Week 1 Discussion 1
Gina Occhipinti
2024-03-14
Discussion 1 - Iris Dataset & Types of Economic Data
Problem 1
In OpenStats Chapter 1, Exercises, Problem 1.9, there is a reference to Fisher’s iris data. (You can find the OpenStats textbook in our Dropbox folder {link in Course Introduction and Materials}, or see the Syllabus on how to access it.The problem is on Page 20 of the 4th edition). Discuss the solutions to this problem, and then conduct a descriptive analysis of the data which are conveniently available in R.
To access the data in R, simply type “iris.” Investigate any additional R libraries that might help support analysis of this data (e.g., describe commandLinks to an external site. (on irisLinks to an external site.) in psych packageLinks to an external site., or stargazer packageLinks to an external site.). Share your code and analysis in the discussion forum. Google or Youtube for help with keywords such as “R” and a description of what you are trying to do if you get stuck. EG - “psych package in R”.
Answer 1
Sepal is the outer parts of the flower (often green and leaf-like) that enclose a developing bud. The petal is the pretty, soft and colorful part, often giving the flower its unique appearance.
Part a) of Problem 1.9
This asks how many cases are included in the data. There are 150 cases, or rows in the data, corresponding with the number of flowers studied as a part of this data set (50 of each of the 3 species).
We can also see this using R.
?iris
nrow(iris)## [1] 150Part b) of Problem 1.9
This asks how many numerical variables are included in the data, what
are they, and if they are continuous or discrete. There are 4 numerical
variables included in the data. They are Sepal.Length,
Sepal.Width, Petal.Length,
Petal.Width. These are continuous variables because the
lengths are measured in centimetersm, and these can vary in
decimals.
We can confirm this using R. For example in the below table of the data, 5.0cm, 4.5cm, 4.4cm, etc. are all examples of continuous variables.
iris## Sepal.Length Sepal.Width Petal.Length Petal.Width Species
## 1 5.1 3.5 1.4 0.2 setosa
## 2 4.9 3.0 1.4 0.2 setosa
## 3 4.7 3.2 1.3 0.2 setosa
## 4 4.6 3.1 1.5 0.2 setosa
## 5 5.0 3.6 1.4 0.2 setosa
## 6 5.4 3.9 1.7 0.4 setosa
## 7 4.6 3.4 1.4 0.3 setosa
## 8 5.0 3.4 1.5 0.2 setosa
## 9 4.4 2.9 1.4 0.2 setosa
## 10 4.9 3.1 1.5 0.1 setosa
## 11 5.4 3.7 1.5 0.2 setosa
## 12 4.8 3.4 1.6 0.2 setosa
## 13 4.8 3.0 1.4 0.1 setosa
## 14 4.3 3.0 1.1 0.1 setosa
## 15 5.8 4.0 1.2 0.2 setosa
## 16 5.7 4.4 1.5 0.4 setosa
## 17 5.4 3.9 1.3 0.4 setosa
## 18 5.1 3.5 1.4 0.3 setosa
## 19 5.7 3.8 1.7 0.3 setosa
## 20 5.1 3.8 1.5 0.3 setosa
## 21 5.4 3.4 1.7 0.2 setosa
## 22 5.1 3.7 1.5 0.4 setosa
## 23 4.6 3.6 1.0 0.2 setosa
## 24 5.1 3.3 1.7 0.5 setosa
## 25 4.8 3.4 1.9 0.2 setosa
## 26 5.0 3.0 1.6 0.2 setosa
## 27 5.0 3.4 1.6 0.4 setosa
## 28 5.2 3.5 1.5 0.2 setosa
## 29 5.2 3.4 1.4 0.2 setosa
## 30 4.7 3.2 1.6 0.2 setosa
## 31 4.8 3.1 1.6 0.2 setosa
## 32 5.4 3.4 1.5 0.4 setosa
## 33 5.2 4.1 1.5 0.1 setosa
## 34 5.5 4.2 1.4 0.2 setosa
## 35 4.9 3.1 1.5 0.2 setosa
## 36 5.0 3.2 1.2 0.2 setosa
## 37 5.5 3.5 1.3 0.2 setosa
## 38 4.9 3.6 1.4 0.1 setosa
## 39 4.4 3.0 