**Please Provide STATA output**

Several years ago, an airplane pilot took this course. For his project he estimated a model of the determinants of used, single-engine airplane prices in the year 2000. This exercise uses data from his project as the basis for an exercise in the detection and correction of heteroskedasticity. The dataset, PLANES, consists of the following variables in Table 3.1:

Table 3.1 Variable Listing

Variable	Description	Hypoth. Sign of Coef.
lnpricei	Natural log of the price in dollars for used, basic single-engine aircraft i	n/a
lnceilingi	Natural log of the service ceiling, or highest possible altitude plane i can fly, in feet.	+
lncruisei	Natural log of the cruising speed in miles per hour of airplane i.	+
lnhorsei	Natrual log of horsepower of engine of airplane i.	+
fixgeari	equal to 1 if aircraft i's landing gear is fixed (not retractable), 0 otherwise.	-
lnfueli	Natural log of the volume of the fuel tank of aircraft i, in gallons.	+
passi	the number of passengers aircraft i can accommodate during flight.	+
tdragi	equal to 1 if aircraft i is a tail dragger, 0 otherwise(A tail dragger is an aircraft that has a wheel connected to its tailhence, a tail dragger.)	-
wtopi	equal to 1 if aircraft i has wings above the fuselage, 0 otherwise.	-
lnagei	Natural log of the age in years of aircraft i.	-

Step 1: Use the Data to Estimate the Model with OLS

Use lnprice_ias the dependent variable and use every other variable in Table3.1 as independent variables in your regression.

a. Which variables have coefficients that are significant in the expected direction at the 5-percent level?

b. What is the meaning of the coefficient on pass?

c. What is the meaning of the coefficient on lnage?

Step 2: Multicollinearity Concerns

Could severe imperfect multicollinearity account for any of the coefficients being insignificant at the 5-percent level? If so, which ones? Use simple correlation coefficients and VIFs to support your answer.

Step 3: Heteroskedasticity Concerns

Plot the residuals from your OLS regression against the passenger capacity. Do the errors look heteroskedastic? Explain.

Step 4: Conduct a Breusch-Pagan Test for Heteroskedasticity

Use all the right-hand variables in the original model to run the Breusch-Pagan auxiliary regression. Write the null and alternative hypotheses, compute the test statistic, and conduct the test at the 5 percent level. Does heteroskedasticity appear to be present?

Step 5: Conduct the White Test for Heteroskedasticity

Test the regression in Step 1 at the 5-percent level for heteroskedasticity using the White test. Use the White test command in your regression package to run the auxiliary regression and to calculate the test statistic. How many variables are on the right-hand side of the auxiliary regression? According to the White test, does there appear to be heteroskedasticity in the model?

Step 6: Estimate with Heteroskedasticity-Corrected Standard Errors:

Re-estimate the model in Step 1 with heteroskedasticity-corrected standard errors, also known as White standard errors. Are the coefficients and adjusted R² the same?

Step 7: Compare Results

Compare the OLS results from Step 1 to the heteroskedasticity-corrected results in Step 6. Compare coefficients and R². For how many of the coefficients are the heteroskedasticity-corrected standard errors larger than the OLS standard errors? Why bother to estimate the heteroskedasticity-corrected errors in the case of heteroskedasticity?

