Question 1

Which one of these statements is not a Gauss-Markov assumption?&#10;A) The error term has a conditional mean of 0&#10;B) Influential observations are absent&#10;C) The error term has constant variance&#10;D) The errors are uncorrelated

Accepted Answer

The Gauss-Markov assumptions do not include a requirement about the absence of influential observations. The assumptions focus on the properties of the error term, such as having a conditional mean of zero, constant variance (homoscedasticity), and being uncorrelated (no autocorrelation).

Question 2

Why should we not include irrelevant variables in our regression analysis?&#10;A) Your R-squared will become too high&#10;B) Because of data limitations&#10;C) It is bad academic fashion not to base your variables on sound theory&#10;D) We increase the risk of producing false significant results

Accepted Answer

Including irrelevant variables can increase the risk of multicollinearity and overfitting, leading to false significant results and reducing the model's predictive accuracy.

Question 3

How can we deal with the breach of the assumption about linearity?&#10;A) Include a squared term&#10;B) Include an interaction term&#10;C) Use robust regression&#10;D) Use the margins command

Accepted Answer

Including a squared term can help model non-linear relationships by allowing the model to capture curvature in the data.

Question 4

What is the best way to find the exact top or bottom point of a squared effect?&#10;A) Through derivation using values from the two coefficients&#10;B) Excluding the squared term and predicting&#10;C) Including the squared term and predicting&#10;D) Graphing the results and comparing the top/bottom point with the value on the X-axis

Accepted Answer

The exact top or bottom point of a squared effect can be found by taking the derivative of the function and setting it to zero to solve for the critical points. This involves using the coefficients of the squared term and the linear term.

Question 5

Name another way of modelling nonlinearity&#10;A) Using the linktest command&#10;B) Using interaction term&#10;C) Using dummy variables&#10;D) Using a bivariate regression model

Accepted Answer

The answer of Name another way of modelling nonlinearity&#10;A) Using...

Question 6

Which statistic(s) can help us detect multicollinearity?&#10;A) Variance inflation factor (VIF)&#10;B) F-statistic&#10;C) Durbin-Watson&#10;D) Tolerance values (1/VIF)

Accepted Answer

Variance inflation factor (VIF) and tolerance values (1/VIF) are both used to detect multicollinearity. VIF measures the amount of variance in a predictor variable that is explained by the other predictor variables in the model, while tolerance measures the proportion of variance in a predictor variable that is not explained by the other predictor variables. High VIF values (typically > 10) and low tolerance values (typically < 0.1) indicate the presence of multicollinearity.

Question 7

What does heteroskedasticity mean?&#10;A) The variance in the residuals is the same regardless of their predicted values&#10;B) There is variance in the residuals&#10;C) We are unable to produce residuals&#10;D) The variance in the residuals differ depending on their predicted values

Accepted Answer

Heteroskedasticity refers to the condition where the variance of the residuals or errors differs across levels of an independent variable, meaning it is not constant.

Question 8

What are the two ways we can check for heteroskedasticity?&#10;A) We can examine a plot of predicted values vs the residuals&#10;B) We can run the Hausman test&#10;C) We can run the hettest command&#10;D) We can compare the F-test of two models

Accepted Answer

The answer of What are the two ways we can...

Question 9

What does robust regression do?&#10;A) Performs an OLS regression with more trustworthy standard errors&#10;B) It gives a weight to each unit based on their distance from the mean of Y&#10;C) Performs three types of regression analysis and presents the mean results&#10;D) It gives a weight to each unit based on their total influence on the model

Accepted Answer

Robust regression assigns weights to data points based on their influence on the model, reducing the impact of outliers.

Question 10

Which one is not a measure of influential (or potentially influential) observations?&#10;A) Leverage&#10;B) Cook-Weisberg&#10;C) DFBETA&#10;D) Cook's distance

Accepted Answer

Cook-Weisberg is not a measure of influential (or potentially influential) observations.

Deck 7: Linear Regression Assumptions and Diagnostics