Question

QUESTION ONE a) A researcher conducts a simple study to determine the relationship between Zambia's non-tradition exports and real exchange rate from 1974 to 2004. The real exchange rate was expressed as the price of one US dollar in terms of Zambian Kwacha. The researcher was convinced that the following function explains the relationship between the two variables and conforms to the necessary theory; NTE = B + RER + U Where NTE stands for the non-traditional export and RER stands for real exchange rate. The researcher's OLS estimates were done using Eviews and the following results were obtained. Dependent Variable: (NTE) Method: Least Squares Date: 01/11/15 Time: 13:23 Sample: 1 40 Included observations: 40 Variable Coefficient Std. Error t-Statistic Prob. C 13.50508 0.567859 23.78246 0.0000 (RER) -0.127573 0.055852 -2.284149 0.0280 i) Use the estimated figures in the e -views output R-squared 0.920723 Mean dependent var 12.21574 to write the Adjusted R-squared 0.909754 S.D. dependent var 0.412363 results in S.E of regression 0.391727 Akaike info criterion 1.012203 standard form Sum squared resid 5.831096 Schwarz criterion 1.096646 Log likelihood 5.217338 and interpret Durbin-Watson stat 0.028038 the results. -18.24405 F-statistic 1.777891 Prob(F-statistic) [3 Marks] ii) Use the confidence interval method to conduct a test for the following hypotheses H: B=0 H:β 0 The results of your test should be explained to earn full marks [3 Marks] iii) Use the P-value method to test the hypotheses given and mentioned in (c) above. The p-value should be clearly stated. [3 Marks] iv) Given that the total sum of squares which is broken down into the explained and residual sum of squares is given by; ESS 0.391727 and RSS = 5.831096 Formulate the ANOVA table, repeat the test you conducted in (iv) above and compare the results. [ 3 Marks] b) A senior actuary wants to analyse the salaries of the 50 actuarial trainees employed in his company, using a linear model based on the number of years in school and years of experience. i) How would you express this model and the available data in terms of the notation used in the class notes; ii) Why should the model in (a) include the error term? [3 Marks] [3 Marks] c) The error term in a linear regression model has some fascinating statistical characteristics. i) The variance of the error term is given by the following definition; Var(u) E(u-E(u))² = σ² Show that; Var(u) = E(u) [3 Marks] ii) Show that: Σμυ) - Συ-Σ(4) [4 Marks] 2/4 [TOTAL: 25 MARKS]

          QUESTION ONE
a) A researcher conducts a simple study to determine the relationship between
Zambia's non-tradition exports and real exchange rate from 1974 to 2004. The
real exchange rate was expressed as the price of one US dollar in terms of
Zambian Kwacha. The researcher was convinced that the following function
explains the relationship between the two variables and conforms to the
necessary theory;
NTE = B + RER + U
Where NTE stands for the non-traditional export and RER stands for real
exchange rate. The researcher's OLS estimates were done using Eviews and the
following results were obtained.
Dependent Variable: (NTE)
Method: Least Squares
Date: 01/11/15 Time: 13:23
Sample: 1 40
Included observations: 40
Variable
Coefficient
Std. Error
t-Statistic
Prob.
C
13.50508
0.567859
23.78246
0.0000
(RER)
-0.127573
0.055852 -2.284149
0.0280
i) Use the
estimated
figures in the e
-views output
R-squared
0.920723 Mean dependent var
12.21574
to write the
Adjusted R-squared
0.909754 S.D. dependent var
0.412363
results
in
S.E of regression
0.391727 Akaike info criterion
1.012203
standard form
Sum squared resid
5.831096 Schwarz criterion
1.096646
Log likelihood
5.217338
and interpret
Durbin-Watson stat
0.028038
the results.
-18.24405 F-statistic
1.777891 Prob(F-statistic)
[3 Marks]
ii) Use the confidence interval method to conduct a test for the following
hypotheses
H: B=0
H:β 0
The results of your test should be explained to earn full marks [3 Marks]
iii) Use the P-value method to test the hypotheses given and mentioned in (c)
above. The p-value should be clearly stated.
[3 Marks]
iv) Given that the total sum of squares which is broken down into the explained
and residual sum of squares is given by;
ESS 0.391727 and RSS = 5.831096
Formulate the ANOVA table, repeat the test you conducted in (iv) above and
compare the results. [
3 Marks]
b) A senior actuary wants to analyse the salaries of the 50 actuarial trainees
employed in his company, using a linear model based on the number of years in
school and years of experience.
i)
How would you express this model and the available data in terms of the
notation used in the class notes;
ii) Why should the model in (a) include the error term?
[3 Marks]
[3 Marks]
c) The error term in a linear regression model has some fascinating statistical
characteristics.
i)
The variance of the error term is given by the following definition;
Var(u) E(u-E(u))² = σ²
Show that;
Var(u) = E(u)
[3 Marks]
ii)
Show that:
Σμυ) - Συ-Σ(4)
[4 Marks]
2/4
[TOTAL: 25 MARKS]

question one a a researcher conducts a simple study to determine the relationship between zambias non tradition exports and real exchange rate from 1974 to 2004 the real exchange rate was ex 51572

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