**DATA from planes.xls**

lnprice	lnceiling	lncruise	lnhorse	fixgear	lnfuel	pass	tdrag	wtop	lnage
9.10498	9.047821	4.682131	4.718499	0	3.401197	2	0	0	3.091043
9.21034	9.047821	4.682131	4.718499	0	3.401197	2	0	0	3.044523
9.350102	9.047821	4.682131	4.718499	0	3.401197	2	0	0	2.995732
9.472705	9.047821	4.70953	4.718499	0	3.401197	2	0	0	2.944439
9.740969	9.047821	4.672829	4.70048	0	3.663562	2	0	1	3.091043
9.798127	9.047821	4.672829	4.70048	0	3.663562	2	0	1	3.044523
9.852194	9.047821	4.672829	4.70048	0	3.663562	2	0	1	2.995732
9.92818	9.047821	4.672829	4.70048	0	3.663562	2	0	1	2.944439
10.06476	9.047821	4.672829	4.70048	0	3.663562	2	0	1	2.890372
10.22194	9.047821	4.663439	4.682131	0	3.663562	2	0	1	2.833213
9.472705	9.047821	4.574711	4.744932	0	3.367296	2	0	0	3.044523
9.546813	9.047821	4.574711	4.744932	0	3.367296	2	0	0	2.995732
9.648595	9.047821	4.574711	4.744932	0	3.367296	2	0	0	2.944439
9.359191	9.159047	4.744932	5.010635	0	3.912023	2	0	0	3.583519
9.359191	9.159047	4.744932	5.010635	0	3.912023	2	0	0	3.526361
9.472705	9.159047	4.744932	5.010635	0	3.912023	2	0	0	3.465736
9.564512	9.159047	4.744932	5.010635	0	3.912023	2	0	0	3.401197
9.615806	9.159047	4.744932	5.010635	0	3.912023	2	0	0	3.332205
9.680344	9.159047	4.744932	5.010635	0	3.912023	2	0	0	3.258096
9.740969	9.159047	4.744932	5.010635	0	3.912023	2	0	0	3.178054
9.282661	9.179881	4.682131	5.010635	0	4.043051	4	0	0	3.526361
9.328123	9.179881	4.682131	5.010635	0	4.043051	4	0	0	3.465736
9.453286	9.179881	4.682131	5.010635	0	4.043051	4	0	0	3.401197
9.546813	9.179881	4.682131	5.010635	0	4.043051	4	0	0	3.258096
9.581903	9.179881	4.682131	5.010635	0	4.043051	4	0	0	3.091043
9.25913	9.179881	4.70953	5.075174	0	4.043051	4	0	0	3.610918
9.350102	9.179881	4.779123	5.105946	0	4.043051	4	0	0	3.583519
9.433484	9.179881	4.779123	5.105946	0	4.043051	4	0	0	3.496508
9.528794	9.179881	4.779123	5.192957	0	4.043051	4	0	0	3.465736
9.680344	9.179881	4.779123	5.192957	0	4.043051	4	0	0	3.401197
9.903487	9.179881	4.779123	5.192957	0	4.043051	4	0	0	3.258096
10.14643	9.179881	4.779123	5.192957	0	4.043051	4	0	0	3.135494
10.43412	9.179881	4.779123	5.192957	0	4.043051	4	0	0	2.995732
10.7364	9.179881	4.779123	5.192957	0	4.043051	4	0	0	2.890372
9.392662	9.480368	4.682131	5.347107	0	3.610918	4	0	1	3.78419
9.433484	9.480368	4.682131	5.347107	0	3.610918	4	0	1	3.688879
9.472705	9.480368	4.736198	5.347107	0	3.73767	4	0	1	3.663562
9.510445	9.480368	4.736198	5.347107	0	3.73767	4	0	1	3.637586
9.546813	9.480368	4.736198	5.347107	0	3.73767	4	0	1	3.610918
9.598998	9.480368	4.736198	5.347107	0	3.73767	4	0	1	3.583519
9.648595	9.480368	4.736198	5.347107	0	3.73767	4	0	1	3.555348
9.664596	9.480368	4.736198	5.347107	0	3.73767	4	0	1	3.526361
9.680344	9.480368	4.736198	5.347107	0	3.73767	4	0	1	3.496508
9.711116	9.392662	4.744932	5.010635	0	3.951244	4	0	1	3.465736
9.769957	9.392662	4.744932	5.010635	0	3.951244	4	0	1	3.433987
9.852194	9.392662	4.744932	5.010635	0	3.951244	4	0	1	3.367296
9.903487	9.392662	4.787492	5.010635	0	3.951244	4	0	1	3.295837
9.952278	9.392662	4.787492	5.010635	0	3.951244	4	0	1	3.258096
