182 objectives to use regression analysis to estimate

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18.2. OBJECTIVES To use regression analysis to estimate the relationship between two variables. To use the least square estimating equation to predict future values of the dependent variables. To examine decision-making situations where multiple regression can be used to make predictions. To establish a regression equation for estimating value of a dependent variable given the values of two or more independent variables. To measure the coefficient of determination to understand the proportion of variation in the dependent variable which is explained by the independent variables. 18.3. CONTENTS
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162 18.3.1. Definition 18.3.2. Simple Linear Regression 18.3.3.1. The least square method 18.3.2.2. Lines of Regression 18.3.2.3. Properties of Regression Coefficients 18.3.2.4. Coefficient of Determination 18.3.2.5. Standard Error of Estimate 18.3.3. Multiple Regression Analysis 18.3.3.1. Estimating Parameters of Multiple Regression Model In regression, we intend to describe the dependence of a variable on a independent variable. We employee regression equations to lend support to hypothesis regarding the possible causation of changes in y by changes in x; for purposes of prediction of y in terms of x; and for purposes of explaining some of the variations of y by x, by using the variable as a statistical control Studies of the effects of temperature on heartbeat rate, protein intake on growth rate in a child, age of person on blood pressure, or dose of an insecticide on mortality of the insect population are all typical examples of regression for the purposes named above. 18.3.1. DEFINITION “Regression is the measure of the above average relationship between two or more v ariables in terms of the original units of the data” – Blair “One of the most frequent used techniques in economics and business research, to find a relation between two or more variables that are related casually is regression analysis” - Taro Yamane “R egression 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. The following steps are necessary to carry out the regression analysis; i. On the basic of theoretical understanding (or otherwise), identify the independent variables(s) and the dependent variable. ii. Make an appropriate guess of the form of the relationship, i.e., linear, parabolic, exponential, etc., between the dependent and independent variables. The scatter diagram will help in identifying the form of the relationship. iii. Estimate the regression parameters of the model identified in step (ii). iv. Carry out an error analysis to see how well the model fits into the sample data.
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163 18.3.2. SIMPLE LINEAR REGRESSION 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; a and b are the parameters of the regression equation. The
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