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# Graphical Representations

• July 15, 2023
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### 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

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