SIMPLE LINEAR REGRESSION

Simple Linear Regression

• Has one dependent variable and one independent variable

• Relationship between two variables is approximated by a straight line

Objectives

• To establish relationship of two variables

• Use equation to forecast new observations 

Simple Linear Regression Model

• Equation describing how y is related to x 

• an error term

y = B0 + B1x + e

• BO and B1 are parameters of the model

• e is a random variable called (error term).

• Regression Equation: E(y) = BO + B1x

  • Graph of regression equation is a straight line

  • BO = y intercept

  • B1 = slope

LEAST SQUARES METHOD

• STEP 1: Slope (b1)

• STEP 2: y-intercept (b0) = y - b1x

COEFFCIENT DETERMINATION

Coefficient of determination - provides measure of the goodness of fit for the estimated regression equation

• How well can the equation explain the estimated value of y

SST = SSR + SSE

r² = SSR/SST