A political analyst is studying the effect of number of hours of campaigns (X) and the percentage votes (Y) received by six candidates in a ward election.

INSTRUCTIONS TO CANDIDATES

ANSWER ALL QUESTIONS

 

Question 1

With clear illustrations and examples, discuss the following terms:

a) Independent and dependent variables

b) Residual term

c) Econometric model vs Economic model

d) Parameters and observations

e) Model transformation

f) Time series data

g) Cross-sectional data

h) Panel data

i) Single equation model

j) Linear in parameters

k) Linear versus multiple regression models

l) Prediction error

m) F-Statistic

n) Adjusted-𝑅2 and why it’s better than 𝑅2

o) Violation of classical linear regression assumptions and what are the resulting issues?

p) Distributed lag model

Question 2

A political analyst is studying the effect of number of hours of campaigns (X) and the percentage votes (Y) received by six candidates in a ward election.

 

Candidate X Y

J 45 55

C 15 35

P 28 42

M 56 65

A 75 78

Z 33 54

 

To study the effect of number of hours of campaigns on percentage votes received, the political analyst specified a regression model.

a) Write down the econometric model you think he specified

b) Use the above data to estimate the least square estimators of the model specified in (a)

c) Interpret the estimates of the estimators derived in (b)

d) Draw the scatter diagram and the regression line

 

e) Using the estimated regression line, obtain the predicted values of the percentage votes received and then obtain the RSS

f) Calculate the coefficient of determination and interpret the results

g) Determine if the estimated coefficients are significant at 5% significant level

h) Predict the percentage of votes received by the candidate who campaigned for 100 hours and 250 hours.

Question 3

To examine the relationship between sales revenue (y) , newspaper advertisement (𝑥1) and television advertisement

(𝑥2) an econometrician estimated a linear regression model and obtained the following results:

 

Coefficient Estimate Standard Error

𝛽0 105 33

𝛽1 0.45 0.024

𝛽2 1.685 0.034

𝑅2 = 0.96 and n=25(Number of observations)

a) Interpret the slope coefficients

b) Test the null hypothesis that 𝛽1 = 0 against the alternative that 𝛽1 > 0. Use the 5% significant level. What does this hypothesis mean?

c) Test the null hypothesis that 𝛽2 = 0 against the alternative that 𝛽2 > 0. Use the 5% significant level. In what sense is this hypothesis indicative of the probability of probability of television expenditure on advertisement?

d) Interpret the 𝑅2

e) Question 3

 

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