# Beginner’s Guide: Exploratory Data Analysis in R

When I started on my journey to learn data science, I read through multiple articles that stressed the importance of understanding your data. It didn’t make sense to me. I was naive enough to think that we are handed over data which we push through an algorithm and hand over the results.

Yes, I wasn’t exactly the brightest. But I’ve learned my lesson and today I want to impart what I picked from my sleepless nights trying to figure out my data. I am going to use the **R **language to demonstrate EDA.

WHY R?

Because it was built from the get-go keeping data science in mind. It’s easy to pick up and get your hands dirty and doesn’t have a steep learning curve, *cough*

Assembly*cough*.

Before I start, This article is a guide for people classified under the tag of ‘Data Science infants.’ I believe both Python and R are great languages, and what matters most is the Story you tell from your data.

## Why this dataset?

Well, it’s where I think most of the aspiring data scientists would start. This data set is a good starting place to heat your engines to start thinking like a data scientist at the same time being a novice-friendly helps you breeze through the exercise.

# How do we approach this data?

- Will this variable help use predict house prices?
- Is there a correlation between these variables?
- Univariate Analysis
- Multivariate Analysis
- A bit of Data Cleaning
- Conclude with proving the relevance of our selected variables.

Best of luck on your journey to master Data Science!

Now, we start with importing packages, I’ll explain why these packages are present along the way…

easypackages::libraries("dplyr", "ggplot2", "tidyr", "corrplot", "corrr", "magrittr", "e1071","ggplot2","RColorBrewer", "viridis")

options(scipen = 5) #To force R to not use scientfic notationdataset <- read.csv("train.csv")

str(dataset)

Here, in the above snippet, we use scipen to avoid scientific notation. We import our data and use the str() function to get the gist of the selection of variables that the dataset offers and the respective data type.

The variable SalePrice is the dependent variable which we are going to base all our assumptions and hypothesis around. So it’s good to first understand more about this variable. For this, we’ll use a Histogram and fetch a frequency distribution to get a visual understanding of the variable. You’d notice there’s another function i.e. summary() which is essentially used to for the same purpose but without any form of visualization. With experience, you’ll be able to understand and interpret this form of information better.

ggplot(dataset, aes(x=SalePrice)) +

theme_bw()+

geom_histogram(aes(y=..density..),color = 'black', fill = 'white', binwidth = 50000)+

geom_density(alpha=.2, fill='blue') +

labs(title = "Sales Price Density", x="Price", y="Density")summary(dataset$SalePrice)

So it is pretty evident that you’ll find many properties in the sub $200,000 range. There are properties over $600,000 and we can try to understand why is it so and what makes these homes so ridiculously expensive. That can be another fun exercise…

## Which variables do you think are most influential when deciding a price for a house you are looking to buy?

Now that we have a basic idea about SalePrice we will try to visualize this variable in terms of some other variable. Please note that it is very important to understand what *type* of variable you are working with. I would like you to refer to this amazing article which covers this topic in more detail here.

Moving on, We will be dealing with two kinds of variables.

- Categorical Variable
- Numeric Variable

Looking back at our dataset we can discern between these variables. For starters, we run a coarse comb across the dataset and guess pick some variables which have the highest chance of being relevant. Note that these are just assumptions and we are exploring this dataset to understand this. The variables I selected are:

- GrLivArea
- TotalBsmtSF
- YearBuilt
- OverallQual

So which ones are Quantitive and which ones are Qualitative out of the lot? If you look closely the *OveralQual* and *YearBuilt* variable then you will notice that these variables can never be Quantitative. Year and Quality both are categorical by nature of this data however, R doesn’t know that. For that, we use *factor()* function to convert a numerical variable to categorical so R can interpret the data better.

`dataset$YearBuilt <- factor(dataset$YearBuilt)`

dataset$OverallQual <- factor(dataset$OverallQual)

Now when we run *str()* on our dataset we will see both YearBuilt and OverallQual as factor variables.

