Econ 3740: Sample Midterm A

Fall 2010 (44 marks)

1. In words, math, and a diagram, show what it means if an estimator β is an unbiased estimator.

[3 marks]

2. The relationship between house size and price may be described as follows:

SIZEi = 72.2 + 5.77 ∗ PRICEi

SIZEi=size in square feet of ith house.

PRICEi=price in thousands of dollars of ith house.

a. Explain meaning of regression coefficients. [2 marks]

b. Suppose you are told that this equation explains more than 80% of variation in size of the house.

Does this imply that high housing prices cause houses to be large? Explain. [2 marks]

c. Say we had measured prices in dollars. What exactly would happen to our coefficient on price? [1

mark]

d. Can we say that these results are statistically significant? Economically significant? [2 marks]

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3. Graph the decomposition of the variance in Y corresponding to the OLS estimator (TSS, RSS,

and ESS.)[5 marks]

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4. Why will having bigger samples generally allow a ‘better’ estimate of β? Illustrate with a dia-

gram [3 marks]

5. Explain the Gauss-Markov Theorum. [3 marks]

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6. a. In a simple regression with one explanatory variable, the estimated correlation coefficient, r

relating X and Y takes the value -.97. Draw a scatterplot corresponding to this relationship between

X and Y . [3 marks].

b. What value will R2 take? Explain what this means in words.[1 mark].

c. Add in a regression line, as estimated in STATA. Show how Y and X relate to this line.[1 mark].

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7.a. What is the difference between the residual of a regression ei and the theoretical error term

εi? [1 mark]

b. I have a large sample of N = 1000 individuals in a survey of the labour force. I tell STATA

”reg lnearnings yrseducation yrsexperience”. Afterwards I tell STATA to give me the mean value of

the residual. What (approximately) will this value be in such a large sample? [1 mark]

c. Give an example of a linear regression specification in which a regressor enters quadratically.

[1 mark]

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8.a. I believe that output in my 100 computer part factories in Asia can be best described by the

production function:

Y = ALαKβ, where A is a constant. For each factory i, how would I write the linear econometric

model which corresponds to this specification? [3 marks]

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9. Name the most important criteria for the inclusion of an explanatory variable in a regression

equation. [1 mark].

10. Describe the optimisation criteria of Ordinary Least Squares (OLS) in words. [2 marks].

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11. You decide to model sales at the frozen yoghurt store near your university. Owner believes stu-

dents make up the bulk of the business and therefore is very happy to help with data collection. Your

estimated model is:

Yt = 262.5 + 3.9Tt − 46.94Pt + 134.43At − 152.1Ct

(0.7) (20.00) (108.0) (138.3)

N=29, R2=0.78.

Yt refers to SALES, Pt refers to the price of yoghurt, At is a dummy equal to one if the owner of the

place places an ad in the school newspaper, Ct is a dummy indicating whether or not school is in

session, and Tt is temperature.

a. This demand equation includes no supply information. Does this satisfy the classical assump-

tions? What further judgements need to be made to justify these assumptions? [1 mark].

b. What are the economic/statistical meanings of the fact that the estimated coefficient of At is

134.43? [1 mark].

c. What economic intuition might explain the sign and significance of Ct?[1 mark].

d. What omitted variables might potentially enhance the fit of the model to the data if they had

been included in the data collection exercise? [1 mark].

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12. Illustrate in two diagrams the case of a linear regression model in which R2=1, and the case of

R2=0. Draw scatter plots and a regression line for the simple regression case.

marks

.

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