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BUAD 310 2 Multiple Linear Regression Basic Multiple Regression Model Measures of Fit Inference Multicollinearity
BUAD 310 3 Fertility index, Switzerland, 1988; Mosteller and Tukey, pages  550-551 VARIABLES Fertility index  AG: Proportion of population in agriculture  ARMY: Proportion of high-mark draftees  ED: Proportion with education past primary  CATH: Proportion catholic  MORT: Infant mortality before age 1 What variables have greatest impact on Fertility? Example:  Swiss Fertility Rates

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BUAD 310 4 Relationship between 1 dependent & 2 or more independent  variables is a linear function Dependent  (Response)  Variable Independent  (Explanatory)  Variables Population  Slopes Population  Y-Intercept Random  Error   Y = β 0 + β 1 X 1 + β 2 X 2 + ... + β k X k + ε Multiple Regression Model
BUAD 310 5 Relationship between 1 dependent & 2 or more independent  variables is a linear function Dependent  (Response)  Variable Independent  (Explanatory)  Variables Population  Slopes Population  Y-Intercept Random  Error Multiple Regression Model   Fert = β 0 + β 1 Ag + β 2 Army + β 3 Ed + β 4 Catholic + β 5 Mort + ε

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BUAD 310 6 Descriptive Statistics:  Fertility  Example Descriptive Statistics: Mort, Fert, Ag, Army, Ed, Catholic Variable N Mean StDev SE Mean Minimum Maximum Fert 47 0.7014 0.1249 0.0182 0.3500 0.9250 Mort 47 0.19943 0.02913 0.00425 0.10800 0.26600 Ag 47 0.5066 0.2271 0.0331 0.0120 0.8970 Army 47 0.1649 0.0798 0.0116 0.0300 0.3700 Ed 47 0.1098 0.0962 0.0140 0.0100 0.5300 Catholic 47 41.14 41.70 6.08 2.15 100.00 Correlations: Mort, Fert, Ag, Army, Ed, Catholic Fert Ag Army Ed Catholic Ag 0.353 Army -0.646 -0.687 Ed -0.664 -0.640 0.698 Catholic 0.464 0.401 -0.573 -0.154 Mort 0.417 -0.061 -0.114 -0.099 0.175
BUAD 310 7 1. Slope ( b i ) Estimated change in  Y  for each 1 unit  increase in  X i   accounting for other  variables in the model 2.  Y -Intercept ( b 0 ) Average value of  Y  when  all   X i  = 0* *Note: be careful of this statement: You need to have  data   where  all   X i   are 0 at the same time for this to make  sense.

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