10.10643	9.392662	4.787492	5.010635	0	3.951244	4	0	1	3.218876
10.14643	9.392662	4.787492	5.010635	0	3.951244	4	0	1	3.178054
10.12663	9.392662	4.787492	5.075174	0	3.988984	4	0	1	3.135494
10.22194	9.392662	4.804021	5.075174	0	3.988984	4	0	1	3.091043
10.29215	9.392662	4.804021	5.075174	0	3.988984	4	0	1	3.044523
10.40426	9.392662	4.804021	5.075174	0	3.988984	4	0	1	2.995732
10.5321	9.392662	4.804021	5.075174	0	3.988984	4	0	1	2.944439
10.64542	9.392662	4.804021	5.075174	0	3.988984	4	0	1	2.890372
10.7579	9.392662	4.787492	5.075174	0	4.219508	4	0	1	2.833213
9.632335	9.392662	4.727388	5.010635	0	3.89182	2	0	1	3.465736
9.740969	9.392662	4.770685	5.192957	0	3.89182	2	0	1	3.433987
9.798127	9.392662	4.779123	5.192957	0	3.89182	2	0	1	3.401197
9.87817	9.392662	4.779123	5.192957	0	3.89182	2	0	1	3.367296
9.952278	9.392662	4.779123	5.192957	0	3.89182	2	0	1	3.332205
10.02127	9.392662	4.820282	5.192957	0	4.094345	2	0	1	3.295837
10.08581	9.392662	4.867535	5.192957	0	4.094345	2	0	1	3.258096
10.14643	9.392662	4.867535	5.192957	0	4.094345	2	0	1	3.218876
10.22194	9.392662	4.867535	5.192957	0	4.094345	2	0	1	3.178054
10.30895	9.392662	4.867535	5.192957	0	4.094345	2	0	1	3.135494
10.37349	9.392662	4.867535	5.192957	0	4.094345	2	0	1	3.091043
9.648595	9.159047	4.820282	5.192957	0	3.871201	4	0	0	3.610918
9.711116	9.159047	4.820282	5.192957	0	3.871201	4	0	0	3.555348
9.740969	9.159047	4.820282	5.192957	0	3.871201	4	0	0	3.496508
9.825526	9.159047	4.820282	5.192957	0	3.871201	4	0	0	3.465736
9.91591	9.159047	4.820282	5.192957	0	3.871201	4	0	0	3.401197
9.975808	9.159047	4.820282	5.192957	0	3.871201	4	0	0	3.332205
10.12663	9.159047	4.820282	5.192957	0	3.871201	4	0	0	3.295837
10.29215	9.159047	4.804021	5.192957	0	3.871201	4	0	0	3.218876
10.4193	9.159047	4.804021	5.192957	0	3.871201	4	0	0	3.135494
10.70324	9.159047	4.828314	5.192957	0	3.871201	4	0	0	2.995732
10.91509	9.159047	4.828314	5.192957	0	3.871201	4	0	0	2.944439
11.08981	9.159047	4.828314	5.192957	0	3.871201	4	0	0	2.890372
11.21855	9.159047	4.828314	5.192957	0	3.871201	4	0	0	2.70805
9.680344	9.159047	4.762174	5.438079	0	4.007333	4	0	1	3.78419
9.798127	9.159047	4.787492	5.438079	0	4.007333	4	0	1	3.73767
9.87817	9.159047	4.812184	5.438079	0	4.430817	4	0	1	3.688879
9.92818	9.159047	4.812184	5.438079	0	4.430817	4	0	1	3.637586
10.02127	9.159047	4.812184	5.438079	0	4.430817	4	0	1	3.526361
10.08581	9.159047	4.812184	5.438079	0	4.430817	4	0	1	3.433987
10.16585	9.159047	4.795791	5.438079	0	4.430817	4	0	1	3.401197
10.32548	9.159047	4.828314	5.438079	0	4.382027	4	0	1	3.258096
10.51867	9.159047	4.828314	5.438079	0	4.382027	4	0	1	3.178054
10.83958	9.159047	4.795791	5.438079	0	4.382027	4	0	1	2.995732
10.99373	9.159047	4.820282	5.438079	0	4.521789	4	0	1	2.944439
11.08981	9.159047	4.820282	5.438079	0	4.521789	4	0	1	2.890372
11.17745	9.159047	4.820282	5.438079	0	4.521789	4	0	1	2.833213
11.28978	9.159047	4.820282	5.438079	0	4.521789	4	0	1	2.772589
9.975808	9.159047	4.812184	5.438079	0	4.430817	4	0	1	3.583519
9.852194	9.792556	4.976734	5.560682	0	4.394449	6	1	1	3.637586
