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15 questions · 1 formulas

Dummy in log-Y model

approx = 100b%; exact = 100(e^b − 1)%

Normal DistributionD–A level★ High priority — official Canvas example

In a regression with ln(price) as dependent variable, pool dummy coefficient = 0.0774. Best interpretation?

→ A) A house with a pool is on average about 7.74% more expensive than a house without a pool, holding the other regressors fixed.

Canvas Example MCQ — Q53

A) A house with a pool is on average about 7.74% more expensive than a house without a pool, holding the other regressors fixed.
B) A house with a pool is on average $7,740 more expensive than a house without a pool.
C) A house with a pool is on average 7.74% less expensive than a house without a pool.
D) A house with a pool is on average $77,740 more expensive than a house without a pool.
E) None of A-D is close; write the correct answer.

For a dummy in log-Y, the standard approximation is 100b% = 7.74%. Exact effect = 100(e^0.0774-1) ≈ 8.05%. The source MCQ is testing the approximation.

Rule: Know both approximate and exact dummy-in-log effects.

Hypothesis TestingE-level★ High priority — official Canvas example

Financial-return regression: interest-rate p=.009, recession p=.089, credit-spread p=.455. At 5%, which explanatory variables reject H0?

→ A) Interest rate only

Canvas Example MCQ — Q71

A) Interest rate only
B) Interest rate and Recession dummy
C) Recession dummy only
D) Credit spread only
E) All three explanatory variables

Only .009 < .05.

Rule: At 5%, .089 is not significant.

Hypothesis TestingE-level★ High priority — official Canvas example

Recession dummy p=.089. Which statement is correct?

→ D) The coefficient is statistically significant at 10% but not 5%.

Canvas Example MCQ — Q74

A) The coefficient is statistically significant at both 5% and 10%.
B) The coefficient is statistically significant at 5% but not 10%.
C) The coefficient is not statistically significant at either 5% or 10%.
D) The coefficient is statistically significant at 10% but not 5%.
E) Because p > 0.05, the coefficient must equal zero.

.089 < .10 but .089 > .05.

Rule: Always compare p to the significance level named in the question.

Omitted Variable BiasD–A level★ High priority — official Canvas example

An omitted variable is correlated with X1 but has no effect on Y. Does it bias the estimated coefficient on X1?

→ C) No, because the omitted variable must also be a determinant of Y.

Canvas Example MCQ — Q80

A) Yes, always.
B) Yes, because correlation with X1 is sufficient.
C) No, because the omitted variable must also be a determinant of Y.
D) No, unless X1 is a dummy variable.
E) None of the above.

Condition 2 holds but condition 1 does not.

Rule: Correlation alone is insufficient.

Logs & DummiesD–A levelNormal priority

Which of the following interpretations of the coefficient of colonial variable is most correct?

→ Answer ambiguous in source

Old Exam — Dec 2022, Q22

Given: The source PDF is internally ambiguous: it highlights both A and B. The displayed output omits the colonial coefficient sign, so the sign cannot be recovered from that page alone.

A) A colonial house in on average about 9.36 % less expensive than non-colonial houses.
B) A colonial house in on average about 9.36 % more expensive than non-colonial houses.
C) A colonial house in on average about 18.45 % less expensive than non-colonial houses.
D) A colonial house in on average about 18.45 % more expensive than non-colonial houses.
E) None of the above (A, B, C, D) is close to be correct.

Do not memorize the old key here. The source highlights both A and B, and the coefficient sign is missing from the displayed output. Rule: dummy in log(Y): positive b -> higher Y; negative b -> lower Y. Approx effect=100b%; exact=100(e^b-1)%.

Rule: Identify model units and form before calculating. Never confuse coefficient size, significance, R2 and prediction accuracy.

⚠ Source answer is ambiguous: the original key highlights both A and B, and the coefficient sign is missing. Excluded from scored practice.

Normal DistributionD–A levelVery high priority

Which of the following interpretations of the coefficient of TRADITIONAL is most correct?

→ A) A traditional house in on average about 15.5 % less expensive than non-traditional houses.