We can now start plotting our variables.

# Relationships are (NOT) so complicated

Taking *YearBuilt* as our first candidate we start plotting.

`ggplot(dataset, aes(y=SalePrice, x=YearBuilt, group=YearBuilt, fill=YearBuilt)) +`

theme_bw()+

geom_boxplot(outlier.colour="red", outlier.shape=8, outlier.size=1)+

theme(legend.position="none")+

scale_fill_viridis(discrete = TRUE) +

theme(axis.text.x = element_text(angle = 90))+

labs(title = "Year Built vs. Sale Price", x="Year", y="Price")

Old houses sell for less as compared to a recently built house. And as for *OverallQual*,

`ggplot(dataset, aes(y=SalePrice, x=OverallQual, group=OverallQual,fill=OverallQual)) +`

geom_boxplot(alpha=0.3)+

theme(legend.position="none")+

scale_fill_viridis(discrete = TRUE, option="B") +

labs(title = "Overall Quality vs. Sale Price", x="Quality", y="Price")

This was expected since you’d naturally pay more for the house which is of better quality. You won’t want your foot to break through the floorboard, will you? Now that the qualitative variables are out of the way we can focus on the numeric variables. The very first candidate we have here is *GrLivArea*.

`ggplot(dataset, aes(x=SalePrice, y=GrLivArea)) +`

theme_bw()+

geom_point(colour="Blue", alpha=0.3)+

theme(legend.position='none')+

labs(title = "General Living Area vs. Sale Price", x="Price", y="Area")

I would be lying if I said I didn’t expect this. The very first instinct of a customer is to check the area of rooms. And I think the result will be the same for *TotalBsmtASF*. Let’s see…

`ggplot(dataset, aes(x=SalePrice, y=TotalBsmtSF)) +`

theme_bw()+

geom_point(colour="Blue", alpha=0.3)+

theme(legend.position='none')+

labs(title = "Total Basement Area vs. Sale Price", x="Price", y="Area")

# So what can we say about our cherry-picked variables?

*GrLivArea* and *TotalBsmtSF* both were found to be in a linear relation with *SalePrice*. As for the categorical variables, we can say with confidence that the two variable which we picked were related to *SalePrice* with confidence.

But these are not the only variables and there’s more to than what meets the eye. So to tread over these many variables we’ll take help from a correlation matrix to see how each variable correlate to get a better insight.

# Time for Correlation Plots

So what is Correlation?

Correlation is a measure of how well two variables are related to each other. There are positive as well as negative correlation.

If you want to read more on Correlation then take a look at this article. So let’s create a basic Correlation Matrix.

M <- cor(dataset)

M <- dataset %>% mutate_if(is.character, as.factor)

M <- M %>% mutate_if(is.factor, as.numeric)

M <- cor(M)mat1 <- data.matrix(M)

print(M)#plotting the correlation matrix

corrplot(M, method = "color", tl.col = 'black', is.corr=FALSE)

## Please don’t close this tab. I promise it gets better.

But worry not because now we’re going to get our hands dirty and make this plot interpretable and tidy.

M[lower.tri(M,diag=TRUE)] <- NA #remove coeff - 1 and duplicates

M[M == 1] <- NAM <- as.data.frame(as.table(M)) #turn into a 3-column table

M <- na.omit(M) #remove the NA values from aboveM <- subset(M, abs(Freq) > 0.5) #select significant values, in this case, 0.5

M <- M[order(-abs(M$Freq)),] #sort by highest correlationmtx_corr <- reshape2::acast(M, Var1~Var2, value.var="Freq") #turn M back into matrix

corrplot(mtx_corr, is.corr=TRUE, tl.col="black", na.label=" ") #plot correlations visually

## Now, this looks much better and readable.

Looking at our plot we can see numerous other variables that are highly correlated with *SalePrice*. We pick these variables and then create a new dataframe by only including these select variables.