9.92818	9.792556	4.976734	5.560682	0	4.394449	6	1	1	3.610918
9.975808	9.792556	4.976734	5.560682	0	4.394449	6	1	1	3.555348
10.04325	9.792556	4.983607	5.703783	0	4.394449	6	1	1	3.526361
10.12663	9.792556	4.983607	5.703783	0	4.394449	6	1	1	3.465736
10.23996	9.792556	4.983607	5.703783	0	4.394449	6	1	1	3.401197
10.34174	9.792556	4.976734	5.703783	0	4.394449	6	1	1	3.332205
10.44871	9.792556	4.976734	5.703783	0	4.394449	6	1	1	3.218876
10.59663	9.792556	4.976734	5.703783	0	4.304065	6	1	1	3.178054
10.77896	9.792556	4.976734	5.703783	0	4.304065	6	1	1	3.091043
11.0021	9.792556	4.976734	5.703783	0	4.430817	6	1	1	2.995732
12.44509	10.12663	5.225747	5.703783	1	4.787492	6	0	0	2.772589
10.02127	9.546813	4.969813	5.298317	1	3.912023	4	0	1	3.367296
10.06476	9.546813	4.997212	5.298317	1	3.912023	4	0	1	3.332205
10.12663	9.546813	4.997212	5.298317	1	4.094345	4	0	1	3.295837
10.1849	9.546813	4.997212	5.298317	1	4.094345	4	0	1	3.258096
10.25766	9.546813	4.997212	5.298317	1	4.094345	4	0	1	3.218876
10.32548	9.546813	4.997212	5.298317	1	4.094345	4	0	1	3.178054
10.389	9.546813	4.997212	5.298317	1	4.094345	4	0	1	3.135494
10.44871	9.546813	4.997212	5.298317	1	4.094345	4	0	1	3.091043
10.72547	9.472705	5.135798	5.298317	1	4.158883	4	0	0	3.135494
10.80973	9.472705	5.135798	5.298317	1	4.158883	4	0	0	3.091043
10.88744	9.472705	5.135798	5.298317	1	4.158883	4	0	0	3.044523
10.97678	9.472705	5.135798	5.298317	1	4.158883	4	0	0	2.995732
11.05879	9.472705	5.135798	5.298317	1	4.158883	4	0	0	2.944439
11.12726	9.472705	5.135798	5.298317	1	4.158883	4	0	0	2.890372
11.23849	9.472705	5.147494	5.347107	1	4.29046	4	0	0	2.833213
10.9682	9.472705	5.147494	5.347107	1	4.29046	4	0	0	3.044523
11.05879	9.472705	5.147494	5.347107	1	4.29046	4	0	0	2.995732
11.14186	9.472705	5.147494	5.347107	1	4.29046	4	0	0	2.944439
11.23849	9.472705	5.147494	5.347107	1	4.29046	4	0	0	2.890372
11.35041	9.472705	5.147494	5.347107	1	4.29046	4	0	0	2.833213
9.985067	9.615806	4.934474	5.192957	1	4.49981	4	0	0	3.583519
10.20359	9.615806	5.056246	5.560682	1	4.49981	4	0	0	3.583519
10.27505	9.615806	5.056246	5.560682	1	4.49981	4	0	0	3.555348
10.54534	9.615806	5.062595	5.560682	1	4.49981	4	0	0	3.496508
10.65726	9.615806	5.081404	5.560682	1	4.49981	4	0	0	3.367296
10.66896	9.952278	5.288267	5.560682	1	4.49981	4	0	0	3.367296
10.71442	9.615806	5.220356	5.560682	1	4.867535	4	0	0	3.555348
10.43412	10.08581	5.147494	5.298317	1	4.276666	4	0	0	3.135494
10.54534	10.08581	5.147494	5.298317	1	4.276666	4	0	0	3.091043
10.63345	10.08581	5.147494	5.298317	1	4.276666	4	0	0	3.044523
10.72547	10.08581	5.147494	5.298317	1	4.276666	4	0	0	2.995732
10.83958	10.08581	5.147494	5.298317	1	4.276666	4	0	0	2.944439
11.0021	10.08581	5.147494	5.298317	1	4.276666	4	0	0	2.890372
11.17043	10.08581	5.147494	5.298317	1	4.276666	4	0	0	2.833213
10.55841	9.680344	5.056246	5.560682	1	4.219508	4	0	0	3.178054
10.62133	9.680344	5.087596	5.560682	1	4.219508	4	0	0	3.135494
10.68052	9.680344	5.087596	5.560682	1	4.219508	4	0	0	3.091043
10.78932	9.680344	5.087596	5.560682	1	4.219508	4	0	0	3.044523
