Highlights
1. (a) A model was constructed to study the spending behaviour of 240 Malaysian consumers. Total spending (S) was regressed on income (I) and financial literacy rate (L). The following estimation was obtained in the survey (standard errors are in parentheses):
Si = 263.6416 + 0.0056 Ii – 2.2316 Li Model 3.1
Se = (11.5932) (0.0019) (0.2099)
R2 = 0.7077 Adjusted R2 = 0.6981
Now suppose an additional variable, wealth (W) is included in the model. From previous studies, it is found that wealth and income are highly correlated variables. The following regression results are obtained
Si = 168.3067 + 0.0055 Ii – 1.7680 Li + 12.8686 Wi Model 3.2
se = (32.8916) (0.0018) (0.2480) (4.1905)
R2 = 0.7473 Adjusted R2 = 0.7347
(i) Compare the regression results obtained from Model 3.1 and Model 3.2, what changes can you observe? What can you say about the collinearity problem in Model 3.2?
(ii) Is it worth adding the variable W to the model? Why?
(b) The data on research and development (R&D) expenditure and sales for 31 industry groupings were collected in 2019, to examine the impact of sales on R&D expenditure. All data were measured in RM millions.
(i) Formulate the econometrics model.
(ii) Using the data given by R&D.xlsx, estimate your model as stated in b (i) and interpret your regression results.
(iii) What problem may exist in your estimation in b (ii)? Use an appropriate test to test whether the problem exists in the model, at 5% level of significance?
(iv) How would you rectify the problem as stated in (iii)? Show the results of the test for the problem and the regression output which is free from the problem.
2. (a) Consider the following model for a sample size, n = 65
Yi = 132.809 – 0.001X1i + 2.794X2i + 0.796X3i + 0.017X4i
t = [2.720] [-0.402] [1.051] [1.282] [0.556]
R2 = 0.9478 Model 4.1
(i) What problem(s) may exist in Model 4.1?
(ii) Discuss three possible solutions to the problem.
(b) (i) Refer to the data given in Sales.xlsx, estimate the following regression model and interpret the regression result. (4 marks)
Yt = β1 + β2 Xt + ut
Where Y = Inventories (RM) X = Sales (RM)
(ii) Check the Durbin–Watson d statistic and comment on the nature of autocorrelation in the data (Si = 0.01).
(iii) Estimate ρ, and transform the data to run the regression on the transformed data. Show the regression output of the transformed model.
(iv) Check for the existence of autocorrelation in the transformed model (Si = 0.01).
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