Now that we have our suspect variables we can use a PairPlot to visualize all these variables in conjunction with each other.

newData <- data.frame(dataset$SalePrice, dataset$TotalBsmtSF,

dataset$GrLivArea, dataset$OverallQual,

dataset$YearBuilt, dataset$FullBath,

dataset$GarageCars )pairs(newData[1:7],

col="blue",

main = "Pairplot of our new set of variables"

)

## While you’re at it, clean your data

We should remove some useless variables which we are sure of not being of any use. Don’t apply changes to the original dataset though. Always create a new copy in case you remove something you shouldn’t have.

clean_data <- dataset[,!grepl("^Bsmt",names(dataset))] #remove BSMTx variablesdrops <- c("clean_data$PoolQC", "clean_data$PoolArea",

"clean_data$FullBath", "clean_data$HalfBath")

clean_data <- clean_data[ , !(names(clean_data) %in% drops)]#The variables in 'drops'are removed.

# Univariate Analysis

Taking a look back at our old friend, *SalePrice*, we see some extremely expensive houses. We haven’t delved into why is that so. Although we do know that these extremely pricey houses don’t follow the pattern which other house prices are following. The reason for such high prices could be justified but for the sake of our analysis, we have to drop them. Such records are called Outliers.

Simple way to understand Outliers is to think of them as that one guy (or more) in your group who likes to eat noodles with a spoon instead of a fork.

So first, we catch these outliers and then remove them from our dataset if need be. Let’s start with the *catching* part.

#Univariate Analysisclean_data$price_norm <- scale(clean_data$SalePrice) #normalizing the price variablesummary(clean_data$price_norm)plot1 <- ggplot(clean_data, aes(x=factor(1), y=price_norm)) +

theme_bw()+

geom_boxplot(width = 0.4, fill = "blue", alpha = 0.2)+

geom_jitter(

width = 0.1, size = 1, aes(colour ="red"))+

geom_hline(yintercept=6.5, linetype="dashed", color = "red")+

theme(legend.position='none')+

labs(title = "Hunt for Outliers", x=NULL, y="Normalized Price")plot2 <- ggplot(clean_data, aes(x=price_norm)) +

theme_bw()+

geom_histogram(color = 'black', fill = 'blue', alpha = 0.2)+

geom_vline(xintercept=6.5, linetype="dashed", color = "red")+

geom_density(aes(y=0.4*..count..), colour="red", adjust=4) +

labs(title = "", x="Price", y="Count")grid.arrange(plot1, plot2, ncol=2)

The very first thing I did here was normalize SalePrice so that it’s more interpretable and it’s easier to bottom down on these outliers. The normalized SalePrice has *Mean= 0* and *SD= 1*. Running a quick *‘summary()’* on this new variable price_norm give us this…

So now we know for sure that there ARE outliers present here. But do we really need to get rid of them? From the previous scatterplots we can say that these outliers are still following along with the trend and don’t need purging yet. Deciding what to do with outliers can be quite complex at times. You can read more on outliers here.

# Bi-Variate Analysis

Bivariate analysis is the simultaneous analysis of two variables (attributes). It explores the concept of a relationship between two variables, whether there exists an association and the strength of this association, or whether there are differences between two variables and the significance of these differences. There are three types of bivariate analysis.

- Numerical & Numerical
- Categorical & Categorical
- Numerical & Categorical

The very first set of variables we will analyze here are *SalePrice* and *GrLivArea*. Both variables are Numerical so using a Scatter Plot is a good idea!

