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Correlation

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Submitted By seanohea
Words 2693
Pages 11
Business Statistics

Topic: Correlation and Regression

Recommended Readings:

Lind D.A., Marchal W.G., and Wathen S.A. (2012), Statistical Techniques in Business and Economics, 15th International Ed., McGraw Hill [Chapter 13] Earlier edts are also suitable.

Waters, D., (2008) Quantitative Methods for Business,4th Ed., Financial Times, Prentice Hall [Chapter 9]

When we look at interval or ratio scale variables there is often a relationship, eg: price and quantity demanded; time spent studying and exam results obtained; gardai (police) on duty and number of crimes as well as alcohol consumed and sensibility! Regression and correlation analysis is useful because it allows us predict the value of one variable from the knowledge of another. The said relationship can be positive or negative. One first step in establishing if any of these relationships exist is to draw a scatter graph.

A Scatter plot or diagram is a chart that portrays the relationship between the two variables. It is the usual first step in correlation analysis

* The Dependent variable is the variable being predicted or estimated. * The Independent variable provides the basis for estimation. It is the predictor variable.

Correlation Analysis
From a scatter plot we have a first picture of the data. The next step is to calculate a measure which can assess the strength of that relationship. The correlation coefficient r which represents correlation in a sample is calculated as:

r = n Σxy- ΣxΣy √ [n Σx2 – (Σx)2][nΣy2 – (Σy)2]

The correlation coefficient r was first identified by Karl Pearson around 1900 and as such the correlation coefficient is also often known as the Pearson coefficient or Product Moment Correlation coefficient. The correlation coefficient is such that its value must lie between (-1 +1). A correlation coefficient of (-1 or +1)

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