Part 3/4/5 Likely Qs

Question 1

Explain, with the use of equations, the difference between the sample regression function and the population regression function.

Answer 1

The population regression function (PRF) is a theoretical relationship that describes how the dependent variable
Y is related to the independent variable
X for the entire population. It is given by: where is the true intercept, is the true slope of the relationship, and
ϵ is the error term representing unobserved factors.

The sample regression function (SRF), on the other hand, is an empirical estimate of this relationship, based on sample data. where is the estimated intercept,
is the estimated slope, and
is the predicted value of
Y based on the sample data. The estimates bo and b1are obtained using a method such as ordinary least squares (OLS) and are used to infer the population parameters

Question 1

Will the value of (a) r squared
(b) Adjusted r squared
, be higher for the second model than the first? Explain your answers.

Answer 1

R squafred
, generally increases when additional variables are added to a model, regardless of whether those variables are relevant or not. . Adding a new variable to a regression model can capture more variance, by chance, if nothing else. Therefore, for the second model is likely to be higher than that for the first model due to the inclusion of an additional variable

(b) Adjusted

accounts for the number of predictors in the model relative to the number of data points and adjusts.

In fact, the penalty for adding an irrelevant variable might reduce the Adjusted

Therefore, the Adjusted
could be higher for the first model if the inclusion of
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Question 2

Explain why it is not possible to include an outlier dummy variable in a regression model when you are conducting a Chow test for parameter stability. Will the same problem arise if you were to conduct a predictive failure test? Why or why not?

Answer 2

Including an outlier dummy variable in a regression model when conducting a Chow test for parameter stability is not possible because the test’s purpose is to determine if there is a structural break in the relationships between the variables across different sub-samples. Adding a dummy variable for outliers would adjust the model specifically for those outliers, thus affecting the test’s ability to detect genuine structural breaks.

For a predictive failure test, the same issue does not necessarily arise. This test is used to predict failures or changes outside the sample on which the model was estimated. An outlier dummy is intended to neutralize the effect of an outlier, not to test for a structural change, so it might not interfere with a predictive failure test in the same way it would with a Chow test.

Question 3

Define autocorrelation

Answer 3

Autocorrelation in econometrics is when the residuals (errors) of a regression model are correlated with each other, meaning that the error for one observation is related to the error for a previous observation.