`ggplot(clean_data, aes(y=SalePrice, x=GrLivArea)) +`

theme_bw()+

geom_point(aes(color = SalePrice), alpha=1)+

scale_color_gradientn(colors = c("#00AFBB", "#E7B800", "#FC4E07")) +

labs(title = "General Living Area vs. Sale Price", y="Price", x="Area")

Immediately, we notice that 2 houses don’t follow the linear trend and affect both our results and assumptions. These are our outliers. Since our results in future are prone to be affected negatively by these outliers, we will remove them.

clean_data <- clean_data[!(clean_data$GrLivArea > 4000),] #remove outliersggplot(clean_data, aes(y=SalePrice, x=GrLivArea)) +

theme_bw()+

geom_point(aes(color = SalePrice), alpha=1)+

scale_color_gradientn(colors = c("#00AFBB", "#E7B800", "#FC4E07")) +

labs(title = "General Living Area vs. Sale Price [Outlier Removed]", y="Price", x="Area")

The outlier is removed and the x-scale is adjusted. Next set of variables which we will analyze are *SalePrice* and *TotalBsmtSF*.

`ggplot(clean_data, aes(y=SalePrice, x=TotalBsmtSF)) +`

theme_bw()+

geom_point(aes(color = SalePrice), alpha=1)+

scale_color_gradientn(colors = c("#00AFBB", "#E7B800", "#FC4E07")) +

labs(title = "Total Basement Area vs. Sale Price", y="Price", x="Basement Area")

The observations here adhere to our assumptions and don’t need purging. If it ain’t broke, don’t fix it. I did mention that it is important to tread very carefully when working with outliers. You don’t get to remove them every time.

# Time to dig a bit deeper

We based a ton of visualization around ‘SalePrice’ and other important variables, but what If I said that’s not enough? It’s not Because there’s more to dig out of this pit. There are 4 horsemen of Data Analysis which I believe people should remember.

**Normality**: When we talk about normality what we mean is that the data should look like a normal distribution. This is important because a lot of statistic tests depend upon this (for example — t-statistics). First, we would check normality with just a single variable ‘SalePrice’(It’s usually better to start with a single variable). Though one shouldn’t assume that univariate normality would prove the existence of multivariate normality(which is comparatively more sought after), but it helps. Another thing to note is that in larger samples i.e. more than 200 samples, normality is not such an issue. However, A lot of problems can be avoided if we solve normality. That’s one of the reasons we are working with normality.**Homoscedasticity**: Homoscedasticity refers to the ‘*assumption that one or more dependent variables exhibit equal levels of variance across the range of predictor variables*’. If we want the error term to be the same across all values of the independent variable, then Homoscedasticity is to be checked.**Linearity**: If you want to assess the linearity of your data then I believe scatter plots should be the first choice. Scatter plots can quickly show the linear relationship(if it exists). In the case where patterns are not linear, it would be worthwhile to explore data transformations. However, we need not check for this again since our previous plots have already proved the existence of a linear relationship.**Absence of correlated errors**: When working with errors, if you notice a pattern where one error is correlated to another then there’s a relationship between these variables. For example, In a certain case, one positive error makes a negative error across the board then that would imply a relationship between errors. This phenomenon is more evident with time-sensitive data. If you do find yourself working with such data then try and add a variable that can explain your observations.

# I think we should start doing rather than saying

Starting with *SalePrice*. Do keep an eye on the overall distribution of our variable.

plot3 <- ggplot(clean_data, aes(x=SalePrice)) +

theme_bw()+

geom_density(fill="#69b3a2", color="#e9ecef", alpha=0.8)+

geom_density(color="black", alpha=1, adjust = 5, lwd=1.2)+

labs(title = "Sale Price Density", x="Price", y="Density")plot4 <- ggplot(clean_data, aes(sample=SalePrice))+

theme_bw()+

stat_qq(color="#69b3a2")+

stat_qq_line(color="black",lwd=1, lty=2)+

labs(title = "Probability Plot for SalePrice")grid.arrange(plot3, plot4, ncol=2)

*SalePrice* is not normal! But we have another trick up our sleeves viz. log transformation. Now, one great thing about log transformation is that it can deal with skewed data and make it normal. So now it’s time to apply the log transformation over our variable.

