included in Rstudio) and then submit the document to your Rpubs account. Once uploaded you will submit the link to that document on Canvas. Please make sure that this link is hyperlinked and that I can see the visualization and the code required to create it.
Part 1 - ggplot Basics
Find the mtcars data in R. This is the dataset that you will use to create your graphics.
- Create a box plot using ggplot showing the range of values of 1/4 mile time (qsec) for each tansmission type (am, 0 = automatic, 1 = manual) from the
mtcarsdata set.
library(ggplot2)
data("mtcars")
str(mtcars)## 'data.frame': 32 obs. of 11 variables:
## $ mpg : num 21 21 22.8 21.4 18.7 18.1 14.3 24.4 22.8 19.2 ...
## $ cyl : num 6 6 4 6 8 6 8 4 4 6 ...
## $ disp: num 160 160 108 258 360 ...
## $ hp : num 110 110 93 110 175 105 245 62 95 123 ...
## $ drat: num 3.9 3.9 3.85 3.08 3.15 2.76 3.21 3.69 3.92 3.92 ...
## $ wt : num 2.62 2.88 2.32 3.21 3.44 ...
## $ qsec: num 16.5 17 18.6 19.4 17 ...
## $ vs : num 0 0 1 1 0 1 0 1 1 1 ...
## $ am : num 1 1 1 0 0 0 0 0 0 0 ...
## $ gear: num 4 4 4 3 3 3 3 4 4 4 ...
## $ carb: num 4 4 1 1 2 1 4 2 2 4 ...mtcars$am <- as.factor(mtcars$am)
ggplot(mtcars, aes(am, qsec)) +
geom_boxplot() +
labs(x="Transmission type",
y="1/4 mile time (seconds)") +
scale_x_discrete(labels = c("Automatic", "Manual")) +
theme_minimal()
- Create a bar graph using ggplot, that shows the number of each
carbtype inmtcars.
ggplot(mtcars, aes(carb)) +
geom_bar() +
labs(x="Number of Carburetors") +
scale_y_continuous(breaks = seq(0, 10, by = 2)) +
theme_minimal()
- Next show a stacked bar graph using ggplot of the number of each
geartype and how they are further divided out bycyl.
unique(mtcars$cyl)## [1] 6 4 8unique(mtcars$gear)## [1] 4 3 5mtcars$gear <- as.factor(mtcars$gear)
mtcars$cyl <- as.factor(mtcars$cyl)
str(mtcars)## 'data.frame': 32 obs. of 11 variables:
## $ mpg : num 21 21 22.8 21.4 18.7 18.1 14.3 24.4 22.8 19.2 ...
## $ cyl : Factor w/ 3 levels "4","6","8": 2 2 1 2 3 2 3 1 1 2 ...
## $ disp: num 160 160 108 258 360 ...
## $ hp : num 110 110 93 110 175 105 245 62 95 123 ...
## $ drat: num 3.9 3.9 3.85 3.08 3.15 2.76 3.21 3.69 3.92 3.92 ...
## $ wt : num 2.62 2.88 2.32 3.21 3.44 ...
## $ qsec: num 16.5 17 18.6 19.4 17 ...
## $ vs : num 0 0 1 1 0 1 0 1 1 1 ...
## $ am : Factor w/ 2 levels "0","1": 2 2 2 1 1 1 1 1 1 1 ...
## $ gear: Factor w/ 3 levels "3","4","5": 2 2 2 1 1 1 1 2 2 2 ...
## $ carb: num 4 4 1 1 2 1 4 2 2 4 ...ggplot(mtcars, aes(gear)) +
geom_bar(aes(fill=cyl)) +
labs(x="Number of Gear", fill="Cylinders") + theme_minimal()
- Draw a scatter plot using ggplot showing the relationship between
wtandmpg.
ggplot(mtcars, aes(wt,mpg)) +
geom_point() + theme_minimal()
- Design a visualization of your choice using ggplot using the data and write a brief summary about why you chose that visualization.
# I am plotting a scatterplot pf horsepower vs 1/4 mile time to see if there is any relation between the two. Looks like there is some relation and 1/4 mile time decreases as horsepower increases.
ggplot(mtcars, aes(hp,qsec)) +
geom_point() + geom_smooth(se = FALSE) +
labs(x="Horsepower",
y="1/4 mile time") +
theme_minimal()## `geom_smooth()` using method = 'loess' and formula 'y ~ x'
Part 2 - Anscombe’s Quartet
- Anscombes quartet is a set of 4 \(x,y\) data sets that were published by Francis Anscombe in a 1973 paper Graphs in statistical analysis. For this first question load the
anscombedata that is part of thelibrary(datasets)inR. And assign that data to a new object calleddata.
library(datasets)
data <- datasets::anscombe- Summarise the data by calculating the mean, variance, for each column and the correlation between each pair (eg. x1 and y1, x2 and y2, etc) (Hint: use the
fBasics()package!)
