Basics of Correlation Analysis in JMP Software

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Basics of Correlation Analysis in JMP
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Introduction
Correlation analysis is one of the basic
statistical procedures used to examine the
relationship between two or more variables.
Knowing how variables are related can yield
valuable insights applicable in various
disciplines starting from economics to biology
and engineering. JMP It is one of the most
commonly used statistical analysis software
designed by SAS company and is very effective for
performing correlation analysis. In this
presentation, we will guide you through the basic
steps of performing correlation analysis in JMP
using Auto MPG dataset which is used to analyze
the performance of a car depending on different
attributes.
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What is Correlation ?
Before exploring the steps involved in JMP, lets
define what correlation is. In simple terms,
correlation measures is the extent (in terms of
direction and strength) to which 2 continuous
variables are related linearly. The correlation
coefficient, denoted as r, ranges from -1 to
1. qr 1 A perfect positive linear
relationship between variables. As one variable
increases, the other increases as well. qr -1
A perfect negative linear relationship. As one
variable increases, the other decreases. qr 0
No linear relationship between the variables. The
closer the correlation coefficient is to 1 or
-1, the stronger the linear relationship.
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Getting Started with JMP Software
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JMP has friendly user interface for both
beginners as well as professional users. For
performing correlation analysis, let us consider
using the Auto MPG dataset containing features
such as MPG, number of cylinders, displacement
and horsepower, weight, acceleration, year of
manufacture and country of origin. The data set
can be either imported from JMP integrated data
library or maybe downloaded from a data base such
as the UCI Machine Learning Repository.
Step 1 Load the Dataset
1.Open JMP and start a new project. 2.Go to File
gt Open and load the "Auto MPG" dataset, which
should be in .jmp, .csv, or .xls format. Once the
dataset is loaded, you will see all the variables
in the data table.
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Step 2 Overview of the Data
After loading the data, spend some time to study
the variables. The key attributes we will focus
on for correlation analysis are qMPG Miles per
gallon, a measure of fuel efficiency. qHorsepower
The power output of the vehicle. qWeight The
weight of the car. qAcceleration The time taken
for the car to accelerate from 0 to 60 mph.
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Step 3 Exploring the Data with Graph Builder
Step 4 Launching the Correlation Platform

• Before performing the correlation, visualizing
  the data using JMPs Graph Builder is helpful.
  See the steps below
• Click on Graph in the toolbar and select Graph
  Builder.
• Drag and drop variables such as MPG, Horsepower,
  and Weight into the graph. This allows you to
  visually inspect potential relationships between
  variables.
• For example, if you plot MPG against Horsepower,
  you might see an inverse relationship, indicating
  that as horsepower increases, MPG decreases.
• Visualizing relationships give you some clarity
  on of how the correlation coefficients will
  behave.

• Now, let us perform the actual correlation
  analysis
• Go to Analyze gt Multivariate Methods gt
  Multivariate.
• In the dialog box, select the variables you want
  to include in the correlation analysis. For this
  example, we will select MPG, Horsepower, Weight,
  and Acceleration.
• Click OK to generate the correlation matrix.

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STEP 5
Interpreting the Correlation Matrix
Once the correlation matrix is generated, a table
gets displayed that shows the correlation
coefficients between all selected variables.
Here's how to interpret the results MPG and
Horsepower You might see a negative correlation,
indicating that as horsepower increases, MPG
decreases. This implies that cars having more
powerful engines are less fuel-efficient. MPG and
Weight There will likely be a strong negative
correlation, implying that heavier cars are less
fule-efficient. Horsepower and Weight These two
variables may show a positive correlation,
indicating that heavier cars usually have more
powerful engines. Acceleration and MPG There
might be a weak positive or negative correlation,
depending on the characteristics of the dataset.
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Step 6 Visualizing Correlation with Pairwise
Plots
JMP also facilitates you to view these
relationships with the help of pairwise plots,
which provide scatterplots for each pair of
variables 1.In the Multivariate dialog box,
click on the red triangle next to the correlation
matrix and select Pairwise Plots. 2.For each pair
of variables, JMP will show scatterplots in order
to visualize the relationship. For example, the
scatterplot of MPG vs Weight will likely show a
downward trend, consistent with the negative
correlation observed in the matrix.
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Advanced Options for Correlation in JMP

• Partial Correlation To make adjustments on the
  effect of one or more variables, a partial
  correlation test is usually done. It can be
  accessed under the red triangle present in the
  basic window of Multivariate platform.
• Non-linear Relationships Although correlation
  analysis describes linear relations, JMP offers
  additional tools for analyzing non-linear
  relations as well. using the Fit Y by X feature
  you can fit different type of models such as
  polynomial and exponential fits.

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Practical Example Correlation Analysis
Interpretation
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lets interpret a hypothetical outcome from the
correlation matrix
Variables Correlation Coefficient (r)
MPG vs Weight -0.85
MPG vs Horsepower -0.78
MPG vs Acceleration 0.42
Horsepower vs Weight 0.79
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from this matrix

• The negative correlation coefficient of -0.85 of
  MPG and Weight indicates that vehicles with
  higher weight have lower miles per gallon.
• The negative coefficient calculated for MPG and
  Horsepower (-0. 78) corroborates the hypothesis
  that cars with physically powerful engines are
  less fuel efficient.
• A moderate positive relationship between MPG and
  Acceleration (0. 42) could imply that cars with
  better acceleration or faster 0-60 times tend to
  get better MPG.
• Lastly, the coefficients calculated for
  Horsepower and Weight wherein the coefficient of
  0.79 shows that, in general, the weight does
  correlate with the power of the cars.

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Benefits of JMP Assignment Help for Students
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Benefits of JMP Assignment Help for Students
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Recommended Textbooks
Applied Multivariate Statistical Analysis by
Richard A. Johnson and Dean W. Wichern This is
a comprehensive book on multivariate statistics,
with detailed coverage of correlation and other
related topics.
Statistics for Business and Economics by Paul
Newbold, William L. Carlson, and Betty Thorne A
great resource for students looking to apply
statistical methods in business contexts,
including correlation analysis.
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