Author: 235208 Alias: Atonwind

Objectives

The objectives of this problem set is to orient you to a number of activities in R. And to conduct a thoughtful exercise in appreciating the importance of data visualization. For each question create a code chunk or text response that completes/answers the activity or question requested. Finally, upon completion name your final output .html file as: YourName_ANLY512-Section-Year-Semester.html and upload it to the “Problem Set 2” assignmenet on Moodle.

Questions

  1. 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 anscombe data that is part of the library(datasets) in R. And assign that data to a new object called data.
# place the code here
library(datasets)
data("anscombe")
data = anscombe
data
##    x1 x2 x3 x4    y1   y2    y3    y4
## 1  10 10 10  8  8.04 9.14  7.46  6.58
## 2   8  8  8  8  6.95 8.14  6.77  5.76
## 3  13 13 13  8  7.58 8.74 12.74  7.71
## 4   9  9  9  8  8.81 8.77  7.11  8.84
## 5  11 11 11  8  8.33 9.26  7.81  8.47
## 6  14 14 14  8  9.96 8.10  8.84  7.04
## 7   6  6  6  8  7.24 6.13  6.08  5.25
## 8   4  4  4 19  4.26 3.10  5.39 12.50
## 9  12 12 12  8 10.84 9.13  8.15  5.56
## 10  7  7  7  8  4.82 7.26  6.42  7.91
## 11  5  5  5  8  5.68 4.74  5.73  6.89
  1. 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!)
# place the code here
summary(data)
##        x1             x2             x3             x4    
##  Min.   : 4.0   Min.   : 4.0   Min.   : 4.0   Min.   : 8  
##  1st Qu.: 6.5   1st Qu.: 6.5   1st Qu.: 6.5   1st Qu.: 8  
##  Median : 9.0   Median : 9.0   Median : 9.0   Median : 8  
##  Mean   : 9.0   Mean   : 9.0   Mean   : 9.0   Mean   : 9  
##  3rd Qu.:11.5   3rd Qu.:11.5   3rd Qu.:11.5   3rd Qu.: 8  
##  Max.   :14.0   Max.   :14.0   Max.   :14.0   Max.   :19  
##        y1               y2              y3              y4        
##  Min.   : 4.260   Min.   :3.100   Min.   : 5.39   Min.   : 5.250  
##  1st Qu.: 6.315   1st Qu.:6.695   1st Qu.: 6.25   1st Qu.: 6.170  
##  Median : 7.580   Median :8.140   Median : 7.11   Median : 7.040  
##  Mean   : 7.501   Mean   :7.501   Mean   : 7.50   Mean   : 7.501  
##  3rd Qu.: 8.570   3rd Qu.:8.950   3rd Qu.: 7.98   3rd Qu.: 8.190  
##  Max.   :10.840   Max.   :9.260   Max.   :12.74   Max.   :12.500
## end of summary()

if (!require("psych")) {
install.packages("psych")
library(psych)
}
## Loading required package: psych
describe(data)
##    vars  n mean   sd median trimmed  mad  min   max range  skew kurtosis
## x1    1 11  9.0 3.32   9.00    9.00 4.45 4.00 14.00 10.00  0.00    -1.53
## x2    2 11  9.0 3.32   9.00    9.00 4.45 4.00 14.00 10.00  0.00    -1.53
## x3    3 11  9.0 3.32   9.00    9.00 4.45 4.00 14.00 10.00  0.00    -1.53
## x4    4 11  9.0 3.32   8.00    8.00 0.00 8.00 19.00 11.00  2.47     4.52
## y1    5 11  7.5 2.03   7.58    7.49 1.82 4.26 10.84  6.58 -0.05    -1.20
## y2    6 11  7.5 2.03   8.14    7.79 1.47 3.10  9.26  6.16 -0.98    -0.51
## y3    7 11  7.5 2.03   7.11    7.15 1.53 5.39 12.74  7.35  1.38     1.24
## y4    8 11  7.5 2.03   7.04    7.20 1.90 5.25 12.50  7.25  1.12     0.63
##      se
## x1 1.00
## x2 1.00
## x3 1.00
## x4 1.00
## y1 0.61
## y2 0.61
## y3 0.61
## y4 0.61
## end of describe()

if (!require("fBasics")) {
install.packages("fBasics")
library(fBasics)
}
## Loading required package: fBasics
## Loading required package: timeDate
## Loading required package: timeSeries
## 
## Attaching package: 'timeSeries'
## The following object is masked from 'package:psych':
## 
##     outlier
## 
## Attaching package: 'fBasics'
## The following object is masked from 'package:psych':
## 
##     tr
## nothing to do here...

