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You are required to do all the parts of this question by hand
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You are required to do all the parts of this question by hand (i.e. using summation notation and a nonprogrammable

calculator).

Suppose that we are interested in the relationship between the agricultural sector and total

output in developing countries and we are given data on variables Y and X where Y measures

per capita GDP in thousands of $US and X measures the percentage of the labour force in the

agricultural sector. The data is

X 9 10 8 7 10 4 5 5 6 7

Y 6 8 8 7 7 12 9 8 9 10

a. Consider the relationship given by ?? ? ?? ? ???? ? ?? and assume that the Gauss Markov

theorem holds. Use this data to calculate ??, ??, ??? (the sum of squared errors) and ??????.

Show your working. Then test the null hypothesis (at the 5% level) that the percentage of

workers in the labour force in agriculture does not affect per capita GDP, choosing a suitable

alternative for your test. Briefly justify your choice of an alternative hypothesis, and comment on

any additional assumptions that you need to make to perform the test. (18 marks)

b. Calculate the total sum of squares (SST) and R2

for this regression, and then comment on the fit

of this model. (5 marks)

c. Suppose that per capita GDP was measured in $US rather than thousands of $US. How would

that change the coefficients and the sum of squared errors for the equation in (a)? Show your

working. (7 marks)


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