1.3 0.2 setosa
## 40 5.1 3.4 1.5 0.2 setosa
## 41 5.0 3.5 1.3 0.3 setosa
## 42 4.5 2.3 1.3 0.3 setosa
## 43 4.4 3.2 1.3 0.2 setosa
## 44 5.0 3.5 1.6 0.6 setosa
## 45 5.1 3.8 1.9 0.4 setosa
## 46 4.8 3.0 1.4 0.3 setosa
## 47 5.1 3.8 1.6 0.2 setosa
## 48 4.6 3.2 1.4 0.2 setosa
## 49 5.3 3.7 1.5 0.2 setosa
## 50 5.0 3.3 1.4 0.2 setosa
## 51 7.0 3.2 4.7 1.4 versicolor
## 52 6.4 3.2 4.5 1.5 versicolor
## 53 6.9 3.1 4.9 1.5 versicolor
## 54 5.5 2.3 4.0 1.3 versicolor
## 55 6.5 2.8 4.6 1.5 versicolor
## 56 5.7 2.8 4.5 1.3 versicolor
## 57 6.3 3.3 4.7 1.6 versicolor
## 58 4.9 2.4 3.3 1.0 versicolor
## 59 6.6 2.9 4.6 1.3 versicolor
## 60 5.2 2.7 3.9 1.4 versicolor
## 61 5.0 2.0 3.5 1.0 versicolor
## 62 5.9 3.0 4.2 1.5 versicolor
## 63 6.0 2.2 4.0 1.0 versicolor
## 64 6.1 2.9 4.7 1.4 versicolor
## 65 5.6 2.9 3.6 1.3 versicolor
## 66 6.7 3.1 4.4 1.4 versicolor
## 67 5.6 3.0 4.5 1.5 versicolor
## 68 5.8 2.7 4.1 1.0 versicolor
## 69 6.2 2.2 4.5 1.5 versicolor
## 70 5.6 2.5 3.9 1.1 versicolor
## 71 5.9 3.2 4.8 1.8 versicolor
## 72 6.1 2.8 4.0 1.3 versicolor
## 73 6.3 2.5 4.9 1.5 versicolor
## 74 6.1 2.8 4.7 1.2 versicolor
## 75 6.4 2.9 4.3 1.3 versicolor
## 76 6.6 3.0 4.4 1.4 versicolor
## 77 6.8 2.8 4.8 1.4 versicolor
## 78 6.7 3.0 5.0 1.7 versicolor
## 79 6.0 2.9 4.5 1.5 versicolor
## 80 5.7 2.6 3.5 1.0 versicolor
## 81 5.5 2.4 3.8 1.1 versicolor
## 82 5.5 2.4 3.7 1.0 versicolor
## 83 5.8 2.7 3.9 1.2 versicolor
## 84 6.0 2.7 5.1 1.6 versicolor
## 85 5.4 3.0 4.5 1.5 versicolor
## 86 6.0 3.4 4.5 1.6 versicolor
## 87 6.7 3.1 4.7 1.5 versicolor
## 88 6.3 2.3 4.4 1.3 versicolor
## 89 5.6 3.0 4.1 1.3 versicolor
## 90 5.5 2.5 4.0 1.3 versicolor
## 91 5.5 2.6 4.4 1.2 versicolor
## 92 6.1 3.0 4.6 1.4 versicolor
## 93 5.8 2.6 4.0 1.2 versicolor
## 94 5.0 2.3 3.3 1.0 versicolor
## 95 5.6 2.7 4.2 1.3 versicolor
## 96 5.7 3.0 4.2 1.2 versicolor
## 97 5.7 2.9 4.2 1.3 versicolor
## 98 6.2 2.9 4.3 1.3 versicolor
## 99 5.1 2.5 3.0 1.1 versicolor
## 100 5.7 2.8 4.1 1.3 versicolor
## 101 6.3 3.3 6.0 2.5 virginica
## 102 5.8 2.7 5.1 1.9 virginica
## 103 7.1 3.0 5.9 2.1 virginica
## 104 6.3 2.9 5.6 1.8 virginica
## 105 6.5 3.0 5.8 2.2 virginica
## 106 7.6 3.0 6.6 2.1 virginica
## 107 4.9 2.5 4.5 1.7 virginica
## 108 7.3 2.9 6.3 1.8 virginica
## 109 6.7 2.5 5.8 1.8 virginica
## 110 7.2 3.6 6.1 2.5 virginica
## 111 6.5 3.2 5.1 2.0 virginica
## 112 6.4 2.7 5.3 1.9 virginica
## 113 6.8 3.0 5.5 2.1 virginica
## 114 5.7 2.5 5.0 2.0 virginica
## 115 5.8 2.8 5.1 2.4 virginica
## 116 6.4 3.2 5.3 2.3 virginica
## 117 6.5 3.0 5.5 1.8 virginica
## 118 7.7 3.8 6.7 2.2 virginica
## 119 7.7 2.6 6.9 2.3 virginica
## 120 6.0 2.2 5.0 1.5 virginica
## 121 6.9 3.2 5.7 2.3 virginica
## 122 5.6 2.8 4.9 2.0 virginica
## 123 7.7 2.8 6.7 2.0 virginica
## 124 6.3 2.7 4.9 1.8 virginica
## 125 6.7 3.3 5.7 2.1 virginica
## 126 7.2 3.2 6.0 1.8 virginica
## 127 6.2 2.8 4.8 1.8 virginica
## 128 6.1 3.0 4.9 1.8 virginica
## 129 6.4 2.8 5.6 2.1 virginica
## 130 7.2 3.0 5.8 1.6 virginica
## 131 7.4 2.8 6.1 1.9 virginica
## 132 7.9 3.8 6.4 2.0 virginica
## 133 6.4 2.8 5.6 2.2 virginica
## 134 6.3 2.8 5.1 1.5 virginica
## 135 6.1 2.6 5.6 1.4 virginica
## 136 7.7 3.0 6.1 2.3 virginica
## 137 6.3 3.4 5.6 2.4 