文档介绍：第13章多重回归模型
Multiple Regression Models
本章概要
The Multiple Regression Model
Contribution of Individual Independent Variables
Coefficient of Determination
Categorical Explanatory Variables
Transformation of Variables
Model Building
The Multiple Regression Model 多重回归模型
Relationship between 1 dependent & 2 or more independent variables is a linear function
Population Y-intercept
Population slopes
Dependent (Response) variable for sample
Independent (Explanatory) variables for sample model
Random Error
Sample Multiple Regression Model 简单多重回归----线性
X2
X1
Y
ei
Multiple Regression Model: Example
(0F)
Develop a model for estimating heating oil used for a single family home in the month of January based on average temperature and amount of insulation in inches.
Sample Regression Model: Example
Excel Output
For each degree increase in temperature, the average amount of heating oil used is decreased by gallons, holding insulation constant.
For each increase in one inch of insulation, the use of heating oil is decreased by gallons, holding temperature constant.
Using The Model to Make Predictions
Estimate the average amount of heating oil used for a home if the average temperature is 300 and the insulation is 6 inches.
The estimated heating oil used is gallons
Coefficient of Multiple Determination
Excel Output
Adjusted r2
reflects the number of explanatory variables and sample size
is smaller than r2
Residual Plots 残差散点图
Residuals Vs Yi
May need to transform Y variable
Residuals Vs X1
May need to transform X1variable
Residuals Vs X2
May need to transform X2 variable
Residuals Vs Time
May have autocorrelation(自回归)
Residual Plots: Example
Excel Output
No Discernable Pattern