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Unit 11: Multiple Regression and Correlation Analysis
Tanima Dutta, Lovely Professional University

Unit 11: Multiple Regression and Correlation Analysis Notes

CONTENTS
Objectives
Introduction
11.1 Regression Analysis
11.1.1 Simple Regression
11.2 Meaning of Multiple Regressions
2
11.3 Coefficient of Determination ( )
11.3.1 Linear Multiple Regression Analysis
11.3.2 Logistic Regression Analysis
11.4 Coefficient of Multiple Determinations
11.5 Summary
11.6 Keywords
11.7 Review Questions
11.8 Further Readings

Objectives

After studying this unit, you will be able to:

 Discuss the Regression analysis;
 Explain the meaning of multiple regressions;

 Describe the coefficient of determination;
 Identify the coefficient of multiple determinations.

Introduction

As you develop Cause & Effect diagrams based on data, you may wish to examine the degree of
correlation between variables. A statistical measurement of correlation can be calculated using
the least squares method to quantify the strength of the relationship between two variables. The
output of that calculation is the Correlation Coefficient, or (r), which ranges between –1 and 1.
A value of 1 indicates perfect positive correlation – as one variable increases, the second increases
in a linear fashion. Likewise, a value of –1 indicates perfect negative correlation – as one variable
increases, the second decreases. A value of zero indicates zero correlation.
Before calculating the Correlation Coefficient, the first step is to construct a scatter diagram.
Most spreadsheets, including Excel, can handle this task. In this case, the process improvement
team is analyzing door closing efforts to understand what the causes could be. The Y-axis
represents the width of the gap between the sealing flange of a car door and the sealing flange
on the body – a measure of how tight the door is set to the body. The fishbone diagram indicated
that variability in the seal gap could be a cause of variability in door closing efforts.

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