virginica
## 138 6.4 3.1 5.5 1.8 virginica
## 139 6.0 3.0 4.8 1.8 virginica
## 140 6.9 3.1 5.4 2.1 virginica
## 141 6.7 3.1 5.6 2.4 virginica
## 142 6.9 3.1 5.1 2.3 virginica
## 143 5.8 2.7 5.1 1.9 virginica
## 144 6.8 3.2 5.9 2.3 virginica
## 145 6.7 3.3 5.7 2.5 virginica
## 146 6.7 3.0 5.2 2.3 virginica
## 147 6.3 2.5 5.0 1.9 virginica
## 148 6.5 3.0 5.2 2.0 virginica
## 149 6.2 3.4 5.4 2.3 virginica
## 150 5.9 3.0 5.1 1.8 virginicaPart c) of Problem 1.9
This asks how many categorical variables are included in the data set and what are they. There is 1 categorical variable included in the data set - species. The categories are setosa, versicolor, and virginica. We can see that from running the functions above and the data set.
Other Ways to Analyze the Data
Let’s take a look at other ways to analyze the data within R. First, we installed the package “psych”, then loaded the library. From there, we were able to describe the data set Iris to learn some more descriptive statistics about it, including the mean and standard deviations, using the describe() function. The second describe() function omits the missing values, it sets the trimming option, and checks the function for non-numeric data. Similarly, the “stargazer” package provides summary statistics details about this data set, including quartiles.
# install.packages("psych")
library(psych)
describe(iris)## vars n mean sd median trimmed mad min max range skew
## Sepal.Length 1 150 5.84 0.83 5.80 5.81 1.04 4.3 7.9 3.6 0.31
## Sepal.Width 2 150 3.06 0.44 3.00 3.04 0.44 2.0 4.4 2.4 0.31
## Petal.Length 3 150 3.76 1.77 4.35 3.76 1.85 1.0 6.9 5.9 -0.27
## Petal.Width 4 150 1.20 0.76 1.30 1.18 1.04 0.1 2.5 2.4 -0.10
## Species* 5 150 2.00 0.82 2.00 2.00 1.48 1.0 3.0 2.0 0.00
## kurtosis se
## Sepal.Length -0.61 0.07
## Sepal.Width 0.14 0.04
## Petal.Length -1.42 0.14
## Petal.Width -1.36 0.06
## Species* -1.52 0.07describe(iris, na.rm = TRUE, trim = 0.1, check = TRUE) ## vars n mean sd median trimmed mad min max range skew
## Sepal.Length 1 150 5.84 0.83 5.80 5.81 1.04 4.3 7.9 3.6 0.31
## Sepal.Width 2 150 3.06 0.44 3.00 3.04 0.44 2.0 4.4 2.4 0.31
## Petal.Length 3 150 3.76 1.77 4.35 3.76 1.85 1.0 6.9 5.9 -0.27
## Petal.Width 4 150 1.20 0.76 1.30 1.18 1.04 0.1 2.5 2.4 -0.10
## Species* 5 150 2.00 0.82 2.00 2.00 1.48 1.0 3.0 2.0 0.00
## kurtosis se
## Sepal.Length -0.61 0.07
## Sepal.Width 0.14 0.04
## Petal.Length -1.42 0.14
## Petal.Width -1.36 0.06
## Species* -1.52 0.07# install.packages("stargazer")
library(stargazer)
stargazer(iris, type = 'text')##
## ===========================================
## Statistic N Mean St. Dev. Min Max
## -------------------------------------------
## Sepal.Length 150 5.843 0.828 4.300 7.900
## Sepal.Width 150 3.057 0.436 2.000 4.400
## Petal.Length 150 3.758 1.765 1.000 6.900
## Petal.Width 150 1.199 0.762 0.100 2.500
## -------------------------------------------# Analysis of the data was done using the stargazer package (v5.2.2; Hlavac, 202022)This article also shares some useful guidance for summarizing data in R, for example using the summary() function, below. The summary(function) includes data about the percentiles for the different variable lengths.
