Regression Method
1 Regression Method
Chapter Topics Multiple regression ● Autocorrelation Slide 2
Slide 2 Chapter Topics • Multiple regression • Autocorrelation
Regression Methods To forecast an outcome (response variable, dependent variable) of a study based on a certain number of factors(explanatory variables, regressors The outcome has to be quantitative but the factors can either by quantitative or categorical Simple regression deals with situations with one explanatory variable, whereas multiple regression tackles case with more than one regressors Slide 3
Slide 3 Regression Methods • To forecast an outcome (response variable, dependent variable) of a study based on a certain number of factors (explanatory variables, regressors). • The outcome has to be quantitative but the factors can either by quantitative or categorical. • Simple Regression deals with situations with one explanatory variable, whereas multiple regression tackles case with more than one regressors
Simple linear regression Collect data Population Random Sampl le Y=bo+bx+e Unknown Relationship s Y =Bo+BX,+E, $ ②$ ②$ $ ②$ Slide 4
Slide 4 Simple Linear Regression – Collect data Population J $ J $ J $ J $ J $ Unknown Relationship Yi Xi i = + + 0 1 Random Sample J $ J $ J $ J $ Y = b +b X + e 0 1
Multiple regression Two or more explanatory variables Multiple linear regression model Y=Bo+BX1+B2X2++B,X,+e where s is the error term and E-N(O, 0) Multiple linear regression equation E()=Bo+B,X1+B2x2+.+BpXp Estimated Multiple linear regression equation Y=b+bx1+b2X2+…+bnX Slide 5
Slide 5 Multiple Regression • Two or more explanatory variables • Multiple linear regression model where is the error term and ~ N(0, 2 ) • Multiple Linear Regression Equation • Estimated Multiple Linear Regression Equation = + + + + + Y X X p X p ... 0 1 1 2 2 E Y = + X + X + + p X p ( ) ... 0 1 1 2 2 Y = b +b X +b X + +bp X p ... ˆ 0 1 1 2 2