## continue to Q3
  1. Create scatter plots for each \(x, y\) pair of data.
# place the code to import graphics here
plot(data$x1, data$y1, main = "Scatter plots for x1 and y1", xlab = "x1", ylab = "y1")

## loop to generate the following code
plot(data$x2, data$y2, main = "Scatter plots for x2 and y2", xlab = "x2", ylab = "y2")

plot(data$x3, data$y3, main = "Scatter plots for x3 and y3", xlab = "x3", ylab = "y3")

plot(data$x4, data$y4, main = "Scatter plots for x4 and y4", xlab = "x4", ylab = "y4")

  1. Now change the symbols on the scatter plots to solid circles and plot them together as a 4 panel graphic
# place the code to import graphics here
par(mfrow=c(2,2))
plot(data$x1, data$y1, main = "Scatter plots for x1 and y1", xlab = "x1", ylab = "y1")

plot(data$x2, data$y2, main = "Scatter plots for x2 and y2", xlab = "x2", ylab = "y2")

plot(data$x3, data$y3, main = "Scatter plots for x3 and y3", xlab = "x3", ylab = "y3")

plot(data$x4, data$y4, main = "Scatter plots for x4 and y4", xlab = "x4", ylab = "y4")

  1. Now fit a linear model to each data set using the lm() function.
# place the code here
lm1 <- lm(data$y1 ~ data$x1)
lm2 <- lm(data$y2 ~ data$x2)
lm3 <- lm(data$y3 ~ data$x3)
lm4 <- lm(data$y4 ~ data$x4)
## end of linear model
  1. 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!)
# place the code to import graphics here
par(mfrow=c(2,2))
plot(data$x1, data$y1, main = "Scatter plots for x1 and y1", xlab = "x1", ylab = "y1")
abline(lm1, col = "Red")
plot(data$x2, data$y2, main = "Scatter plots for x2 and y2", xlab = "x2", ylab = "y2")
abline(lm2, col = "Red")
plot(data$x3, data$y3, main = "Scatter plots for x3 and y3", xlab = "x3", ylab = "y3")
abline(lm3, col = "Red")
plot(data$x4, data$y4, main = "Scatter plots for x4 and y4", xlab = "x4", ylab = "y4")
abline(lm4, col = "Red")

  1. Now compare the model fits for each model object.
# place the code to import graphics here
anova(lm1)

Analysis of Variance Table

Response: data\(y1 Df Sum Sq Mean Sq F value Pr(>F) data\)x1 1 27.510 27.5100 17.99 0.00217 ** Residuals 9 13.763 1.5292
— Signif. codes: 0 ‘’ 0.001 ’’ 0.01 ’’ 0.05 ‘.’ 0.1 ‘’ 1

# end of lm1
anova(lm2)

Analysis of Variance Table

Response: data\(y2 Df Sum Sq Mean Sq F value Pr(>F) data\)x2 1 27.500 27.5000 17.966 0.002179 ** Residuals 9 13.776 1.5307
— Signif. codes: 0 ‘’ 0.001 ’’ 0.01 ’’ 0.05 ‘.’ 0.1 ‘’ 1

# end of lm2
anova(lm3)

Analysis of Variance Table

Response: data\(y3 Df Sum Sq Mean Sq F value Pr(>F) data\)x3 1 27.470 27.4700 17.972 0.002176 ** Residuals 9 13.756 1.5285
— Signif. codes: 0 ‘’ 0.001 ’’ 0.01 ’’ 0.05 ‘.’ 0.1 ‘’ 1

# end of lm3
anova(lm4)

Analysis of Variance Table

Response: data\(y4 Df Sum Sq Mean Sq F value Pr(>F) data\)x4 1 27.490 27.4900 18.003 0.002165 ** Residuals 9 13.742 1.5269
— Signif. codes: 0 ‘’ 0.001 ’’ 0.01 ’’ 0.05 ‘.’ 0.1 ‘’ 1

# end of lm4
  1. In text, summarize the lesson of Anscombe’s Quartet and what it says about the value of data visualization.

It looks funny when all 4 scatter plots have the vary similar linear modal, thanks to the data visualization, it gives us another angle of view to see the numbers in the data. If we don’t have multiplie point of views, we may be deceive by the data and plots.