2. Suppose the price of an apartment (1) in a house depends on number of rooms (
ID: 1104138 • Letter: 2
Question
2. Suppose the price of an apartment (1) in a house depends on number of rooms (X) and the size of an apartment (X). Let's assume the price is measured in $1000 and the size is measured in meter squares. a) Write down the linear population regression model for the price of an apartment. b) Provide the interpretation for the room coefficient. c) Provide the interpretation for the coefficient of size of an apartment. d) How would you modify the model in part (a) if it is believed that the change in price for an additional room depends on the size of an apartment? e) From part (a), thoroughly explain how you would test the hypothesis if the change in price for additional size of the apartment doesn't depend on number of rooms. 3. Assume your grade (G) from econometrics depends on number of hours of studying (H) per week and Noise (N). Let your grade is measured out of b) Thoroughly explain how you would test a hypothesis if Noise on c) Thoroughly explain how you would test a hypothesis if your grade from d) How would you modify the model in part (a) if it is believed that 100 scores and noise is measured by number of cries of people outside. a) Write down the linear population regression model. average reduces your grade from econometrics. econometrics is not determined by hours of studying and noise. additional score on econometrics from additional hours of studying is diminishing? e) How would you modify the model in part (a) if it is believed that marginal contribution of studying to your grade depends on noise? 4. Let the IQ of an individual worker depends on mother's education (%) and on father's education (X3), so that education is measured by years of schooling. The score of I0 is ranged between 0 and 200. a) Write down the linear population regression model for IQ. b) Thoroughly explain how you would test if mother's education improves an individual worker's IQ c) Thoroughly explain how you would test if mother's education and father's educations have an equal impact on individual worker's 1Q. d) How would you estimate the model in part (a) if mother's education and father's education was related as X,-8.1 + 0.5 e) How would you modify the model in part (a) if the I0 of an individual also depends on his Mathematics skills measured by Maths score?Explanation / Answer
2.
Answer for A
Linear Population regression model for the price of an apartment is given below
Y= a + b1(no of rooms) + b2 (size of an apartment) + e
we konw no of rooms = X2& size of an apartment = X3 & e is an error which has normal distribution with ~N(0, Variance of e)
Answer for B
Coefficient of Room in an above PRL states that 1 unit increase in Rooms provides b1 units increase in Y keeping other variables constant.
Answer for C
Coefficient of size of an apartment in an above PRL states that 1 unit increase in apartment size provides b2 units increase in Y keeping other variables constant.
Answer for D
Y = a+ b2 (X3) + v where v = e+ b1 (X2) ( Case of Misspecification of model if Covariance (v,X3) =! 0
Answer for E
Hypothesis H0 -> b1=0
Hypothesis H1-> b1=! 0
Answer for E
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