Page 1 PRESENTATION ON REGRESSION ANALYSIS Page 2 PRESENTATION ON REGRESSION ANALYSIS Definition The Regression Analysis is a technique of studying the dependence of one variable (called dependant variable), on one or more variables (called explanatory variable), with a view to estimate or predict the average value of the dependent variables in terms of the known or fixed values of the independent variables. THE REGRESSION TECHNIQUE IS PRIMARILY USED TO : • Estimate the relationship that exists, on the average, between the dependent variable and the explanatory variable • Determine the effect of each of the explanatory variables on the dependent variable, controlling the effects of all other explanatory variables • Predict the value of dependent variable for a given value of the explanatory variable Page 3 PRESENTATION ON REGRESSION ANALYSIS Definition The Regression Analysis is a technique of studying the dependence of one variable (called dependant variable), on one or more variables (called explanatory variable), with a view to estimate or predict the average value of the dependent variables in terms of the known or fixed values of the independent variables. THE REGRESSION TECHNIQUE IS PRIMARILY USED TO : • Estimate the relationship that exists, on the average, between the dependent variable and the explanatory variable • Determine the effect of each of the explanatory variables on the dependent variable, controlling the effects of all other explanatory variables • Predict the value of dependent variable for a given value of the explanatory variable Assumptions of the Linear Regression Model 1. Linear Functional form 2. Fixed independent variables 3. Independent observations 4. Representative sample and proper specification of the model (no omitted variables) 5. Normality of the residuals or errors 6. Equality of variance of the errors (homogeneity of residual variance) 7. No multicollinearity 8. No autocorrelation of the errors 9. No outlier distortion Page 4 PRESENTATION ON REGRESSION ANALYSIS Definition The Regression Analysis is a technique of studying the dependence of one variable (called dependant variable), on one or more variables (called explanatory variable), with a view to estimate or predict the average value of the dependent variables in terms of the known or fixed values of the independent variables. THE REGRESSION TECHNIQUE IS PRIMARILY USED TO : • Estimate the relationship that exists, on the average, between the dependent variable and the explanatory variable • Determine the effect of each of the explanatory variables on the dependent variable, controlling the effects of all other explanatory variables • Predict the value of dependent variable for a given value of the explanatory variable Assumptions of the Linear Regression Model 1. Linear Functional form 2. Fixed independent variables 3. Independent observations 4. Representative sample and proper specification of the model (no omitted variables) 5. Normality of the residuals or errors 6. Equality of variance of the errors (homogeneity of residual variance) 7. No multicollinearity 8. No autocorrelation of the errors 9. No outlier distortion • Regression analysis is the most often applied technique of statistical analysis and modeling. • If two variables are involved, the variable that is the basis of the estimation, is conventionally called the independent variable and the variable whose value is to be estimated+ is called the dependent variable. • In general, it is used to model a response variable (Y) as a function of one or more driver variables (X 1 , X 2 , ..., X p ). • The functional form used is: Y i = ? 0 + ? 1 X 1i + ? 2 X 2i + ... + ? p X pi + ? • The dependent variable is variously known as explained variables, predictand, response and endogenous variables. • While the independent variable is known as explanatory, regressor and exogenous variable. Introduction to Regression Analysis Page 5 PRESENTATION ON REGRESSION ANALYSIS Definition The Regression Analysis is a technique of studying the dependence of one variable (called dependant variable), on one or more variables (called explanatory variable), with a view to estimate or predict the average value of the dependent variables in terms of the known or fixed values of the independent variables. THE REGRESSION TECHNIQUE IS PRIMARILY USED TO : • Estimate the relationship that exists, on the average, between the dependent variable and the explanatory variable • Determine the effect of each of the explanatory variables on the dependent variable, controlling the effects of all other explanatory variables • Predict the value of dependent variable for a given value of the explanatory variable Assumptions of the Linear Regression Model 1. Linear Functional form 2. Fixed independent variables 3. Independent observations 4. Representative sample and proper specification of the model (no omitted variables) 5. Normality of the residuals or errors 6. Equality of variance of the errors (homogeneity of residual variance) 7. No multicollinearity 8. No autocorrelation of the errors 9. No outlier distortion • Regression analysis is the most often applied technique of statistical analysis and modeling. • If two variables are involved, the variable that is the basis of the estimation, is conventionally called the independent variable and the variable whose value is to be estimated+ is called the dependent variable. • In general, it is used to model a response variable (Y) as a function of one or more driver variables (X 1 , X 2 , ..., X p ). • The functional form used is: Y i = ? 0 + ? 1 X 1i + ? 2 X 2i + ... + ? p X pi + ? • The dependent variable is variously known as explained variables, predictand, response and endogenous variables. • While the independent variable is known as explanatory, regressor and exogenous variable. Introduction to Regression Analysis Derivation of the Intercept n n n i i i i i i n n n n i i i i i i i i n i i n n n i i i i i i a y b x n n i i i i y a bx e e y a bx e y a b x Because by definition e y a b x na y b x a y bx = = = = = = = = = = = = - = = = + + = - - = - - = = - - ?? ? = - = - ? ?? ? ? ?? ? ? ? 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0Read More

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