Detecting outliers in R

Outliers are data points that are significantly different from other observations in a dataset. They can occur for a variety of reasons, such as measurement error, data entry errors, or other factors. For example, in a dataset of housing prices, an outlier might be a property that is priced significantly higher or lower than the other properties in the dataset. Outliers can have a significant impact on the overall analysis of a dataset, and so it is important to identify and handle them appropriately.

There are several methods for identifying outliers in a dataset, such as using statistical measures like the mean and standard deviation, or using visualization techniques like box plots or scatter plots. Once outliers have been identified, they can be handled in several ways. One common approach is to simply remove them from the dataset, although this can be problematic if the outliers are legitimate observations that should be included in the analysis. Another approach is to treat them differently in statistical analysis, such as by applying robust statistical methods that are less sensitive to outliers.

It is important to note that outliers can indicate a mistake or error in the data, but sometimes it could represent a real phenomena that is interesting to investigate. Thus, it's always important to investigate the cause of outliers before making a decision on how to handle them.

Data

The mpg (miles per gallon) dataset is a dataset containing information on various car models and their fuel efficiency. It typically includes columns for the car's make and model, number of cylinders, horsepower, weight, and miles per gallon (both city and highway). This dataset is commonly used for teaching data analysis and visualization techniques, as well as for regression analysis and machine learning. It is also available in R, Python and other programming languages. The data includes observations for 234 cars.

The columns in the dataset are:

• mpg: Miles per gallon, continuous
• cylinders: Number of cylinders, multi-valued discrete
• displacement: Engine displacement (cu. inches), continuous
• horsepower: Engine horsepower, continuous
• weight: Vehicle weight (lbs.), continuous
• acceleration: Time to accelerate from 0 to 60 mph (sec.), continuous
• model year: Model year (modulo 100), multi-valued discrete
• origin: Origin of car (1. American, 2. European, 3. Japanese), multi-valued discrete
• car name: Name of car

This dataset is commonly used for teaching data analysis and visualization techniques, as well as for regression analysis and machine learning. It is not just available in R, but in Python and other programming languages.

Method

You can use the "ggplot2" and "dplyr" packages in R to identify outliers in the "mpg" dataset. Here's an example of how you might use these packages to create a box plot of the "hwy" variable and identify outliers:

This code will create a box plot of the "hwy" variable from the "mpg" dataset using the ggplot() function and the geom_boxplot() geometry to create the boxplot, it also adds the title, x and y labels using ggtitle(), xlab(), ylab() functions respectively.

Then, it uses the Tukey method to identify outliers, the Tukey method defines an outlier as any data point that is more than 1.5 times the interquartile range (IQR) away from the upper or lower quartile. It uses the quantile() and IQR() functions to calculate the quantiles and IQR of the "hwy" variable, and the which() function to find the observations that are considered outliers. Finally, it prints the identified outliers.

It's important to note that this method is based on the assumptions of the data, and the Tukey method is just one of the many methods available to identify outliers, other methods include Z-score, Mahalanobis distance, etc. It's always good to check the data and try different methods to confirm the outliers. Additionally, it is important to visually inspect the data using plots such as boxplots, scatter plots, etc. before and after identifying outliers.