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What does this example suggest about heteroskedasticity and the specification of the equation?

Estimate a model where price is estimated as a function of rating

 

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Question 1

yeast, hop and malt and brewing process determines the style of beer. Consumer NZ tasted and ranked 37 New Zealand craft beers including wheat beers, lagers and pale ales. A rank was assigned to each beer on the basis of 1 star (less than 12 points), 2 stars (12-14 points) and 3 stars (more than 14 points). The price per 250ml glass of each beer was also reported.

The ranks for each beer was used to construct a variable called rating which takes the values 1, 2 or 3 depending on the number of stars awarded and the variable price was also constructed that contained the price per 250ml glass of each beer. The data are in the file beer.wf1.

 

1. Estimate a model where price is estimated as a function of rating. Report your output. From these results can you establish if there is a positive relationship between rating and price?

 

2. Estimate another regression but now using 3 separate rating variables. These are rating1 which takes the value 1 if the rank of the beer is 1 star and 0 otherwise; rating2 which takes the value 1 if the rank of the beer is 2 stars and 0 otherwise and rating 3 which takes the value 1 if the rank of the beer is 3 stars and 0 otherwise. Let rating1 be the omitted category. Report your results. Using these results, what do you conclude about the fit of the model? Interpret the parameter estimates of the explanatory variables rating2 and rating3. Do these results make sense?

 

3. Among the 37 beers tested, 3 were included from NZ’s biggest breweries. This information can be used to construct another variable called big which takes the value 1 if the beer comes from one of NZ’s biggest breweries or 0 otherwise. Re-estimate the model in 2 above but now also include the variable big as an explanatory variable. Report your results.

Using these results, what do you conclude about the fit of the model? Interpret the estimated coefficient on the explanatory variable big. Perform a test to test the hypothesis that the coefficient on rating2 is equal to the coefficient on rating3. What do you conclude from this test?

 

4. The Table below reports some summaries of the data. Using this information and also the results from part 3 above what would you conclude are the best value type of beers to buy when you include the beers from the big breweries and also when you don’t include them? You will need to justify your answer.

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Question 2

The variables in Pokies.wf1 include the EGM expenditures per adult for the fiscal year 2012/21013 (exp_per_adult), number of EGMs per 1000 adults in $2013 (EGMS), and the unemployment rate (ur) for a sample of 70 LGAs from Victoria, Australia. Use the data in Pokies.wf1 to answer this question.

(i) Estimate an equation that explains the EGM expenditures per adult for the fiscal year 2012/21013 (exp_per_adult) in terms of the number of EGMs per 1000 adults in $2013 (EGMS) and the unemployment rate (ur) for a sample of 70 LGAs from Victoria, Australia. Report the results using the usual standard errors in the usual form.

 

(ii) Apply the full White test for heteroskedasticity. Using the chi-square form of the statistic obtain the p-value. Also perform a Ramsey RESET test using 2 fitted values. Report the p-value of the F-statistic for this test. What do you conclude?

 

(iii) Add in a quadratic term for EGM. Re-estimate the model. Report the results using the usual standard errors. Apply the full White test for heteroskedasticity. Using the chisquare form of the statistic obtain the p-value. Also perform a Ramsey RESET test using 2 fitted values. Report the p-value of the F-statistic for this test. What do you conclude?

 

(iv) What does this example suggest about heteroskedasticity and the specification of the equation?

 

(v) For the specification estimated in (iii), at what value of EGMS does additional EGMS actually lower predicted exp_per_adult? Find the value mathematically.

 

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