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Multiple linear regression MLR

Post on 06-Jan-2016

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Multiple linear regression MLR. Assumptions. The model is linear in the parameters The error terms are statistically independent The independent variables are linearly independent. All populations have equal variances. Linear in parameters. Not linear in parameters. - PowerPoint PPT Presentation

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• Multiple linear regressionMLR

• AssumptionsThe model is linear in the parametersThe error terms are statistically independentThe independent variables are linearly independent.All populations have equal variances

• Linear in parameters

• Not linear in parametersViolation of assumptions

• Linear in parameter but nonlinear in variablesNot a violation of assumptions

• Violation of the assumption that the model is linear in parametersThis is called a misspecification error.

This means the model has been written improperly.

There is such a thing as nonlinear regression

• The error terms are statistically independentIf the errors terms are statistically independent, then the value of the error term at time t will not be correlated with the values of the error terms at any other time period.

The ACF of statistically independent error terms will be the ACF of noise.

• The error terms are statistically independentThe violation of this assumption is called serial correlation.

Serial correlation can be detected using the DurbinWatson test or the ACF of the residuals.Look at plot of residuals

• Causes of serial correlationOmitting a relevant variable from a regression equation.

A misspecification error.

• Consequences of serial correlationThe estimates of the standard deviation of the regressions coefficients ( ) will be wrongSo the T-test and pvalues will be wrong as well

• Consequences for forecastingCan be very severe

• Fixes for serial correlationFind the missing relevant variable.

Write the regression equation correctly to avoid misspecification.

Lagged dependent variable

• The independent variables are linearly independentThe independent variables are not linearly independent if you can write one of them as some linear combination of the others.

• Perfect multicolinearity

• Near multicolinearity

• Detection of multicolinearityPlot the independent variables.Compute the correlations between the independent variables.Look for logical inconsistencies in the regression statistics.

• Fix for multicolinearityFind this and you will become very famous amongst econometricians.

Cant really omit one of the offending variables.

At times it doesnt really matter for forecasting. (St. Louis Model)

• HeteroscedasticityViolation of the assumption that the populations that the samples come from all have the same variance.

• Consequences of heteroscedasticiySame as with serial correlation as far as the estimates of is concerned

Makes the forecasts increasingly uncertain

• Fix for heteroscedasticityIn this course we will take logs of the dependent variables and perhaps the logs of all variables

More sophisticated methods exist but are difficult to use and also require a good deal of work