THESE ARE NOT OFFICIAL SOLUTIONS BUT DUE CARE HAS BEEN TAKEN IN PREPARING THEM, USE AS AN AID TO HELP YOU CREATE YOUR ON AND SCORE ABOVE 75%. PLEASE DO NOT PLAGIARISE.
Part (a): Causes of bias in OLS es mators (5 marks)
The ques on asks you to iden fy and explain which of the following scenarios causes bias in Ordinary
Least Squares (OLS) es mators:
1. Var(ϵi)=σi^2:This implies heteroscedas city, which means the variance of the error term is not
constant across observa ons. Heteroscedas city does not cause bias in OLS es mators but leads
to inefficient es mates, meaning the standard errors may be wrong, but the OLS es mators
remain unbiased.
o Answer: No bias.
2. A simple correla on coefficient of 0.98 between two explanatory variables and a VIF (Variance
Infla on Factor) of 8: This indicates mul collinearity (high correla on between independent
variables). Mul collinearity does not cause bias in OLS es mates but leads to large standard
errors, making the es mates less reliable.
o Answer: No bias.
3. Omi ng an important variable: If an important variable that influences the dependent variable
is omi ed from the model, it results in omi ed variable bias. This is a significant issue in OLS
because the effect of the omi ed variable gets wrongly a ributed to the included variables,
leading to biased es mates.
o Answer: Yes, this causes bias.
Part (b): Interpre ng regression coefficients in the house price model (13 marks)
, The given equa on is:
ln(P)=β0+β1ln(CO2)+β2(rooms)+ϵ
(i)
β1 (coefficient of ln(CO2): Higher pollu on (measured by CO2 levels) is expected to lower house prices.
Therefore, we expect β1 to be nega ve.
β2 (coefficient of rooms): More rooms in a house typically increase its price, so we expect β2 to be
posi ve.
(ii)
The coefficient of lnCO2, indicates the elas city of house prices with respect to CO2 levels. Specifically, it
shows the percentage change in house prices for a 1% change in CO2 levels. If β1=−0.5 for example, it
would mean that a 1% increase in CO2 levels leads to a 0.5% decrease in house prices.
(iii)
Yes, it is possible for CO2 and the number of rooms to be nega vely correlated. For example, larger
homes with more rooms may be located in suburban or rural areas with lower pollu on levels (lower
CO2), while smaller homes might be in more densely populated, polluted urban areas. This would result
in a nega ve correla on between rooms and CO2 levels.
(iv)
If rooms and CO2 are nega vely correlated, omi ng rooms from the model will bias the
es mate of β1
When you omit a variable (rooms) that is nega vely correlated with CO2 and posi vely related
to house prices, the effect of CO2 on house prices will be overes mated, resul ng in an upward
bias in the es mate of β1
(v)
A high R^2(0.76) indicates that 76% of the varia on in house prices is explained by the independent
variables in the model, which is generally a good sign. However, it does not necessarily imply that the
model is "good" in all respects. Other factors to consider include:
Specifica on errors (e.g., omi ed variables, incorrect func onal form).
Mul collinearity or heteroscedas city may s ll be present.
Adjusted R^2is o en a be er indicator than R2R^2R2 because it accounts for the number of
predictors.
Ques on 2 A
(a) Double Log
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