Graphical Representations

Univariate Analysis - Analysis of a single variable is called Univariate Analysis.

Graphs using which we can visualize single variables are:

• Bar Plot
• Index Plot
• Dot Plot
• Strip Plot
• Violin Plot
• Stem & Leaf Plot
• Candle Plot
• Pie Chart
• Time Series Plots
• Histogram
• Density Plot
• Boxplot or Box & Whisker Plot
• Q-Q Plot or
• Quantile - Quantile Plot

Graphical Representations

For univariate analysis, the histogram, box plot, and Q-Q plot are the most often used plots.

Histogram

Another name for a histogram is a Frequency Distribution Plot.

The histogram's main use is to show the distribution's shape.

Histograms are used to detect the existence of outliers as a secondary purpose.

Box Plot is also called as Box and Whisker Plot

• Box Plot gives the 5 point summary, namely, Min, Max, Q1 / First Quartile, Q3 / Third Quartile, Median / Q2 / Second Quartile
• Middle 50% of data is located in the Inter Quartile Range (IQR) = Q3 - Q1
• Formula used to identify outliers is Q1 - 1.5 (IQR) on the lower side and Q3 + 1.5 (IQR) on the upper side
• Primary Purpose of Boxplot is to identify the existence of outliers
• Secondary Purpose of Boxplot is to identify the shape of distribution

Q-Q plot is also called Quantile Quantile Plot

• Q-Q plot is used to check whether the data are normally distributed or not. If data are non-normal then we resort to transformation techniques to make the data normal
• The line in the Q-Q plot connects from Q1 to Q3
• X-axis contains the standardized values of the random variable
• Y-axis contains random values, which are not standardized
• If the data points fall along the line then data are considered to be Normally Distributed

Bivariate Analysis

Analysing two variables is known as bivariate analysis.

To determine whether two variables are correlated, use a scatter plot.

The primary purpose of the Scatter Plot is to determine the following:

• Direction - Whether the direction is Positive or Negative or No Correlation
  
• Strength - Whether the strength is Strong or Moderate or Weak
  
• Check whether the relationship is Linear or Nonlinear
  

Finding out if the relationship is linear or non-linear is the Scatter Plot's secondary goal.

• Determining strength using a scatter plot is subjective
• Objectively evaluate strength using Correlation Coefficient (r)
• Correlation coefficient value ranges from +1 to -1
• Covariance is also used to track the correlation between 2 variables
• However, Correlation Coefficient normalizes the data in correlation calculations whereas Covariance does not normalize the data in correlation calculation
• |r| > 0.85 implies that there is a strong correlation between the variables
• |r| < = 0.4 implies that there is a weak correlation
• |r| > 0.4 & |r|< = 0.85 implies that there is a moderate correlation

Multivariate Analysis

The two main plots to perform Multivariate analysis are:

• Pair Plot
• Interaction Plot