Finishing Regression!!!

1
Finishing Regression!!!
2
Regression Assumptions

• Linearity
• Interval or ratio data
• Independent variables are independent of each
  other
• No measurement error
• Error term mean is zero
• Error term is normally distributed

3
Regression Assumptions, cont.

• Error term is not correlated with independent
  variables
• Error terms of independent variables are not
  correlated (no autocorrelation)
• Error variance is constant (homoscedasticity)

4
What If Some Of The Assumptions Are Violated?

• The assumptions are important
• It is best to work with data which satisfies them

5
What If Some Of The Assumptions Are Violated?

• But,
• Some are, truly, assumptions (i.e.it is difficult
  to tell)
• Regression is a robust analytic method (it can
  yield pretty accurate results with data that do
  not fully satisfy the assumptions)
• There are ways around some of the assumptions

6
Multicollinearity

• Independent Variables Are Not Independent Of Each
  Other
• Obtain a correlation matrix of all independent
  variables
• Search for independent variables which are highly
  correlated
• Only use one of the highly correlated variables

7
Lower-Level Data

• May be able to use dummy variables for nominal
  independent variable
• Break the variable up into its constituent
  categories
• Assign scores of 0 (to indicate the absence of
  the property) or 1 (to indicate its presence)

8
Lower-Level Data, cont.

• Dummy variables, cont.
• Enter all categories, except one, into the
  multiple regression equation
• Slopes indicate the difference between the
  category of the independent variable and the
  omitted category
• Probit analysis uses a dichotomized or
  trichotomized dependent variable

9
Nonlinear Relationships

• There are very many possible nonlinear
  associations
• Standard linear regression will tend to
  underestimate the strength of association and
  provide poor predictions
• There are several ways of handling nonlinear
  relationships

10
Nonlinear Relationships, cont.

• Transforming data is one of them
• What particular sort of transformation to apply
  largely depends upon the nature of the
  relationship

11
Nonlinear Relationships, cont.

• Identifying the existence of nonlinearities can
  be relatively simple with bivariate regressions
  (just eyeball the scatterplot), requires some
  number crunching with multiple regression
• But, nonlinearities can be dealt with

12
(No Transcript)