Question 1. Sheet Q1 contains data on house
characteristics. Assume house prices follow the following equation. This
equation shows the actual, not estimated, value of house. No one knows
this equation, we will try to find something close to this using data we have.

Remodeled is a flag which is 1 if the
house is remodeled, and 0 otherwise. Error has normal distribution with mean
5000 and standard deviation of 2000.

Moreover, price per SQFT of neighborhood
1 is $15 higher than price calculated above, and price per SQFT of neighborhood
2 is $5 less than price calculated above.

A.
Simulate house prices using the above
information (note: after one simulation of errors, copy the values, and use the
copied ones; otherwise they would change each time you make any change)

B.
Now we want to find a model for price of
house, so we can use it to estimate price of other houses. Again, remember
after this we have no idea about equation above. We just have some data and
want to find a model for price of house.

Assume that no
data is available on whether a house is remodeled. So we can not use this
variable. Using the other variables, estimate a model for house prices. Write
the equation for the linear model you are going to estimate, and find
coefficients using Excel solver (don’t forget the intercept!)

C.
Calculate average and standard deviation of
errors of model in part B.

D.
Re-estimate model of part B, this time
without intercept. Calculate average of errors, and compare it with average
errors in part C. What does this comparison tell you?

E.
Estimate model of part B using the Golden
Rule of Beta Hat (refer to lecture 2, slide 15), and calculate variance of errors.

F.
Estimate matrix of variance-covariance
matrix for coefficients, using the following formula:

is variance of error terms from part E.

G.
Diagonal of variance-covariance matrix,
shows variance of each coefficient. Estimate t-statistic for each coefficient
using the formula:

H.
Identify which coefficients are
statistically significant at 5% level of significance. Using only significant
coefficients, estimate house price for a 3500 SQFT house in neighborhood 3,
with 10 years age.

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