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MBA 612 Lecture 13 Notes-retry - Lecture 13 Lecture...

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Lecture 13 Lecture component radj 2 = 1 - unexplained variance dfunexplained df or radj 2 = 1 - = ( - ) ( - ) = ( - ) ( - ) i 1n yi yi 2 n p i 1n yi yi 2 n 1 P is defined as the total number of variables in the regression problem. ie: p=m+1 Note that the above formula for radj 2 is the same as 1- sessy2 where and A regression problem has the same number of normal equations to solve as there are independent variables. (However, some formulations of the normal equations have m + 1 normal equations) Multi-Colinearity is when any 2 or more independent variables are correlated. This becomes very problematic in multiple regression if the multicolinearity is severe. The problem occurs in the interpretation of the regression coefficients, standardized or un- standardized. Let’s take as an example the sale of the house. We have several variables that define and have influence on the total price of the house. The price of the house is based on many different components (like year the home was built, square footage etc., money spent maintaining the home, etc.) . Ie: I once ran a multiple regression equation with selling price of the home as the dependent variable, with many independent variables. One of the independent variable was the existence of a garbage disposal (this variable is called a dummy variable, where the value of 1 indicates the condition exist, and zero indicates that it does not) The coefficient in front of the dummy variable turned out to be plus $7000. Certainly the existence of a garbage disposal by itself does not add 7,000 dollars to the value of the home. It is just an indicator of so much else about the home; the age of the home, the upkeep of the home, the neighborhood that the home is in, the probability that there are other conveniences in the home, etc. The fact that multicolinearity usually exists at some level means that one should never interpret the regression coefficients in a vacuum. One has to be extremely careful about their interpretation, especially when high degrees of multicolinearity exist. Multiple Regression has no value (no need )if the multi-colinearity is non-existent (no difficulty separating the influence of one independent variable from the other) meaning the r 2 between the independent variables is zero, or the correlation matrix of the independent variables is an identity matrix. If this is the case then the multiple regression 1
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problem could be solved by simply stringing together the simple standardized regression coefficients from simple linear regression. I It also has no value if the correlation matrix of the independent variables has nothing but ones. One could not separate the influence of the so-called independent variables, because the truth of the matter would be , there is only one independent variable.
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