Econometrics Worksheet

Econometrics Worksheet (3) level (6)
1:Choose the correct answer:
1) In the multiple regression model, the adjusted coefficient of determination, 2
A) cannot be negative.
B) will never be greater than the regression R2.
C) equals the square of the correlation coefficient r.
D) cannot decrease when an additional explanatory variable is added.
2) In the multiple regression model, you estimate the effect on Yi of a unit change in one of the Xi while holding all other regressors constant. This
A) makes little sense, because in the real world all other variables change.
B) corresponds to the economic principle of mutatis mutandis.
C) leaves the formula for the coefficient in the single explanatory variable case unaffected.
D) corresponds to taking a partial derivative in mathematics.
3) When testing the joint hypothesis, you should
A) use t-statistics for each hypothesis.
B) use DW-statistic.
C) use the standard error.
D) use the F-statistics.
4) The overall regression F-statistic tests the null hypothesis that
A) all slope coefficients are zero.
B) all slope coefficients and the intercept are zero.
C) the intercept in the regression and at least one, but not all, of the slope coefficients, is zero.
D) the slope coefficient of the variable of interest is zero, but that the other slope coefficients are not.
5) In the multiple regression model, the t-statistic for testing that the slope is significantly different
from zero is calculated
A) by dividing the estimate by its standard error.
B) from the square root of the F-statistic.
C) by multiplying the p-value by 1.96.
D) using the adjusted R2 and the confidence interval.
2: Obtain a dataset from the World Bank, World Development Indicator for three
variables over 25 years for any country of your choice and run a multiple
regression using Eviews program, you should define which of the variables is
your dependent variable (Y) and which are your independent variables
(?2 ??? ?3)? and then answer the following questions

1. Show a full descriptive statistics for all your variables
2. Show two scatter graphs for the relationships between your variables (Y and
   ?2) and then (Y and ?3) and anticipate the kind of relationship between the
   variables.
3. Estimate the intercept (?1) and the partial slope (?2) and (?3), and provide a
   clear interpretation for each of them and screenshot your estimation output.
4. Write the estimated regression equation.
5. What is the value of ?
   2
   , and what does it mean?
6. What is the overall significance of the estimated model
7. Show the confidence Interval for (?2) and (?3) for 90, 95, 99 confidence level.
   Screenshot your answers
8. Test the Hypothesis that there is NO relationship between ?2 and Y: That is the
   true slope (?2) is zero: ?0: ?2 = 0 (at 5%)
9. What is the value of :
10. Show a graph of the actual, fitted and residuals? Can you explain the graph?
    3: Data on 3 Variables; Y (GDP), ?? (women empowerment) and ?? (number of
    female with higher education) produced the following matrices:
11. Calculate the intercept and the two partial slope of the regression and interpret these.
12. Write the estimated regression equation
13. Obtain the variance and standard error of (?̂
    2
    ) and (?̂
    3
    )
14. Obtain the multiple coefficient of determination (?
    2
    ), and the adjusted (?
    2
    ) and
    interpret them
15. Using the Confidence interval, test the hypothesis (?0
    : ?̂
    2 = 0) against (?1
    : ?̂
    2≠ 0) (?
    =5%).
16. Test the hypothesis (?0
    : ?̂
    3
    = 0) against (?1
    : ?̂
    3 ≠ 0) (? =5%), using the test of
    significance.
17. Test the joint hypothesis that ?0
    : ?̂
    2 = ?̂
    3
    = 0 (? =5% )
18. If we assume X2 = 100 and X3= 75, predict the future individual value of Y