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?

Various regression equations

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 An Unbiased Estimator.

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 R 2?

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 = (X TX) -1X TY.  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: t c = 2.00.

Please use the confidence intervals to check the following hypotheses:

     H 0:  b 2 = 2   (i.e. the trend)
     H A:  b 2 >< 2


     H 0:  b 3 = 0.09   (i.e. the trend^2)
     H A:  b 3 >< 0.09

     H 0:  b 1 = 0   (i.e. the intercept)
     H A:  b 1 >< 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 R 2 statistic.

Please calculate the adjusted R 2 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?

Linear System of Equations

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