Subject Code : ETF2100
Assignment Task :

Question 1: 

*Please begin this question on a new page 

(a) Estimate the following regression model by least squares and include your EViews output in your answer

Humidity

 

(b) Interpret your estimate of β4. 

(c) What is the estimated difference between the expected value of PM2.5 when the wind comes from a southeasterly direction compared to the case where the wind comes from a northeasterly direction, assuming humidity, dew point and wind speed are the same. Show your work and provide a full interpretation. 

(d) Test at the 1% level of significance the null hypothesis that the southeasterly wind has the same effect on the expected value of PM2.5 concentration as the northeasterly wind, assuming all other variables remain constant, against the alternative hypothesis that the northeasterly wind reduces PM2.5 concentration more than the southeasterly wind. Use a t-statistic approach and write down all the steps used to conduct your test. You can use Eviews to calculate the test statistics 

 

Question 2: FOR ALL STUDENTS  

(a) We suspect that the relationship between humidity and PM2.5 concentration may be a quadratic relationship. We extend the model in Question 1 to allow for this relationship as follows. Es timate this model and include your output.

Humidity1

(b) Using the F-test at 5% significance level, test whether humidity helps explain variation in PM2.5 concentration. You must write out the test in full including null and alternative hypotheses stated in terms of the parameters. Compute the F-statistic manually by estimating both the restricted and unrestricted model. Make sure to write down the restricted model and unrestricted model fully, and show the Eviews output for the restricted model.  

(c) What do the estimates for β2 and β3 tell you about the relationship between humidity and PM2.5 concentration, keeping all other variables constant. Hint: Think about the signs of these coefficients and what they say about the shape of the quadratic function. Make sure to explain your answer in the context of the question.  

(d) For your model in question

2 (a), find and interpret the marginal effect of humidity on PM2.5 concentration when humidity is

(i) 25 percentage points, and

(ii) 80 percentage points. 

Question 3: FOR ALL STUDENTS

(a) Starting from the model in Question 1, you suspect that the change in PM2.5 concentration associated with an increase in windspeed of 1 km/h depends on the direction from which the wind comes from. Extend the model in Question 1 to allow for this relationship. Estimate this model and include your output. (1 Marks) Hint: All wind direction dummies should be interacted. 

(b) For your model in question 3(a), find and interpret the marginal effect of windspeed when the wind comes from (i) a north western direction, and (ii) a south eastern direction.

 

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  • Posted on : November 05th, 2018

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