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Unit 10: Correlation: Scatter Diagram Method, Karl Pearson's Coefficient of Correlation
            Pavitar Parkash Singh, LPU

                      Unit 10: Correlation: Scatter Diagram Method,                                  Notes

                         Karl  Pearson's Coefficient of Correlation




             CONTENTS
             Objectives
             Introduction
             10.1 Scatter Diagram Method
             10.2 Karl Pearson’s Coefficient of Correlation
             10.3 Summary
             10.4 Key-Words
             10.5 Review Questions
             10.6 Further Readings


            Objectives


            After reading this unit students will be able to:
            •   Discuss Scatter Diagram Method.
            •   Explain Karl Pearson’s Coefficient of Correlation.

            Introduction

            A scatter diagram is used to show the relationship between two kinds of data. It could be the
            relationship between a cause and an effect, between one cause and another, or even between one
            cause and two others. To understand how scatter diagrams work, consider the following example.
            Suppose you have been working on the process of getting to work within a certain time period. The
            control chart you constructed on the process shows that, on average, it takes you 25 minutes to get to
            work. The process is in control. You would like to decrease this average to 20 minutes. What causes
            in the process affect the time it takes you to get to work ? There are many possible causes, including
            traffic, the speed you drive, the time you leave for work, weather conditions, etc. Suppose you have
            decided that the speed you drive is the most important cause. A scatter diagram can help you determine
            if this is true.
            In this case, the scatter diagram would be showing the relationship between a “cause” and an “effect.”
            The cause is the speed you drive and the effect is the time it takes to get to work. You can examine this
            cause and effect relationship by varying the speed you drive to work and measuring the time it takes
            to get to work. For example, on one day you might drive 40 mph and measure the time it takes to get
            to work. The next day, you might drive 50 mph. After collecting enough data, you can then plot the
            speed you drive versus the time it takes to get to work. Figure 1 is an example of a scatter diagram for
            this case. The cause (speed) is on the x-axis. The effect (time it takes to get to work) is on the y-axis.
            Each set of points is plotted on the scatter diagram.
            In statistics, the Pearson product-moment correlation coefficient (r) is a common measure of the
            correlation between two variables X and Y. When measured in a population the Pearson Product
            Moment correlation is designated by the Greek letter rho (?). When computed in a sample, it is
            designated by the letter “r” and is sometimes called “Pearson’s r.” Pearson’s correlation reflects the
            degree of linear relationship between two variables. It ranges from + 1 to – 1. A correlation of + 1
            means that there is a perfect positive linear relationship between variables. A correlation of – 1 means
            that there is a perfect negative linear relationship between variables. A correlation of 0 means there is



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