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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.

Old Exam — Dec 2021 re-exam, Q21

Given: Interaction coefficient on X3xX4 is -0.22; it changes the advertising slope in summer.

• A) On an average, we would expect $220,000 less in loans during the months of June, July, and August.
• B) Advertising is more effective during June, July, and August.
• C) On an average, we would expect $220,000 more in loans during the months of June, July, and August.
• D) Advertising is less effective in June, July, and August.
• E) None of the above (A, B, C, D) is correct.

Advertising slope outside summer is 0.032. In summer it becomes 0.032-0.22, so the interaction lowers the advertising effect -> D.

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

Computer Lab 5 — Exercise 3, Task 2

• A) $7,612.20 (b1 alone)
• B) $8,911.60 (b1+b6)
• C) $1,299.40 (b6 alone)
• D) $15,223.80 (2×b1)

When UTOWN=0, the SQFT interaction term drops out, so the size effect is simply b1 = 7.6122 ($000 per 100 sqft) = $7,612.20 per 100 sqft increase.

Rule: Effect of X when D=0 in an interaction model Y=b0+b1X+b2D+b3XD is b1.

Computer Lab 5 — Exercise 3, Task 2

• A) $8,911.60 (b1+b6)
• B) $7,612.20 (b1 alone)
• C) $1,299.40 (b6 alone)
• D) $6,312.80 (b1−b6)

When UTOWN=1, the size effect is b1+b6 = 7.6122+1.2994 = 8.9116 ($000 per 100 sqft) = $8,911.60.

Rule: Effect of X when D=1 in an interaction model is b1+b3 (here b1+b6).

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.

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.

Computer Lab 6 — Exercise 1, Task 5

• A) Cross-validation and model selection occurred strictly within the training data; the hold-out set was used only once for final evaluation
• B) Using more variables automatically guarantees better out-of-sample prediction
• C) The hold-out RMSE was used repeatedly to pick the best of many candidate models
• D) Adding interactions always improves prediction regardless of how the model is selected

To avoid overfitting to the test data, all model search and tuning (cross-validation) was confined to the 800 training observations; the 100 hold-out observations were used only once, to report final, honest performance.

Rule: Model search/tuning must happen within training data only; the test/hold-out set should be touched only once, at the end.

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.

Computer Lab 6 — Exercise 4, Probit vs LPM nonlinearity

• A) Because Probit is nonlinear: the marginal/discrete effect of PIRAT depends on the predicted probability level itself, which differs by BLACK status even without an explicit interaction term
• B) Because the Probit model actually includes an interaction term between PIRAT and BLACK
• C) Because Probit coefficients differ by group automatically
• D) This is a calculation error; Probit should give identical effects just like LPM

Even without an interaction term, Probit's nonlinear Φ(·) link function makes the implied probability effect of any regressor depend on the overall linear index (and thus on BLACK, which shifts the index), unlike LPM where effects are mechanically constant across groups.

Rule: Nonlinear models (Probit/Logit) naturally produce covariate-dependent marginal effects even without explicit interaction terms, unlike the linear LPM.

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

• A) b1
• B) b1 + b3
• C) b3
• D) b1 + b2 + b3

Differentiate with respect to X. Correct method: b1 + b3.

Rule: ∂Y/∂X = b1 + b3·D