library("fBasics")## Loading required package: timeDate## Loading required package: timeSeriessapply(data, mean)## x1 x2 x3 x4 y1 y2 y3 y4
## 9.000000 9.000000 9.000000 9.000000 7.500909 7.500909 7.500000 7.500909sapply(data, sd)## x1 x2 x3 x4 y1 y2 y3 y4
## 3.316625 3.316625 3.316625 3.316625 2.031568 2.031657 2.030424 2.030579#Pair 1
correlationTest(data$x1,data$y1)##
## Title:
## Pearson's Correlation Test
##
## Test Results:
## PARAMETER:
## Degrees of Freedom: 9
## SAMPLE ESTIMATES:
## Correlation: 0.8164
## STATISTIC:
## t: 4.2415
## P VALUE:
## Alternative Two-Sided: 0.00217
## Alternative Less: 0.9989
## Alternative Greater: 0.001085
## CONFIDENCE INTERVAL:
## Two-Sided: 0.4244, 0.9507
## Less: -1, 0.9388
## Greater: 0.5113, 1
##
## Description:
## Sun Aug 9 21:09:29 2020#Pair 2
correlationTest(data$x2,data$y2)##
## Title:
## Pearson's Correlation Test
##
## Test Results:
## PARAMETER:
## Degrees of Freedom: 9
## SAMPLE ESTIMATES:
## Correlation: 0.8162
## STATISTIC:
## t: 4.2386
## P VALUE:
## Alternative Two-Sided: 0.002179
## Alternative Less: 0.9989
## Alternative Greater: 0.001089
## CONFIDENCE INTERVAL:
## Two-Sided: 0.4239, 0.9506
## Less: -1, 0.9387
## Greater: 0.5109, 1
##
## Description:
## Sun Aug 9 21:09:29 2020#Pair 3
correlationTest(data$x3,data$y3)##
## Title:
## Pearson's Correlation Test
##
## Test Results:
## PARAMETER:
## Degrees of Freedom: 9
## SAMPLE ESTIMATES:
## Correlation: 0.8163
## STATISTIC:
## t: 4.2394
## P VALUE:
## Alternative Two-Sided: 0.002176
## Alternative Less: 0.9989
## Alternative Greater: 0.001088
## CONFIDENCE INTERVAL:
## Two-Sided: 0.4241, 0.9507
## Less: -1, 0.9387
## Greater: 0.511, 1
##
## Description:
## Sun Aug 9 21:09:29 2020#Pair 4
correlationTest(data$x4,data$y4)##
## Title:
## Pearson's Correlation Test
##
## Test Results:
## PARAMETER:
## Degrees of Freedom: 9
## SAMPLE ESTIMATES:
## Correlation: 0.8165
## STATISTIC:
## t: 4.243
## P VALUE:
## Alternative Two-Sided: 0.002165
## Alternative Less: 0.9989
## Alternative Greater: 0.001082
## CONFIDENCE INTERVAL:
## Two-Sided: 0.4246, 0.9507
## Less: -1, 0.9388
## Greater: 0.5115, 1
##
## Description:
## Sun Aug 9 21:09:29 2020- Create scatter plots for each \(x, y\) pair of data.
#Pair 1
p1 <- ggplot(data, aes(x1,y1)) + geom_point() + theme_minimal()
#Pair 2
p2 <- ggplot(data, aes(x2,y2)) + geom_point() + theme_minimal()
#Pair 3
p3 <- ggplot(data, aes(x3,y3)) + geom_point() + theme_minimal()
#Pair 4
p4 <- ggplot(data, aes(x4,y4)) + geom_point() + theme_minimal()
p1
p2
p3
p4
- Now change the symbols on the scatter plots to solid circles and plot them together as a 4 panel graphic
library(gridExtra)
grid.arrange(p1, p2, p3, p4, ncol = 2)
- Now fit a linear model to each data set using the
lm()function.
lm(x1~y1, data = data)##
## Call:
## lm(formula = x1 ~ y1, data = data)
##
## Coefficients:
## (Intercept) y1
## -0.9975 1.3328lm(x2~y2, data = data)##
## Call:
## lm(formula = x2 ~ y2, data = data)
##
## Coefficients:
## (Intercept) y2
## -0.9948 1.3325lm(x3~y3, data = data)##
## Call:
## lm(formula = x3 ~ y3, data = data)
##
## Coefficients:
## (Intercept) y3
## -1.000 1.333lm(x4~y4, data = data)##
## Call:
## lm(formula = x4 ~ y4, data = data)
##
## Coefficients:
## (Intercept) y4
## -1.004 1.334- Now combine the last two tasks. Create a four panel scatter plot matrix that has both the data points and the regression lines. (hint: the model objects will carry over chunks!)
#Pair 1
p1 <- ggplot(data, aes(x1,y1)) + geom_point() + geom_smooth(method = "lm") + theme_minimal()
#Pair 2
p2 <- ggplot(data, aes(x2,y2)) + geom_point() + geom_smooth(method = "lm") + theme_minimal()
#Pair 3
p3 <- ggplot(data, aes(x3,y3)) + geom_point() + geom_smooth(method = "lm") + theme_minimal()
#Pair 4
p4 <- ggplot(data, aes(x4,y4)) + geom_point() + geom_smooth(method = "lm") + theme_minimal()
grid.arrange(p1, p2, p3, p4, ncol = 2)
- Now compare the model fits for each model object.
#Pair 1
lm(x1~y1, data = data)Call: lm(formula = x1 ~ y1, data = data)
Coefficients: (Intercept) y1
-0.9975 1.3328
#Pair 2
lm(x2~y2, data = data)Call: lm(formula = x2 ~ y2, data = data)
Coefficients: (Intercept) y2
-0.9948 1.3325
#Pair 3
lm(x3~y3, data = data)Call: lm(formula = x3 ~ y3, data = data)
Coefficients: (Intercept) y3
-1.000 1.333
#Pair 4
lm(x4~y4, data = data)Call: lm(formula = x4 ~ y4, data = data)
Coefficients: (Intercept) y4
-1.004 1.334
- In text, summarize the lesson of Anscombe’s Quartet and what it says about the value of data visualization.