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ECN225 Econometrics 2 – 2020
Questions and Answers
Question 1
(a)
It has been observed that paintings signed by Monet tended to sell more than paintings not signed
by him. Because Signed is an indicator variable equal to 1 if the painting was signed, the estimated
coefficient for Signed has the expected sign because it is positive.
(b)
The estimated intercept of 1.833 indicates that unsigned paintings by Monet sell for, on average,
$1.833 million. The estimated coefficient for Signed indicates that signed paintings have a price
which is on average higher by $1.526 million as compared to unsigned paintings.
(c)
To test whether the regression provides statistically significant evidence that paintings signed by
Monet sold for more than unsigned paintings, on average, we must test whether the estimated
coefficient for Signed is statistically different from 0.
The hypothesis test is that:
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H0: 𝛽 =0
HA: 𝛽 ≠0
The test statistic is:
1.526 − 0
𝑡= = 3.58
0.426
We then must choose an appropriate significance level, which in this case we will choose to be 5%.
The critical value of this test, using the normal distribution, is 1.96. Comparing the test statistic with
the critical value of 3.58 allows us to reject the null hypothesis with 95% confidence.
Therefore, the regression does provide statistically significant evidence that paintings which are
signed sell for more than unsigned paintings.
(d)
The probability distribution of the coefficient on the variable Signed is normal, as we can apply the
Central Limit Theorem. The formula for the 95% confidence interval is:
[𝑥̅ − 1.96 𝜎 ≤ 𝜇 ≤ 𝑥̅ + 1.96 𝜎]
Plugging in the given values yields:
[1.241 − 1.96 (0.445) ≤ 𝜇 ≤ 1.241 + 1.96 (0.445)]
[0.3688 ≤ 𝜇 ≤ 2.1132]
(e)
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The estimated intercept is the average price for paintings which are unsigned (i.e. Signed = 0) and
from the first House (i.e. House1) such that the other two House indicator variables are equal to 0.
This indicates that unsigned paintings from the first House sell for an average of 2.021.
(f)
The regressor House1 must be omitted from this regression otherwise there is a perfect linear
relationship between House1, House2, and House3. This would mean that the coefficients cannot be
calculated. By omitting the regressor House1, this coefficient becomes the “base”.
(g)
The estimated coefficients on regressors House2 and House3 represent the difference in average
price between the “base” of the average price in House1. Therefore the estimated coefficient of
0.269 for House2 indicates that the average price of paintings in House 2 is $0.269 million higher
than House 1, all else being held equal. Similarly, the estimated coefficient of -1.504 for House3
indicates that the average price of paintings in House 3 is $1.504 million higher than House 1, all else
being held equal.
ECONOMICS HELP, visit LondonEconomicsTutors.co.uk.
Discounted prices compared to all other websites
ECN225 Econometrics 2 – 2020
Questions and Answers
Question 1
(a)
It has been observed that paintings signed by Monet tended to sell more than paintings not signed
by him. Because Signed is an indicator variable equal to 1 if the painting was signed, the estimated
coefficient for Signed has the expected sign because it is positive.
(b)
The estimated intercept of 1.833 indicates that unsigned paintings by Monet sell for, on average,
$1.833 million. The estimated coefficient for Signed indicates that signed paintings have a price
which is on average higher by $1.526 million as compared to unsigned paintings.
(c)
To test whether the regression provides statistically significant evidence that paintings signed by
Monet sold for more than unsigned paintings, on average, we must test whether the estimated
coefficient for Signed is statistically different from 0.
The hypothesis test is that:
, FOR MORE HIGH-QUALITY PAST PAPER MODEL ANSWERS, ONLINE TUTORING AND
ECONOMICS HELP, visit LondonEconomicsTutors.co.uk.
Discounted prices compared to all other websites
H0: 𝛽 =0
HA: 𝛽 ≠0
The test statistic is:
1.526 − 0
𝑡= = 3.58
0.426
We then must choose an appropriate significance level, which in this case we will choose to be 5%.
The critical value of this test, using the normal distribution, is 1.96. Comparing the test statistic with
the critical value of 3.58 allows us to reject the null hypothesis with 95% confidence.
Therefore, the regression does provide statistically significant evidence that paintings which are
signed sell for more than unsigned paintings.
(d)
The probability distribution of the coefficient on the variable Signed is normal, as we can apply the
Central Limit Theorem. The formula for the 95% confidence interval is:
[𝑥̅ − 1.96 𝜎 ≤ 𝜇 ≤ 𝑥̅ + 1.96 𝜎]
Plugging in the given values yields:
[1.241 − 1.96 (0.445) ≤ 𝜇 ≤ 1.241 + 1.96 (0.445)]
[0.3688 ≤ 𝜇 ≤ 2.1132]
(e)
, FOR MORE HIGH-QUALITY PAST PAPER MODEL ANSWERS, ONLINE TUTORING AND
ECONOMICS HELP, visit LondonEconomicsTutors.co.uk.
Discounted prices compared to all other websites
The estimated intercept is the average price for paintings which are unsigned (i.e. Signed = 0) and
from the first House (i.e. House1) such that the other two House indicator variables are equal to 0.
This indicates that unsigned paintings from the first House sell for an average of 2.021.
(f)
The regressor House1 must be omitted from this regression otherwise there is a perfect linear
relationship between House1, House2, and House3. This would mean that the coefficients cannot be
calculated. By omitting the regressor House1, this coefficient becomes the “base”.
(g)
The estimated coefficients on regressors House2 and House3 represent the difference in average
price between the “base” of the average price in House1. Therefore the estimated coefficient of
0.269 for House2 indicates that the average price of paintings in House 2 is $0.269 million higher
than House 1, all else being held equal. Similarly, the estimated coefficient of -1.504 for House3
indicates that the average price of paintings in House 3 is $1.504 million higher than House 1, all else
being held equal.
