Chapter 3.1 Regression Diagnostics

Question 1

Reminder: Least Squares Estimation
If … i.e. it is invertible

Answer 1

𝐗𝐗 is full rank, then 𝐗𝑇𝐗 is positive definite,

Question 2

Gauss-Markov Theorem
The Gauss-Markov theorem states that in a … in which the errors
* have … and
* are … and
* have …
the … of the coefficients is given by the ordinary least squares (OLS) estimator.

Answer 2

linear regression model
expectation zero
uncorrelated
equal variances,

best linear unbiased estimator (BLUE)

Question 3

what do unbiased and best mean?

Answer 3

expected value of estimated coefficient = true value of coefficient

best–> lowest variance of the estimate as compared to other linear unbiased estimators

Question 4

Differentiate between Bias, Consistency, Efficiency

Answer 4

Unbiased: Expected Value for estimator is TRUE

variance of estimated coeff decreases with increasing n

efficient: estimator ß has lower variance than any other estimator

Question 5

The OLS estimator is the best linear unbiased estimator (BLUE), if…

1) Linearity: …
2) No ….; No linear dependency between predictors
3) Homoscedasticity; …
4) No autocorrelation; There is
5) … (see slides)

Answer 5

Linear relationship in parameters 𝛽

multicollinearity of predictors

The residuals exhibit constant variance

no correlation between the 𝑖 and 𝑗 residual terms

Expected value of the residual vector, given X, is zero

Question 6

Outliers
An outlier is an observation that is unusually small or large.
Several possibilities need to be investigated when an outlier is observed: explain 3 of them.

There are also methods for “robust” regression.

Answer 6

• There was an error in recording the value.
• The point does not belong in the sample.
• The observation is valid.

check slide 14 for cook’s distance