clean_data$log_price <- log(clean_data$SalePrice)plot5 <- ggplot(clean_data, aes(x=log_price)) +

theme_bw()+

geom_density(fill="#69b3a2", color="#e9ecef", alpha=0.8)+

geom_density(color="black", alpha=1, adjust = 5, lwd=1)+

labs(title = "Sale Price Density [Log]", x="Price", y="Density")plot6 <- ggplot(clean_data, aes(sample=log_price))+

theme_bw()+

stat_qq(color="#69b3a2")+

stat_qq_line(color="black",lwd=1, lty=2)+

labs(title = "Probability Plot for SalePrice [Log]")grid.arrange(plot5, plot6, ncol=2)

# Now repeat the process with the rest of our variables.

## We go with GrLivArea first

## After Log Transformation

## Now for TotalBsmtSF

# Hold On! We’ve got something interesting here.

Looks like *TotalBsmtSF* has some zeroes. This doesn’t bode well with log transformation. We’ll have to do something about it. To apply a log transformation here, we’ll create a variable that can get the effect of having or not having a basement (binary variable). Then, we’ll do a log transformation to all the non-zero observations, ignoring those with value zero. This way we can transform data, without losing the effect of having or not the basement.

#The step where I create a new variable to dictate which row to transform and which to ignore

clean_data <- transform(clean_data, cat_bsmt = ifelse(TotalBsmtSF>0, 1, 0))#Now we can do log transformation

clean_data$totalbsmt_log <- log(clean_data$TotalBsmtSF)clean_data<-transform(clean_data,totalbsmt_log = ifelse(cat_bsmt == 1, log(TotalBsmtSF), 0 ))plot13 <- ggplot(clean_data, aes(x=totalbsmt_log)) +

theme_bw()+

geom_density(fill="#ed557e", color="#e9ecef", alpha=0.5)+

geom_density(color="black", alpha=1, adjust = 5, lwd=1)+

labs(title = "Total Basement Area Density [transformed]", x="Area", y="Density")plot14 <- ggplot(clean_data, aes(sample=totalbsmt_log))+

theme_bw()+

stat_qq(color="#ed557e")+

stat_qq_line(color="black",lwd=1, lty=2)+

labs(title = "Probability Plot for TotalBsmtSF [transformed]")grid.arrange(plot13, plot14, ncol=2)

We can still see the ignored data points on the chart but hey, I can trust you with this, right?

# Homoscedasticity — Wait is my spelling correct?

The best way to look for homoscedasticity is to work try and visualize the variables using charts. A scatter plot should do the job. Notice the shape which the data forms when plotted. It could look like an equal dispersion which looks like a cone or it could very well look like a diamond where a large number of data points are spread around the centre.

Starting with ‘SalePrice’ and ‘GrLivArea’…

`ggplot(clean_data, aes(x=grlive_log, y=log_price)) +`

theme_bw()+

geom_point(colour="#e34262", alpha=0.3)+

theme(legend.position='none')+

labs(title = "Homoscedasticity : Living Area vs. Sale Price ", x="Area [Log]", y="Price [Log]")

We plotted ‘SalePrice’ and ‘GrLivArea’ before but then why is the plot different? That’s right, because of the **log transformation.**

If we go back to the previously plotted graphs showing the same variable, it is evident that the data has a conical shape when plotted. But after log transformation, the conic shape is no more. Here we solved the homoscedasticity problem with just one transformation. Pretty powerful eh?

Now let’s check ‘SalePrice’ with ‘TotalBsmtSF’.

`ggplot(clean_data, aes(x=totalbsmt_log, y=log_price)) +`

theme_bw()+

geom_point(colour="#e34262", alpha=0.3)+

theme(legend.position='none')+

labs(title = " Homoscedasticity : Total Basement Area vs. Sale Price", x="Area [Log]", y="Price [Log]")

## That’s it, we’ve reached the end of our Analysis. Now all that’s left is to get the dummy variables and… you know the rest. :)

This work was possible thanks to Pedro Marcelino. I found his Analysis on this dataset in Python and wanted to re-write it in R. Give him some love!