Old Exam — Oct 2022, Q16

Given: TRADITIONAL coefficient=-0.1547 in a log-price model.

A) A traditional house in on average about 15.5 % less expensive than non-traditional houses.
B) A waterfront house in on average about 1.55 % less expensive than non-traditional houses.
C) A waterfront house in on average about 1.55 times less expensive than non-traditional houses.
D) A waterfront house in on average about 0.15% less expensive than non-traditional houses.
E) None of the above (A, B, C, D) is close to be correct.

TRADITIONAL is a dummy in ln(PRICE), b=-0.1547. Approximate effect=-15.47%. Exact effect=100(e^-0.1547-1)≈-14.3%. Among the choices, A is the intended approximation.

Rule: Identify model units and form before calculating. Never confuse coefficient size, significance, R2 and prediction accuracy.

Normal DistributionD–A levelVery high priority

Which of the following interpretations of the coefficient of WATERFRONT is most correct?

→ B) A waterfront house in on average 13.5 % more expensive than not waterfront houses.

Old Exam — Oct 2021, Q21

Given: WATERFRONT is a dummy in a log-price model with coefficient≈0.135.

A) A waterfront house in on average 1.35 times more expensive than not waterfront houses.
B) A waterfront house in on average 13.5 % more expensive than not waterfront houses.
C) A waterfront house in on average 13.5 % more expensive than traditional houses.
D) A waterfront house in on average 135 % more expensive than not waterfront houses.
E) None of the above (A, B, C, D) is close to be correct.

Dummy in ln(price): b≈0.135. Approx effect≈13.5% higher; exact=100(e^0.135-1)≈14.5%. Intended answer B.

Rule: Identify model units and form before calculating. Never confuse coefficient size, significance, R2 and prediction accuracy.

Model Fit & RMSED–A levelVery high priority

Using the above model, predict the prices of a house with 2500 square feet that is close to the university. Use the natural predictor (not the corrected predictor). The predicted price is closest to

→ B) $282 742

Old Exam — Oct 2022, Q18

Given: Same as Q17 but dummy CLOSE=1.

A) $228 665
B) $282 742
C) $235 545
D) $265 350
E) None of the above (A, B, C, D) is close to be correct.

Current exam rule: prediction uses the stated fitted equation; lower RMSE/AIC/SC is preferred when the criterion is being minimized; hold-out data must remain outside estimation/selection. Source answer: B) $282 742.

Rule: The old exam supplied a spreadsheet/software. For the 2026 paper exam, expect the necessary values/table/output to be printed. Use the method, not the historical data file.

Logs & DummiesD–A levelNormal priority

Suppose that she obtained 1 2 3 4 ˆ 3.8 0.23 1.31 0.032 1.05 y x x x x = + − + + by using data from the past 24 months. How would we interpret the coefficient on 4x ?

→ B) On an average, we would expect an additional $1.05 million in loans during June, July, and August.

Old Exam — Dec 2021 re-exam, Q20

Given: Y is monthly residential lending in $m; X4=1 for Jun-Jul-Aug. Coefficient on X4 is +1.05.

A) On an average, we would expect an additional 1.05 loans per month during June, July, and August.
B) On an average, we would expect an additional $1.05 million in loans during June, July, and August.
C) On an average, we would expect an additional 1.05% increase in loans during June, July, and August.
D) There is no difference in the total residential loan amount between the months of June and September.
E) None of the above (A, B, C, D) is correct.

X4 is a seasonal dummy and Y is measured in millions of dollars. Holding other regressors fixed, X4=1 adds 1.05 million dollars of expected loans -> B.

Rule: Interactions and quadratics mean the marginal effect is not constant. Log coefficients require percentage interpretation.

InteractionsD–A levelNormal priority

In the interaction model PRICE = ... + b3·UTOWN + b6·(SQFT×UTOWN), with b3=27.453 and b6=1.2994, is it correct to interpret b3 = 27.453 as a constant $27,453 university premium regardless of house size?

