Data Analysis and Economic Forecasting
Examination 2

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

Theoretical Questions

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

2. What is the difference between the normal distribution and chi-square distribution?

What is the difference between a chi-square distribution and F-statistic?

3. What is R 2?

What are its shortcomings?

Is there a better metric to fix this?

4. Which equations below are linear in parameters?

Examples of nonlinear and linear least squares

Empirical Questions

5. Below you have five observations for two samples. These observations are not paired. Please calculate the t-test for equal variances, when t c = 2.31.

Sample 1 Sample 2
1 5 3
2 2 4
3 5 4
4 3 7
5 5 6


Please calculate the t-test assuming the variances are unequal.

What are the degrees of freedom?

6. Below you have five observations for two treatments given. Each observation is one patient who received both treatments, i.e. observations are pair. Are the two treatments significantly different from each other, using a t c = 2.77?

Treat 1 Treat 2
1 1 4
2 1 6
3 5 2
4 1 2
5 4 4

7. You have a 3 X 2 contingency table below. Use the Chi-Square test to determine if men and women differ for their favorite breakfast beverage.

Favorite Breakfast Beverage
Type Men Women
Juice 3 10
Soda 3 3
Coffee/Tea 10 3

What are the degrees of freedom?

Using an alpha = 0.05, what do you conclude?

Critical Values for the Chi-Square, alpha = 0.05

df 1 2 3 4 5
Chi-square 3.84 5.99 7.81 9.49 11.07

8. Using the same data as in Question #7, please use the Yate's Correction.

What is your conclusion?

9. You have a 2 X 2 contingency table below for the acceptance rate for the Department of Economics. Please use Fisher's Exact Probability test to determine all the probability states..

Men Women
Rejected 1 3
Accepted 1 7

(i) Are there any differences between the men and women?

(ii) How do you determine the Level of Significance, i.e. alpha?

10. 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?

11. 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 not equal sign 2

H 0: b 3 = 0.09 (i.e. the trend^2)
H A: b 3 not equal sign 0.09

H 0: b 1 = 0 (i.e. the intercept)
H A: b 1 not equal sign 0

12. 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 Significant F
Regression
Residual 5.13727
Total 58 98.1916


You know you estimated a regression with one x variable and the intercept and you have 59 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?

13. Using the same ANOVA from Question #12, please calculate the following:

ANOVA
df SS MS F Significant F
Regression
Residual 5.13727
Total 58 98.1916


Please calculate the R 2 statistic.

Please calculate the adjusted R 2 statistic.