ECMT5001: Final Examination (2022s2)
代考计量经济学final where E is the weekly medical expense borne by the government (in $1000), and H is the weekly number of hospitalised patients due to COVID-19.
The total score of this exam is 60 marks. Attempt all questions. Correct all numerical answers to 2 decimal places.
1.[Total: 20 marks] Carol was studying how the COVID-19 pandemic exerts a financial stress on the government. She considered the following regression 代考计量经济学final
ln(E) = β0+ β1 ln(H) + u;
where E is the weekly medical expense borne by the government (in $1000), and H is the weekly number of hospitalised patients due to COVID-19.
She ran the regression on 120 days sampled randomly in 2021. The regression result is displayed below.
(a) [3 marks] Interpret the slope coefficient.
ln(dE) = 2:3 + 0:8 ln(H), R 2 = 0:16:
(b) [3 marks] If the number of hospitalised patients reduced by half, how would this change the medical expense? 代考计量经济学final
(c) [2 marks] Obtain the sample correlation between ln(E) and ln(H).
(d) Carol suspected that the relationship between ln(E) and ln(H) is nonlinear. She asked Mimi to modify the above regression. Mimi proposed the following regression
ln(E) = β0 + β1 ln(H) + β2 ln(H2 ) + v;
but Carol was not happy with this idea.
i.[3 marks] Which assumption does this regression violate? Explain why.
ii.[3 marks] Express β0 and β1 in terms of α0, α1 and α2.
(e) [6 marks] Baobao proposed the following regression
ln(E) = ϒ0 + ϒ1 ln(H) + ϒ2 [ln(H)]ϒ2 + w.
Baobao observed that R2 = 0:2 after running the regression on the same dataset collected by Carol.
Test whether the nonlinear relationship is significant at the 5% level. Show all your steps.
2.[Total: 20 marks] As requested by Carol, Bob ran the following regression
y = β0 + β1x + u:
Using a dataset of size n = 5, Bob reported back to Carol the following regression result.Some entries were not visible because Bob spilled over some co§ee on the report.
(a) [3 marks] Compute
(b) [3 marks] Compute the residual sum of squares
(c) [3 marks] Compute R2
(d) [3 marks] Compute the realised F statistic for the test of overall regression signifi-cance
(e) [3 marks] Compute the p-value of the F test in (d).
(f) [2 marks] Compute the realised t statistic of
(g) [3 marks] Compute the p-value of a two-sided t test in (f).
3.[Total: 20 marks] As Bob grows bigger, Simon becomes more interested in the determi-nants of the house prices in Sydney suburbs. He considered the following model 代考计量经济学final
price = α0 + α1 urate + u, (1)
where price is the average house price (in million dollars) of a suburb, and urate is the proportion of people in the suburb with a university degree. The OLS estimate of α1is = 1:2.
(a) [6 marks] Simon observed that houses tend to be less valued where crimes are prevalent, and people living in high crime areas tend to be less educated. However,Simon forgot to include the variable crate (the crime rate of a suburb) in regression(1). Would the true marginal e§ect of urate on price be likely bigger or smaller than 1.2 due to the omission of crate? Explain.
(b) [10 marks] For each of the following cases, point out which of the linear regression assumptions is violated. If all the assumptions are satisÖed, write down “N/A”.
i.the variation of price depends on urate.
ii.some variables (e.g. average household income) is relevant for price but was omitted from regression (1).
iii. the data were sampled from wealthy suburbs only. 代考计量经济学final
iv.the variable nurate (the proportion of people in the suburb without a university degree) is included as an additional regressor in regression (1).
v.the variable brate (the proportion of people in the suburb with a Bachelor degree) is included as an additional regressor in regression (1).
(c) [4 marks] Simon decided to include brate (as defined in (b)(v)) as an additional regressor. It was observed that the sample correlation between brate and urate is 0.98. What is this problem, and what consequences will this problem lead to?Explain.