Lecture 5- Bias

Question 1

Methods of detecting outliers and influential cases

Answer 1

• Graphs
• Standardised residual
• Cook’s distance
• DF beta statistics (unstandardised and standardised)

Question 2

How to detect outliers and influential cases using standardised residual

Answer 2

• 95% of standardised residuals SHOULD lie between +/- 2
• 99% of standardised residuals SHOULD lie between +/- 2.5
• If the absolute value of standardised residuals is +/- 3, is likely to be an outlier

Question 3

How to detect outliers and influential cases using Cook’s distance

Answer 3

• Measure the influence of a single case on the model as a whole
• Absolute values greater than 1 may be cause for concern

Question 4

How to detect outliers and influential cases using DF beta statistics

Answer 4

• The change in b when a case is removed

- Be wary of standardised values with absolute values > 1

Question 5

The population model should have

Answer 5

• Homoscedastic errors

- Independent errors

Question 6

Key assumptions of the general linear model

Answer 6

• Linearity and additivity
• Spherical errors
• Normality of something or other

Question 7

A models errors refer to the

Answer 7

Differences between predicted values and observed values of the outcome variable in the population model
These values cannot be observed

Question 8

A model’s residuals refer to the

Answer 8

Differences between predicted values and observed values of the outcome variable in the sample model
These values can be observed and are representative of the population model errors

Question 9

The population error in prediction for one case should

Answer 9

Not be related to the error in prediction for another case (autocorrelation)

Question 10

Because population errors can’t be observed

Answer 10

Sample residuals are inspected

Question 11

Variance of population errors (residuals) should be

Answer 11

Consistent at different values of the predictor variable

Question 12

Violation of the assumption in spherical errors

Answer 12

• bs are unbiased but not optimal

- Standard error is incorrect, therefore t-tests, p-values and confidence intervals will also be incorrect

Question 13

Do normality of model errors matter

Answer 13

Not really

Question 14

When errors are normally distributed b will be

Answer 14

Unbiased and optimal but there may be classes of estimator that are more accurate

Question 15

p-values associated with the bs of the model assume that

Answer 15

The test statistic associated with them follows a normal distribution

Question 16

Confidence intervals for bs are constructed using

Answer 16

The standard error, which is derived from a sampling distribution of b that is assumed to be normal

Question 17

What are robust procedures

Answer 17

• The bootstrap
• Heteroskedasticity
• Consistent standard errors

Question 18

What is the bootstrap procedure

Answer 18

• Standard errors are derived empirically using a resampling technique
• Results in robust confidence intervals and p-values
• Designed for small samples where normality matters

Question 19

What are DF beta statistics

Answer 19

• How much beta changes when a case is removed

- Wary of standardised values with absolute values greater than 1

Question 20

Normality is relevant to

Answer 20

• Population model errors

- Sampling distribution

Question 21

Independent observations tend to lead to

Answer 21

Independent errors