第九章：回归分析教学案例.ppt

Regression Analysis Chapter 11 Regression and Correlation Techniques that are used to establish whether there is a mathematical relationship between two or more variables, so that the behavior of one variable can be used to predict the behavior of others. Applicable to “Variables” data only. “Regression” provides a functional relationship (Y=f(x)) between the variables; the function represents the “average” relationship. “Correlation” tells us the direction and the strength of the relationship. The analysis starts with a Scatter Plot of Y vs X. The analysis starts with a Scatter Plot of Y vs X Regression and Correlation Excel will do Regression analysis and Correlation analysis: Tools>> Data analysis>> Regression (Correlation) Simple Linear Regression Is there a Relationship Between the Variables? What Direction is the Relationship? How Strong is the Relationship? Low High Low High ... . . . . . . . . . . . . .. . . Y X Simple Linear Regression Is there a Relationship Between the Variables? What Direction is the Relationship? How Strong is the Relationship? Low High Low High ... . . . . . . . . . . . . .. . . Y X ? ? ? Simple Linear Regression b = Y intercept = the Y value at point that the line intersects Y axis. m = slope = rise run Y X 0 b rise run A simple linear relationship can be described mathematically by Y = mX + b Simple Linear Regression Y X 0 10 5 5 0 rise run slope = rise run = (6 - 3) (10 - 4) = 1 2 intercept = 1 Y = 0.5X + 1 Simple regression example Step 1: Scatter plot Scatter plot suggests that there is a ‘linear’ relationship between Rent and Size Step 2: Analysis via EXCEL Interpreting EXCEL output Regression Equation Rent = 177.12082+1.0651439*Size Meaning of the regression coefficient What does the coefficient of Size mean? For every additional square feet, Rent goes up by $1.0651493 Using regression for prediction Predic