16. Obtain two Regression lines. res 124 67 121 108 51 73 97 91 Sale 111 57 70 91 97 39 61 80 75 71 Purchases 47 And also calculate r.
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Unit-8 REGRESSION ANALYSIS INTRODUCTION So far we have studied correlation analysis, which measures the direction and strength of the relationship between two variables. After establishing the correlation existing between the two variables one may be interested in estimating the value of one variable with the help of value of another variable. The statistical method with the help of which we are in a possible to estimate or predict the unknown value of one variable from the known value of another variables is called Regression. The Regression succeeds the correlation once the correlation ship between the two variations is established, the regression analysis proceeds with the estimation of probable values. Sir. Francis Galton, a British biometrician, introduced the concept regression for the first time in 1877: while studying the correlation between the heights of sons and their fathers. He concluded in his studies, “Tall fathers tend to have tall sons and short fathers short sons. The average height of the sons of a group of tall fathers is less than that of the fathers. While the average height of the sons of a group of short fathers is greater than that of the fathers. It means the coming generations of tall or short parents tend to step back to average height of population. Now a days a modern statistician prefer to use the term Regression in the sense of estimation, which is an important statistical tool in a economics business. Meaning Regression means returning or stepping back to the average value. In statistics, the term Regression means simple the average relationship. We can predict or estimate the value of dependent variable from the given related values of independent variable with the help of a Regression Technique. The measure of Regression studies the nature of correlation ship to estimate the most probable values. It establishes a functional relationship between the independent and dependent variables. Definition According to Blair “Regression is the measure of the average relationship between two or more variable in terms of the original units of the data” According to Taro Yamame “ One of the most frequently used technique in economics and business research to find a relation between two or more variables that are related casually, is regression analysis. According to Wallis and Robert “It is often more important to find out what the relation actually is, in order to estimate or predict one variable and statistical technique appropriate in such a case is called regression analysis. USES OF REGRESSION ANALYSIS Regression analysis is of great practical use even more than the correlation analysis; the following are some uses, 1. Regression analysis helps in establishing a functional relationship between two or more variables once this is established, it can be used for various advanced analytic purpose. 2. With the use of electronic machine and computers tedium of collection of regression equation particularly expressing multiple and a non-linear relationship has been reduced a great deal. 3. Since most of the problems of economic analysis are based on cause and effect relationship. The regression analysis is a highly valuable tool in economic and business research. 4. The regression analysis is very useful for prediction purpose. Once a functional relationship is known, the value of dependent variable can be predicted from the given value of the independent variable. CORRELATION AND REGRESSION These two techniques are directed towards a common purpose of establishing the degree and the direction of relationship between two or more variables but the methods of doing so are different. The choice of one or the other will depend on the purpose. In spite certain similarities between these two, but there are some basic differences in the two approaches, which have been summarized below: 138