﻿ Ken Szulczyk's Exam 1 for Data Analysis and Economic Forecasting
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# Data Analysis and Economic Forecasting Examination 1

These questions are from the test bank.  Some questions have multiple parts.

## Theoretical Questions

1. What is an unbiased estimator?

How do econometricians measure an estimator's bias?

What do econometricians mean by efficiency?

What does Mean Squared Error do for us?

2. What are time-series, cross-sectional, and panel data?

Does the type of data matter how we analyze the data?

3. What is the difference between standard error and standard deviation?

4. Why do econometricians use the t-statistic, rather than the z-values from a normal distribution?

5. Which equations below are linear in parameters?

6. Using the Gauss-Markov Theorem and given various assumptions are true, what is a BLUE estimator?

Is the BLUE assumption important for forecasting?

7. Prove that Least Squares is an unbiased estimator, where .

8. You have a linear system of equations.  What do you do in each of the following cases?

If n > k, how do you proceed?

If n = k, how do you proceed?

If n < k, how do you proceed?

where n is number of observations and k is number of parameters (including the intercept)

9. What is R2?

What are its shortcomings?

Is there a better metric to fix this?

10. You have data that is normally distributed.

What kind of distribution do the data have if you take linear combinations of it?

What kind of distribution do the data have if you square the data?

What kind of distribution do the data have if you take a ratio of the data squared?

11. The least squares estimator is b = (XTX)-1XTY.  What would prevent you from taking the inverse?

What is multicollinearity?

## Empirical Questions

12. Parts of your Excel output are missing, please calculate the missing values:

 Coefficients Standard Error t Stat P-value Intercept 77.66559 3.102398 trend -2.64965 0.238578 trend^2 0.045568 0.003854

How could you use Excel to get the p-value for the t-statistic, if you know the degrees of freedom is df=43 ?

What hypothesis are you conducting when you test the statistical significance of the t-statistics?

13. Parts of your Excel output are missing, please calculate the missing values:

 Coefficients Standard Error Lower 95% Upper 95% Intercept 77.66559 3.102398 trend -2.64965 0.238578 trend^2 0.045568 0.003854

Please calculate the confidence intervals for the parameter estimates, if the critical t value is: tc = 2.00.

Please use the confidence intervals to check the following hypotheses:

H0b2 = 2   (i.e. the trend)
HAb2 >< 2

H0b3 = 0.09   (i.e. the trend^2)
HAb3 >< 0.09

H0b1 = 0   (i.e. the intercept)
HAb1 >< 0

14. A computer virus infected  your Excel program.  Thus many calculations are missing from the ANOVA table.  Please manually calculate the remaining values.

 ANOVA df SS MS F Significance F Regression Residual 5.137275 Total 98.19162

You know you estimated a regression with one x variable and the intercept and you have 60 observations.

How could you use Excel to get the probability value for the F-statistic?

What hypothesis are you conducting when you reject or fail to reject the F-statistic?

15. Using the same ANOVA from Question #14, please calculate the following:

 ANOVA df SS MS F Significance F Regression Residual 5.137275 Total 58 98.19162

Please calculate the R2 statistic.

Please calculate the Akaike Information Criterion (AIC)

Please calculate the Schwarz Information Criterion (SIC)

16. How could you use Excel to solve this system of equations?

I am looking for the use of three particular commands in Excel

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