Reference no: EM132797071

TECO201 Elements Of Econometrics - Top Education Institute

Question 1

Based on 11 annual observations, the following regression were obtained:

Model A:	Yt	=	2.6911	-0.4795Xt
		se	0.1216	0.1140	r2=0.6628
Model A:	Yt	=	0.7774	-0.2530lnXt
		se	0.0152	0.0494	r2=0.7448

Where Y is the cups of coffee consumed per person per day and X is the price of coffee in $ per pound

i) Interpret the slop coefficients in the two model (1 mark)
ii) You are told that the mean value of Y & X is 2.43 and 1.11 respectively, estimate the price elasticity for model A (2 marks)
iii) What is the price elasticity for model B (2 marks)

Question 2

Considering the following model

Salest=B1+B2D2t+ B3D3t+ B4D4t +ui

Where Sales =the retail sales of hobby, toy and game stores
D2=1 in the second quarter,
=0 if otherwise
D3=1 in the third quarter,
=0 if otherwise
D4=1 in the fourth quarter,
=0 if otherwise
Using the data for the period 1992 to 2012, a business analyst obtained the following regression result:

Salest=930.412+58.667D2t+ 57.609D3t+ 1338.109D4t
t-value (21.6) (0.96) (0.931) (21.63) R2=0.913

i) What is the interpretation of the coefficients?
ii) Given B2>B3, what conclusion would you can draw?
iii) Discuss the logical reason for why the results are this way.

Question 3
A sample of 200 Sydney households was taken to investigate how far Australian households tend to travel when they take vacation. Measuring distance in miles per year, the following model was estimated:

miles = β0 + β1income + β2age + β3kids + u
Where age is the average age of the adult members of the household.

After sorting observations by income and applying OLS to the first 100 and the second 100 observations the following estimates for the SSR were obtained: RSS2=2.95*107 and RSS1=1.04*107.

Use Goldfeld-Quandt test to test for homoskedasticity, including the specification of the null and the alternative hypothesis.

i) Calculate the ratio

λ = (RSS2 / df)/RSS1 / df

Where RSS are sum squared residences from two regressions, and df is degree of freedom calculated by (n-k-1), n is number of observation and k is the number of parameters.
ii) Find F value from F-distribution table given the significant level of 5%.
iii) Make your decision and conclusion.

Question 4
To explain what determines the price of air conditioners, a business analyst obtained the following regression results based on a sample of 19 air conditioners:

Yi=-68.236+0.023X2i +19.729X3i+7.653X4i R2=0.84 Se (0.005) (8.992) (3.082)

where Yi = the price, in dollars
X2 = the BTU rating of air conditioner X3 = the energy efficiency ratio
X4 = the number of settings

i) Interpret the regression results.
ii) At α = 5%, test the hypothesis that the BTU rating has no effect on the price of an air conditioner versus that it has a positive effect.