summary(datasets::iris)## Sepal.Length Sepal.Width Petal.Length Petal.Width
## Min. :4.300 Min. :2.000 Min. :1.000 Min. :0.100
## 1st Qu.:5.100 1st Qu.:2.800 1st Qu.:1.600 1st Qu.:0.300
## Median :5.800 Median :3.000 Median :4.350 Median :1.300
## Mean :5.843 Mean :3.057 Mean :3.758 Mean :1.199
## 3rd Qu.:6.400 3rd Qu.:3.300 3rd Qu.:5.100 3rd Qu.:1.800
## Max. :7.900 Max. :4.400 Max. :6.900 Max. :2.500
## Species
## setosa :50
## versicolor:50
## virginica :50
##
##
## Problem 2
We talk about three different types of data in Economics (cross sectional, time series and panel data). If you type “data()” in R, you will find some internal datasets preloaded in R (including iris dataset). Pick any dataset and tell/show us what category of data it belongs to with an appropriate chart/summary statistics.
See some different types of charts in base R and some simple code in base R to create these charts.
You will find lots of code online, as well as some resources in Tools for Success.
Try the commands in the help file to see if you have any quick visualizations to support your answer.
Read up on descriptive statistics blogs online that can give you some ideas. STHDA, Stats and R.
Draw a scatterplot if cross-sectional data.
Show us the timeplots if time series data,
Use a two-way table command on the ID variables if panel data.
Answer 2
For this example, I will use the Orange data set, which is a data frame that has 35 rows and 3 columns of records of the growth of orange trees.
data()
Orange## Grouped Data: circumference ~ age | Tree
## Tree age circumference
## 1 1 118 30
## 2 1 484 58
## 3 1 664 87
## 4 1 1004 115
## 5 1 1231 120
## 6 1 1372 142
## 7 1 1582 145
## 8 2 118 33
## 9 2 484 69
## 10 2 664 111
## 11 2 1004 156
## 12 2 1231 172
## 13 2 1372 203
## 14 2 1582 203
## 15 3 118 30
## 16 3 484 51
## 17 3 664 75
## 18 3 1004 108
## 19 3 1231 115
## 20 3 1372 139
## 21 3 1582 140
## 22 4 118 32
## 23 4 484 62
## 24 4 664 112
## 25 4 1004 167
## 26 4 1231 179
## 27 4 1372 209
## 28 4 1582 214
## 29 5 118 30
## 30 5 484 49
## 31 5 664 81
## 32 5 1004 125
## 33 5 1231 142
## 34 5 1372 174
## 35 5 1582 177?OrangeBased on the graphs below, the Orange data set is time series data, as it is analyzing how an orange tree’s circumference changes over time or over the life of the tree.
require(stats); require(graphics)
coplot(circumference ~ age | Tree, data = Orange, show.given = FALSE)
fm1 <- nls(circumference ~ SSlogis(age, Asym, xmid, scal),
data = Orange, subset = Tree == 3)
plot(circumference ~ age, data = Orange, subset = Tree == 3,
xlab = "Tree age (days since 1968/12/31)",
ylab = "Tree circumference (mm)", las = 1,
main = "Orange tree data and fitted model (Tree 3 only)")
age <- seq(0, 1600, length.out = 101)
lines(age, predict(fm1, list(age = age)))
Another way to view this data is with the simple plot() function. We can see for each of the 5 trees, how their circumference has changed over their lives.
require(stats) # for lowess, rpois, rnorm
require(graphics) # for plot methods
plot(Orange)