tailieunhanh - KInh tế ứng dụng_ Lecture 5: Simple versus Multiple Regression

Multiple regression is the extension of simple regression, to take account of more than one independent variable X. In multiple regression, we study the relationship between Y and a number of explanatory variable (X1, X2, , Xk). The model we assume is as follows: Yi = β0 + β1X1 + β2X2 + + βkXk + ei | Applied Econometrics 1 Simple versus Multiple Regression Applied Econometrics Lecture 5 Simple versus Multiple Regression Truth is rarely pure and never simple 1 Multiple regression model Multiple regression is the extension of simple regression to take account of more than one independent variable X. In multiple regression we study the relationship between Y and a number of explanatory variable Xi X2 . Xk . The model we assume is as follows Yi po piXi P2X2 . pkXk ei 2 Simple versus multiple regression Direct and indirect effects Example 1 In a fertility survey of 4700 Fiji women Kendall and O Muirchearttaigh 1977 the following variables were observed for each women. AGE women s present age at time of the study EDUC women s education in years CHILDN number of children the women has borne From this data two regression equations were calculated CHILDN AGE - EDUC EDUC - AGE Questions a For a women who is one year older than another calculate i The expected change in CHILDN if EDUC is constant ii The expected change in EDUC iii The expected change in CHILDN if EDUC is changing too b What is the simple regression coefficient of CHILDN against AGE Written by Nguyen Hoang Bao May 22 2004 Applied Econometrics 2 Simple versus Multiple Regression Solution a Noting that the change in age is one we can now answer the questions i Since EDUC is constant the expected change for CHILDN is given by the multiple regression coefficient bi . the arrow pointing from AGE to CHILDN There is an expected increase of children. ii The expected change in EDUC is given by the regression coefficient b . the arrow pointing down from AGE to EDUC There is an expected increase of - years of education that is fewer years of education. iii Since EDUC is changing simultaneously the expected change in CHILDN is found from the simple regression of CHILDN against AGE which is unfortunately not given. Let us see if we can calculate it from the .