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” assignment to your R Pubs account and submit the link to Moodle. Points will be deducted for uploading the improper format.

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.

data <- anscombe

2. 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!)

mean(data$x1)

## [1] 9

mean(data$x2)

## [1] 9

mean(data$x3)

## [1] 9

mean(data$x4)

## [1] 9

mean(data$y1)

## [1] 7.500909

mean(data$y2)

## [1] 7.500909

mean(data$y3)

## [1] 7.5

mean(data$y4)

## [1] 7.500909

#Calculating Variance
var(data$x1)

## [1] 11

var(data$x2)

## [1] 11

var(data$x3)

## [1] 11

var(data$x4)

## [1] 11

var(data$y1)

## [1] 4.127269

var(data$y2)

## [1] 4.127629

var(data$y3)

## [1] 4.12262

var(data$y4)

## [1] 4.123249

cor(data$x1,data$y1)

## [1] 0.8164205

cor(data$x2,data$y2)

## [1] 0.8162365

cor(data$x3,data$y3)

## [1] 0.8162867

cor(data$x4,data$y4)

## [1] 0.8165214

3. Create scatter plots for each \(x, y\) pair of data.

plot(data$x1,data$y1, main="Comparing x1 and y1", 
   xlab="x1 ", ylab="y1 ", pch=20)

plot(data$x2,data$y2, main="Comparing x2 and y2", 
   xlab="x2 ", ylab="y2 ", pch=21)

plot(data$x3,data$y3, main="Comparing x3 and y3", 
   xlab="x3 ", ylab="y3 ", pch=22)

plot(data$x4,data$y4, main="Comparing x4 and y4", 
   xlab="x4 ", ylab="y4 ", pch=23)

4. Now change the symbols on the scatter plots to solid circles and plot them together as a 4 panel graphic

par(mfrow=c(2,2))
plot(data$x1, data$y1, pch=20)
plot(data$x2, data$y2, pch=20)
plot(data$x3, data$y3, pch=20)
plot(data$x4, data$y4, pch=20)

5. Now fit a linear model to each data set using the lm() function.

fit1 <- lm(data$y1~data$x1, data=data)
fit2 <- lm(data$y2~data$x2, data=data)
fit3 <- lm(data$y3~data$x3, data=data)
fit4 <- lm(data$y4~data$x4, data=data)

6. 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!)

par(mfrow=c(2,2))
plot(data$x1, data$y1, pch=20)
abline(fit1)
plot(data$x2, data$y2, pch=20)
abline(fit2)
plot(data$x3, data$y3, pch=20)
abline(fit3)
plot(data$x4, data$y4, pch=20)
abline(fit4)

7. Now compare the model fits for each model object.

library(rcompanion)
compareLM(fit1,fit2,fit3,fit4)

## $Models
##   Formula            
## 1 "data$y1 ~ data$x1"
## 2 "data$y2 ~ data$x2"
## 3 "data$y3 ~ data$x3"
## 4 "data$y4 ~ data$x4"
## 
## $Fit.criteria
##   Rank Df.res   AIC  AICc   BIC R.squared Adj.R.sq  p.value Shapiro.W
## 1    2      9 39.68 43.11 40.88    0.6665   0.6295 0.002170    0.9421
## 2    2      9 39.69 43.12 40.89    0.6662   0.6292 0.002179    0.8762
## 3    2      9 39.68 43.10 40.87    0.6663   0.6292 0.002176    0.7407
## 4    2      9 39.67 43.09 40.86    0.6667   0.6297 0.002165    0.9607
##   Shapiro.p
## 1  0.545600
## 2  0.092950
## 3  0.001574
## 4  0.780000

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

Data Visualization is a great way to find hidden insights, insights you would not find through description analytics. Even though the mean and variance were similar as per the mean and variance calculations, the scatterplots for x2y2 and x4y4 said a different story and we could see that they had outliers and were not linearly correlated to each other.

Data Visualization helps us take important decisions with respect to the outliers that we would not have found otherwise through descriptive analytics