第13章多重回归模型 ultiple Regression Models
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
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 I dependent 2 or more independent variables is a linear function Population Random Population slopes Y-intercept Error Y=Bo+BX+BX2i+ooo+BXoi+ai Y=0+X+b,X2i+000+boXi +ei Dependent(Response) Independent(Explanatory) variable for sample variables for sample model
The Multiple Regression Model 多重回归模型 Yi X i X i pXpi i = + + +•••+ + 0 1 1 2 2 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 Yi b b X i b X i bpXpi ei ˆ = 0 + 1 1 + 2 2 +•••+ +
Sample multiple regression Model 简单多重回归-线性 Y=50+,X+b,X2i +..+b, Xoi +e Y=b+bX1+b2×2+oo+bxp
Sample Multiple Regression Model 简单多重回归----线性 X2 X1 Y Yi b b X i b X i bpXpi ˆ = 0 + 1 1 + 2 2 +•••+ Yi b b X i b X i + bpXpi + ei = + + + • • • 0 1 1 2 2 ei
Multiple regression Model: Example Develop a model for oil (Gal)Temp (F)Insulation estimating heating oil 275.30 40 3 363.80 27 3 used for a single family 164.30 40 10 home in the month of 40.80 73 january based on average 94.30 64 temperature and amount 230.90 34 6 of insulation in inches 366.70 9 6 300.60 8 10 237.80 23 10 121.40 63 3 31.40 65 10 203.50 41 441.10 21 3 323.00 38 52.50 58 10
O il (G a l) T e m p In su la tio n 275.30 4 0 3 363.80 2 7 3 164.30 4 0 1 0 40.80 7 3 6 94.30 6 4 6 230.90 3 4 6 366.70 9 6 300.60 8 1 0 237.80 2 3 1 0 121.40 6 3 3 31.40 6 5 1 0 203.50 4 1 6 441.10 2 1 3 323.00 3 8 3 52.50 5 8 1 0 Multiple Regression Model: Example ( Develop a model for 0F) estimating heating oil used for a single family home in the month of January based on average temperature and amount of insulation in inches