Econ 3370 HW 3

1. The OLS estimator for a single-variable regression can be expressed as a.

2. Consider a dataset with 32,000 observations. Two random variables X and Y contain information collected by survey to describe each observation in the sample. Consider the single-variable regression

A researcher first estimates the regression above with the entire sample (n=32,000), then splits the sample in half and estimates the same regression on the subsamples (n=16,000 each). When comparing the coefficient from each set of results, which of the following are true? Choose all that apply.

1. If X and Y are normally distributed, each estimate will be exactly the same.

2. Since the sample (and subsamples) have a large number of observations n, each estimateshould be exactly the same.

3. If there is a strong correlation between X and Y, AND there is no measurement error in X,the estimates will be exactly the same.

4. If there is a strong correlation between X and Y, AND there is no measurement error in X,AND the stochastic error term is normally distributed, the estimates will be exactly thesame.

5. None of the above

Caterpillar: Confidential Green

Justify your answer choice for question 2 with 3 or 4 sentences. Use econometric terminology (hint: your answer choice in question 1 will help).

After estimating the multivariate regression model
a researcher uses the results to produce the prediction equation

True or false: the prediction equation is purely stochastic.
True or false: the residual is theoretical and impossible to calculate, since is unobservable.

We introduced R-Squared to measure goodness of fit. Which of the following describe the intuition behind R-Squared?

1. R-Squared must be between 0 and 1.

2. The higher the R-Squared, the closer the prediction equation/regression line fits thesample.

3. R-Squared is only one way to describe the quality of a regression model.

4. Adding additional explanatory variables to the regression will increase the R-Squaredeven if the new variable has no theoretical relationship with the outcome.

5. All of the above

Explained sum of squares (ESS)
a. Describes how the variance in the outcome variable is explained by the residual. b. Describes how the variance in the outcome variable is omitted from the model. c. Describes how the variance in the outcome variable is explained by the model. d. All of the above
e. BandConly

For a multivariate OLS model, assume there are N sample observations, and k explanatory variables, such that we have the following general form

Use three sentences or less to define degrees of freedom and explain how adding additional explanatory variables (hence increasing k) will affect the degrees of freedom. Will the degrees of freedom increase or decrease? Assume a fixed number of observations N.

Caterpillar: Confidential Green