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Betöltés...
Átirat

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y=3.1+0.74x

Regression Assumptions

1. Linearity

(Correct functional form)

Consider the following model:

0

1. Linearity

What's the issue?

  • If functional form is incorrect, both the coefficients and standard errors in your output are unreliable

Detection:

Remedies:

  • Residual plots
  • Likelihood ratio (LR) test
  • Get the specification correct (trial and error)

Constant Variance

(no heteroskedasticity)

Consider the following model:

0

2. Constant

Error Variance

What's the issue?

  • Under heteroskedasticity, standard errors in output cannot be relied upon

Detection:

Remedies:

  • Goldfeldt-Quant test
  • Breusch-Pagan test
  • White's standard errors
  • Weighted least squares
  • Log things!

Independent error terms (no autocorrelation)

Consider the following model:

0

3. Independent

Error

Terms

What's the issue?

  • Under autocorrelation, standard errors in output cannot be relied upon

Detection:

Remedies:

  • Investigate omitted variables
  • Durbin-Watson test
  • Generalised difference equation
  • Breusch-Godfrey test

(Cochrane-Orchutt or AR(1) methods)

Normality of errors

Consider the following model:

0

4.Normal

errors

What's the issue?

  • If normality is violated and n is small, standard errors in output are affected

Remedies:

Detection:

  • Change functional form (log?)
  • Histogram or Q-Q plot
  • Shapiro-Wilk test
  • Komolgorov-Smirnov test
  • Anderson-Darling test

No multicollinearity

Consider the following model:

Multi-collinearity occurs where the X variables are themselves related

What's the issue?

5. No multi-collinearity

  • Coefficients and standard errors of affected variables are unreliable.

Detection:

(ρ)

  • Look at correlation between X variables
  • Look at Variance Inflation Factors (VIF)

Remedies:

  • Remove one of the variables

NOTE: Adding an interaction term will not fix the problem

Exogeneity

(no omitted variable bias)

Consider the following model:

Socio-economic status affects both X and Y variables,

thus would cause omitted variable bias.

TECHNICALLY - Socio-economic status would affect in the model, thus, Education is no longer wholly exogenous as it can be explained in part by the error term.

6. Exogeneity

What's the issue?

  • Model can only be used for predictive purposes (can not infer causation)

Detection:

Remedy:

  • Intuition
  • Checking correlations
  • Using instrumental variables
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