# Thu we 1 2 17 078 2392 a b andb thus the estimated

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Thu, we 1 2 1.7, 0.78, 23.92 a b andb Thus, the estimated linear multiple regression function is 1 2 1.7 0.78 23.92 i i i Y X X This regression function can be used to estimate the sales performance of any salesman when hios aptitude test score and his effort index are known. For example, a salesman whose aptitude test score is 40 and effort index is 0.8 will have a sales performance of 1.7 0.78(40) 23.92(0.8) 52.04 Y Y or Rs= 52040. 18.4. REVISION POINTS 1) The regression analysis is used to predict the value of one character or variable from the value of the other character or variable. 2) The variable whose value is influenced or is to be predicted, is called a dependent variable. 3) The variable which influences the values is called an independent variable. 4) A linear regression equation with more than one dependent variables is called multiple linear regression model. 5) The coefficient of determination 2 R is used to measure of the goodness of fit of a regression line. 18.5. INTEXT QUESTIONS 1) State the purpose of Regression analysis. 2) Discuss the steps necessary to carryout regression analysis. 3) What are the underlying assumptions in regression analysis? 18.6. SUMMARY “Regression analysis attempts to establish the nature of the relationship between variables that is to study the functional relationship between the variables and there by provide a mechanism for prediction or forecasting. A simple and most common form of mathematical relationship used between two variables is the linear or the straight line. The form of the relationship can be expressed as Y a bX , where Y represents the dependent variable and X is the independent variable;

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181 a and b are the parameters of the regression equation. The least squares method is used to fit a straight line to the points on the scatter diagram. The coefficient of determination, 2 R is a widely used measure of the goodness of fit of a regression line. It measures the extent or strength, of the association that exists between the two variables, X and Y. A multiple regression equation or model is used in the same way as that a simple linear regression is used for understanding the relationship among variables of interest and for estimating the average value of dependent variable. y given a set of values of independent variables in the data set. Assumptions for multiple linear regression model are same as for the simple linear regression model. 18.7. TERMINAL EXERCISES 1) Explain different methods of regression analysis. 2) Discuss the characteristics of least squares regression analysis. 18.8. SUPPLEMENTARY MATERIALS 1) analysis 2) analysis 18.9. ASSIGNMENTS 1) a) Fit a regression equation X on Y.
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• Spring '12
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