# Managerial Statistic

**Topics:**Pearson product-moment correlation coefficient, Correlation and dependence, Spearman's rank correlation coefficient

**Pages:**5 (1160 words)

**Published:**July 10, 2013

Distinguish between primary data and secondary data?

OBJECTIVE

The main objective of this topic is to measure the degree of relationship between the variables under consideration.The correlation analysis refers to the techniques used in measuring the closeness of the relationship between the variables. DEFINITION

Some important definitions of correlation are given below:

1. “Correlation analysis deals with the association between two or more variables”. ---- Simpson & kafka. 2. “When the relationship is of quantitative nature, the appropriate statistical tool for discovering and measuring the relationship and expressing it in brief formula is known as correlation”.----- Croxton & Cowden. 3.Correlation analysis attempts to determine the “degree of relationship between variables”.----- Ya Lun Chou. Thus correlation is a statistical device which helps us in analyzing the covariation of two or more variables. TYPES OF CORRELATION

Correlation is described or classified in several different ways.Three of the most important ways of classifying correlation are: 1.Positive or negative 2.Simple, partial and multiple 3. Linear and non-linear The various methods of studying correlation are

1.Scatter Diagram Method

2.Karl Pearson’s Coefficient of correlation.

3.Method of Least Squares [Of these , the first two methods shall be discussed as follows. ]

SCATTER DIAGRAM

What it is: A scatter diagram is a tool for analyzing relationships between two variables. One variable is plotted on the horizontal axis and the other is plotted on the vertical axis. The pattern of their intersecting points can graphically show relationship patterns. Most often a scatter diagram is used to prove or disprove cause-and-effect relationships. While the diagram shows relationships, it does not by itself prove that one variable causes the other. When to use it: Use a scatter diagram to examine theories about cause-and-effect relationships and to search for root causes of an identified problem. Draw the diagram. Draw roughly equal horizontal and vertical axes of the diagram, in xy plane Title and label the diagram.

Interpret the data. Scatter diagrams will generally show one of five possible correlations between the variables: Strong Positive Correlation :The value of Y clearly increases as the value of X increases. Strong Negative Correlation :The value of Y clearly decreases as the value of X increases. Weak Positive Correlation: The value of Y increases slightly as the value of X increases. Weak Negative Correlation :The value of Y decreases slightly as the value of X increases. No Correlation :There is no demonstrated connection between the two variables. KARL PEARSON'S CORRELATION COEFFICIENT (r):---

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 no linear relationship between the two variables. Correlations are rarely if ever 0, 1, or -1. If you get a certain outcome it could indicate whether correlations were negative or positive. Mathematical Formula:--

: The quantity r, called the linear correlation coefficient, measures the strength and the direction of a linear relationship between two variables. The linear correlation coefficient is sometimes referred to as the Pearson product moment correlation coefficient in honor of its developer Karl Pearson.

The mathematical...

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