10.89674	9.729135	5.123964	5.652489	1	4.382027	6	0	0	3.433987
11.13459	9.729135	5.123964	5.652489	1	4.304065	6	0	0	3.401197
11.22524	9.729135	5.123964	5.652489	1	4.304065	6	0	0	3.258096
11.35627	9.729135	5.123964	5.652489	1	4.304065	6	0	0	3.178054
11.41311	9.729135	5.123964	5.652489	1	4.304065	6	0	0	3.091043
11.48247	9.729135	5.123964	5.652489	1	4.304065	6	0	0	3.044523
11.58058	9.729135	5.123964	5.652489	1	4.304065	6	0	0	2.995732
11.73206	9.729135	5.123964	5.652489	1	4.304065	6	0	0	2.944439
11.81303	9.729135	5.123964	5.652489	1	4.304065	6	0	0	2.890372
11.88449	9.729135	5.123964	5.652489	1	4.304065	6	0	0	2.833213
11.13459	9.740969	5.283204	5.736572	1	4.49981	6	0	1	3.044523
11.11245	9.740969	5.135798	5.703783	1	4.49981	6	0	1	2.995732
11.23849	9.740969	5.398163	5.736572	1	4.49981	6	0	1	2.995732
11.25156	9.740969	5.135798	5.703783	1	4.49981	6	0	1	2.944439
11.38509	9.740969	5.398163	5.736572	1	4.49981	6	0	1	2.944439
11.42409	9.740969	5.398163	5.703783	1	4.49981	6	0	1	2.890372
11.53762	9.740969	5.398163	5.736572	1	4.49981	6	0	1	2.890372
11.60824	9.740969	5.398163	5.703783	1	4.49981	6	0	1	2.833213
11.71994	9.740969	5.398163	5.736572	1	4.49981	6	0	1	2.833213
11.81303	9.740969	5.398163	5.703783	1	4.49981	6	0	1	2.772589
11.91839	9.740969	5.398163	5.703783	1	4.49981	6	0	1	2.772589
11.63071	9.680344	5.267858	5.652489	1	4.304065	6	0	0	3.044523
11.68688	9.680344	5.267858	5.652489	1	4.304065	6	0	0	2.995732
11.77529	9.680344	5.267858	5.652489	1	4.304065	6	0	0	2.944439
11.98293	9.680344	5.247024	5.652489	1	4.304065	6	0	0	2.890372
12.08673	9.680344	5.247024	5.652489	1	4.304065	6	0	0	2.833213
11.94471	10.23996	5.332719	5.347107	1	4.325456	4	0	0	2.639057
12.08673	10.23996	5.308268	5.347107	1	4.325456	4	0	0	2.564949
11.21182	10.04325	5.231109	5.736572	1	4.49981	6	0	1	3.091043
11.31447	10.04325	5.231109	5.736572	1	4.49981	6	0	1	3.044523
11.46163	10.04325	5.231109	5.736572	1	4.49981	6	0	1	2.995732
11.65269	10.04325	5.231109	5.736572	1	4.49981	6	0	1	2.944439
11.8056	10.04325	5.231109	5.736572	1	4.49981	6	0	1	2.890372
11.97035	10.04325	5.231109	5.736572	1	4.49981	6	0	0	2.833213
11.16337	9.903487	5.105946	5.703783	1	4.624973	6	0	0	2.995732
11.22524	9.723164	5.062595	5.703783	1	4.624973	6	0	0	2.995732
11.3266	9.903487	5.17615	5.703783	1	4.624973	6	0	0	2.995732
11.19821	9.680344	5.010635	5.703783	1	4.624973	6	0	0	2.944439
11.23849	9.903487	5.105946	5.703783	1	4.624973	6	0	0	2.944439
11.37939	9.680344	5.062595	5.703783	1	4.624973	6	0	0	2.944439
11.46688	9.903487	5.17615	5.703783	1	4.624973	6	0	0	2.944439
11.3022	9.680344	5.010635	5.703783	1	4.624973	6	0	0	2.890372
11.39076	9.903487	5.105946	5.703783	1	4.624973	6	0	0	2.890372
11.51293	9.680344	5.062595	5.703783	1	4.624973	6	0	0	2.890372
11.58989	9.903487	5.17615	5.703783	1	4.624973	6	0	0	2.890372
11.3266	9.680344	5.010635	5.703783	1	4.624973	6	0	0	2.833213
11.55215	9.903487	5.105946	5.703783	1	4.624973	6	0	0	2.833213
11.62625	9.680344	5.062595	5.703783	1	4.624973	6	0	0	2.833213
11.69525	9.903487	5.17615	5.703783	1	4.624973	6	0	0	2.833213