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Chapter 4
(4.1 to 4.4)

Classical linear regression model assumptions and diagnostics

1

Violation of the Assumptions of the CLRM



Recall that we assumed of the CLRM disturbance terms: 1. E(ut) = 0 2. Var(ut) = σ2 < ∞ 3. Cov (ui,uj) = 0 4. The X matrix is non-stochastic or fixed in repeated samples 5. ut ∼ N(0,σ2)

2

Outline

• Violation of Assumption 1 • Violation of Assumption 2 (heteroscedasticity)
– How to detect? – Consequences – How to deal?

3

Violation of Assumption 1: E(ut) = 0
Assumption 1: The mean of the disturbances is zero. • If a constant term is included in the regression equation, this assumption will never be violated. Interpretation of the intercept: The average value which y would take if all of the explanatory variables took a value of zero.

4

Assumption 1: E(ut) = 0 cont.…..

ˆ (ut )with constant
ˆ (ut )without constant

5

Violation of Assumption 1: E(ut) = 0
Assumption 1: The mean of the disturbances is zero. • If the regression did not include an intercept, and the average value of the errors was nonzero, several undesirable consequences could arise.

1. R2 = ESS/TSS can be negative, implying that the sample average, , ‘explains’ more of the variation in y than the explanatory variables.

2. A regression with no intercept parameter could lead to potentially severe biases in the slope coefficient estimates.
6

Violation of Assumption 2: Var(ut) = σ2 < ∞
Assumption 3: The error variances are constant. • • We have so far assumed that the variance of the errors is constant, σ2 - This is known as assumption of homoscedasticity. If the errors do not have a constant variance, we say that they are heteroscedastic.

Detection of Heteroscedasticity • Informal Method:
– Graphical methods Goldfeld-Quandt test White’s test



Formal tests:
– –
7

Detection of Heteroscedasticity: Graphical Method
Steps: • Estimate liner regression model. • Obtain residuals, . • Plot residuals against...

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