BSB123 Lecture Notes - Lecture 10: X&Y, Correlation And Dependence, Statistical Significance
Multiple regression
- More than 1 independent variable
- Assume a linear relationship between each of the explanatory variables and the dependent
variable
- Similar regression estimate equation to simple regression, however all significant variables
are included
- Categorical variable
oNot measured on a quantitative scale
oUse dummy variable instead
Assumes two values: 0 and 1
1 – implies case is in a particular category
0 – case is not
Use one less dummy than the number of categories
oReference category
Omitted variable when using dummy variable
There must always be a reference category e.g. if there are three different
outcomes for a qualitative variable, two will become dummy variables
(denoted 1), and the third will be omitted (in each case, the third category
will be denoted 0)
- Model Building
oInclude all independent variables in the regression model
oCan add/delete independent variables to determine the best model (known as
stepwise regression)
oIf an independent variable has high correlation with the dependent variable, it is
expected to have a high contribution to the explanation of the dependent variable
- Multicollinearity
oOccurs when an independent variable has a high correlation with the dependent
variables, but also with other independent variables, leading to the independent
variables becoming redundant
oIncreases the standard errors of regression coefficient of the affected variables,
causing estimation problem
oSolution: Exclude the offending variable
This generally means including the variable which better fulfils the
requirements of the regression
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