→ A) No — because of the interaction term, the university premium depends on SQFT: Premium = b3 + b6×SQFT

Computer Lab 5 — Exercise 3, Task 2

A) No — because of the interaction term, the university premium depends on SQFT: Premium = b3 + b6×SQFT
B) Yes, b3 alone always gives the full location premium
C) No, because UTOWN has no effect on price at all
D) Yes, but only express it per square foot

With an interaction term present, the university premium at a given SQFT is b3 + b6×SQFT, which varies with house size — it is not the constant $27,453 that b3 alone suggests.

Rule: When X is interacted with D, the effect of D itself depends on the level of X: Effect of D = b2+b3X.

InteractionsD–A levelNormal priority

Two otherwise identical houses of 2,000 sqft (SQFT=20) differ only in UTOWN status. Using Premium = 27.453 + 1.2994×SQFT ($000), what is the predicted price difference attributable to being near the university?

→ A) ≈$53,441

Computer Lab 5 — Exercise 3, Task 3

A) ≈$53,441
B) ≈$27,453
C) ≈$25,988
D) ≈$60,211

Premium = 27.453 + 1.2994×20 = 27.453 + 25.988 = 53.441 ($000) ≈ $53,441.

Rule: For two observations differing only in the dummy D, use Difference = b2 + b3×X directly rather than recomputing the whole regression.

Logs & DummiesE-levelNormal priority

The WATERFRONT dummy coefficient in a ln(PRICE) regression is 0.2036. What is the exact percentage price difference for waterfront vs non-waterfront houses, using 100×[exp(b)−1]?

→ A) ≈22.58%

Computer Lab 5 — Exercise 4, Dummy in log model

A) ≈22.58%
B) ≈20.36%
C) ≈2.036%
D) ≈45.16%

Exact effect = 100×[exp(0.2036)−1] = 100×[1.2258−1] ≈ 22.58%.

Rule: For a dummy in a log(Y) model, use the quick approximation 100b% or the exact 100[exp(b)−1]%; the exact value is always somewhat larger in magnitude for positive b.

LogitD–A levelVery high priority

In LPM Model 2 (no PIRAT×BLACK interaction), a Black applicant's predicted denial probability falls from 28.26% to 25.47% (a 2.80 pp drop) when PIRAT falls from 0.35 to 0.30. A White applicant shows the exact same 2.80 pp drop over the same PIRAT change. Why are these two changes identical?

→ A) Because Model 2 has no interaction between PIRAT and BLACK, so the PIRAT slope is forced to be the same for both races

Computer Lab 6 — Exercise 4, LPM Task 2

A) Because Model 2 has no interaction between PIRAT and BLACK, so the PIRAT slope is forced to be the same for both races
B) Because BLACK has no effect on denial probability at all
C) Because LPM models always produce identical slopes for every subgroup by mathematical necessity
D) Coincidence; the two groups just happened to have the same PIRAT effect in this example

Without a PIRAT×BLACK interaction term, the coefficient on PIRAT (0.5592) applies uniformly across all values of BLACK, forcing an identical slope for both groups; adding an interaction term would allow the slope to differ by race.

Rule: Without an interaction term, a regression imposes the same slope for all subgroups defined by the dummy variable.

Hypothesis TestingE-level★ High priority — official Canvas example

A financial-return regression reports p-values: interest rate p = .009, recession dummy p = .089, credit spread p = .455. At the 10% level, which variables reject H0: β = 0?

→ C) Interest rate and Recession dummy

Canvas Example MCQ — Q72

A) Interest rate only
B) Recession dummy only
C) Interest rate and Recession dummy
D) Interest rate and Credit spread
E) All three explanatory variables

.009 < .10 and .089 < .10; .455 > .10.

Rule: Reject H0 when p < α; changing α can change the conclusion.

Logs & DummiesE-levelNormal priority

ln(Price) regressed on a dummy with coefficient 0.25. You need the EXACT percentage effect.

→ B) 100(e^0.25 − 1)%

Formula Battle — method recognition (built from the Formula Book)

A) 25%
B) 100(e^0.25 − 1)%
C) 0.25 SEK
D) e^0.25

Exponentiate the coefficient. Correct method: 100(e^0.25 − 1)%.

Rule: Exact = 100(e^b − 1)%