{"id":246,"date":"2019-08-01T09:39:46","date_gmt":"2019-08-01T09:39:46","guid":{"rendered":"http:\/\/hsp16.epgpbooks.inflibnet.ac.in\/?post_type=chapter&p=246"},"modified":"2019-08-01T09:40:23","modified_gmt":"2019-08-01T09:40:23","slug":"simple-linear-correlation","status":"publish","type":"chapter","link":"https:\/\/ebooks.inflibnet.ac.in\/hsp16\/chapter\/simple-linear-correlation\/","title":{"rendered":"Simple Linear Correlation"},"content":{"raw":"
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1. Introduction<\/strong><\/p>\r\n \r\n

What is measure of correlation?<\/strong><\/p>\r\n \r\n

Correlation refers to the linear relationship among the variables. For example, the blood pressure of a patient may be correlated with age, food habits and family history and so on. If we study the degree of relationship among the above variables, it is known as correlation.<\/p>\r\n \r\n

In this module, we are going to discuss various types of correlation and different methods of calculating correlation. The estimation of correlation depends of upon the type of data. If the data type is in actual values, we can calculate Karl pearson correlation co efficient. If the data is somewhat qualitative in nature , we have to calculate rank correlation.<\/p>\r\n \r\n

2.\u00a0 <\/strong>Objectives<\/strong><\/p>\r\n \r\n

1.\u00a0\u00a0\u00a0\u00a0\u00a0 <\/strong>To study about various types of correlation<\/strong><\/p>\r\n

2.\u00a0\u00a0\u00a0\u00a0\u00a0 <\/strong>To study the methods of estimating correlation<\/strong><\/p>\r\n \r\n

3.\u00a0 <\/strong>Types of correlation<\/strong><\/p>\r\n \r\n

Simple or Partial or Multiple:<\/strong><\/p>\r\n \r\n

If the relationship between two variables are analysed, it is called simple correlation. When more than two variables are considered, the correlation between two of them when all other variables are hold constant, i.e., when the linear effects of all other variables on them are removed, is called partial correlation. When more than two variables are considered, the correlation between one of them and its estimate based on the group consisting of the other variables is called multiple correlation.<\/p>\r\n \r\n

Linear or Non-linear or No Correlation:<\/strong><\/p>\r\n \r\n

When we plot the values of X and Y, if all the points lie on a line or scattered around the line, it is called linear correlation. When all the points lie exactly on a curve or scattered around a curve, there is non-linear correlation between the two variables.<\/p>\r\n \r\n

When the points are scattered neither around a line nor around a curve, there is no correlation between the two variables. The following diagrams show these three kinds<\/span><\/p>\r\n\"\"<\/a>\r\n\r\nMethods:<\/strong>\r\n\r\n \r\n

The following four methods are available under simple linear correlation and among them, product moment method is the best one.<\/p>\r\n \r\n

i) Scatter Diagram<\/p>\r\n

ii) Karl Pearson\u2019s correlation coefficient or product moment correlation coefficient (r)<\/p>\r\niii) Spearman\u2019s rank correlation coefficient (p)\r\n\r\niv) Correlation coefficient by concurrent deviation method (rc)\r\n\r\n \r\n\r\nSCATTER DIAGRAM<\/strong>\r\n\r\n \r\n\r\nWhen we plot the values of X and Y in a graph sheet, the resulting diagram with N points is called scatter diagram.\r\n\r\n \r\n\r\nPossible types of scatter diagram under simple linear correlation are as given below. From a diagram, it can be found out whether the correlation is positive or negative and whether it is perfect or high or low.\r\n\r\n \r\n\r\n\"\"<\/a>\r\n

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The merits of this method are as follows. This is easy to draw, non mathematical and simple to understand. This does not involve computations. The greatest demerit is that this is not quantitative. As no numerical value is computed, comparison is not\u00a0possible sometimes. Decisions based on this are not as accurate as those based on correlation coefficients.<\/span><\/p>\r\n \r\n

KARL PEARSON\u2019S COEFFICIENT OF CORRELATION (r)<\/strong><\/p>\r\n \r\n

This is also called product moment correlation coefficient. This is denoted by r. This is covariance between the two variables divided by the product of their standard deviations. This can be calculated by using any one of the formulae. Choice of a formula depends on the nature of the data. Different formulae are seen under the following examples.<\/span><\/p>\r\n\"\"<\/a>\r\n\r\n\"\"<\/a>\r\n\r\n\"\"<\/a>\r\n\r\n\"\"<\/a>\r\n