1. Perform and interpret the correlation analysis between all seven variables.

2. Present and discuss the scatter diagram of Y against X₁.

3. Estimate equation

Y = γ₀ + γ₁X₁ + v                                                                                        (CW1.1)

using Ordinary Least Squares method and interpret the magnitude and sign of the estimated coefficient ˆγ₁. (Hint: mind the scale of X₁ and Y .)

4. Refer to results from Question 3 (specification CW1.1). Assuming that the explanatory

variable X₁ in Equation (CW1.1) takes on average value, what is the point forecast of the Economic Rate of Return? What is the prediction interval? Provide an interpretation of the prediction interval. (Hint: this question requires the use of a calculator.)

5. Estimate equation

Y = β₀ + β₁X₁ + β₄X₄ + β₆X₆ + u                                                         (CW1.2)

using Ordinary Least Squares method. Present and interpret the estimates of the values of the parameters (β^ˆ₀, β^ˆ₁, β^ˆ₄, and β^ˆ₆) and their estimated standard errors, the value of the residual sum of squares, and the R–Squared and Adjusted R–Squared.

6. Using the result from Question 5 (Equation CW1.2), for each of the population param-

eters, β₀, β₁, β₄, and β₆, perform a test of the null hypothesis, H₀ : β_j = 0, against the alternative hypothesis, H₁ : β_j 6= 0, j = 0,1,4,6. Also, perform the test of the joint hypothesis, H₀ : β₁ = 0,β₄ = 0,β₆ = 0, against the alternative hypothesis, H₁ : β₁ 6= 0 or β₄ 6= 0 or β₆ 6= 0. Assume that the variance is unknown, and the probability density function of the random disturbance term is normal.

7. The estimated coefficient at X₁ becomes statistically insignificant in Question 5 (Equa-

tion CW1.2) compared to Question 3 (Equation CW1.1). Assess if this may be a result of multicollinearity in the model CW1.2. Discuss available remedies to tackle the problem of multicollinearity.

8. Estimate equation

Y = δ₀ + δ₄X₄ + δ₅X₅ + δ₆X₆ + w                                                          (CW1.3)

using Ordinary Least Squares method. Present and interpret the estimates of the values of the parameters and their estimated standard errors. Compare the value of the residual sum of squares, and the R–Squared and Adjusted R–Squared to those from Question 5 (Equation CW1.2).

9. Producing any additional evidence that is considered to be helpful, assess whether or

not heteroskedasticity is a feature of the estimated model (Equation CW1.3). Discuss available remedies to tackle the problem of heteroskedasticity.

REFERENCES

[1] Lucian Bu¸se, Mirela Ganea, and Daniel Cˆırciumaru. Using Linear Regression in the Analysis of Financial-Economic Performances. University of Craiova Faculty of Economics and Business Administration, Craiova, Romania.

Grade Criteria

Grading Criteria: The coursework mark will be an overall summary of performance across the following criteria:

(i). Knowledge of relevant theoretical models, methodologies and issues

(ii). Critical evaluation and informed argument accurately supported by evidence

(iii). Synthesis of relevant material from a range of sources

(iv). Originality of thought and analytical skill

(v). Structure and clarity of presentation.