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4 questions · 1 formulas

Confidence interval

b ± t_crit × SE (90%: 1.645, 95%: 1.96, 99%: 2.576)

Trap: SE = b / t if only t is shown.

Normal DistributionD–A levelVery high priority

The 99% confidence interval for β-coefficient for the lsqrft variable is closest to__________.

→ A) (0.5027, 0.9026)

Old Exam — Dec 2022, Q21

Given: For ln(sqft): coefficient=0.7026, SE=0.0759. Use a 99% critical value about 2.63.

A) (0.5027, 0.9026)
B) (0.5517, 0.8535)
C) (0.5887, 0.8174)
D) Not possible to compute given the information in the summary output.
E) None of the above (A, B, C, D) is close to be correct.

99% CI ≈ b ± 2.63 SE = 0.7026 ± 2.63(0.0759) ≈ (0.503,0.902), matching A.

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

Regression BasicsD–A levelVery high priority

The 90% confidence interval for β5 (WATERFRONT variable) is closest to__________.

→ A) (0.0301, 0.1817)

Old Exam — Oct 2022, Q15

Given: WATERFRONT coefficient=.1059, t=2.3011. For 90% CI use roughly b ± 1.645 SE.

A) (0.0301, 0.1817)
B) (0.0616, 0.1512)
C) (0.0954, 0.1747)
D) Not possible to compute given the information in the summary output.
E) None of the above (A, B, C, D) is close to be correct.

SE of WATERFRONT ≈ 0.1059/2.3011≈0.0460. 90% CI ≈0.1059±1.645(0.0460)=(0.030,0.182) -> A.

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

Regression BasicsD–A levelVery high priority

The 95% confidence interval for β5 is closest to__________.

→ C) (0.0954, 0.1747)

Old Exam — Oct 2021, Q20

Given: WATERFRONT coefficient≈0.135, SE≈0.020207; use b ± 1.96 SE.

A) (‒1.8260, 2.0961)
B) (0.1148, 0.1552)
C) (0.0954, 0.1747)
D) Not possible to compute given the information in the summary output. 8

95% CI≈0.135±1.96(0.020207)≈(0.0954,0.1747) -> C.

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

Model Fit & RMSED–A levelVery high priority

When you performed the regression analysis above, you did not correct for problem with heteroscedasticity. Suppose that you have a problem with heteroscedasticity in the above model. Therefore, you estimate the model using the White heteroscedasticity-consistent estimator. (You do not need to do it to answer this question!) Which of the following statements is true? The White’s heteroscedasticity-consistent estimator prevent us from computing incorrect values_____

→ A) for test statistics or incorrect interval estimates in the presence of heteroskedasticity.

Old Exam — Oct 2022, Q19

Given: Concept question about White/heteroskedasticity-consistent standard errors.

A) for test statistics or incorrect interval estimates in the presence of heteroskedasticity.
B) for test statistics or incorrect interval estimates in the presence of homoscedasticity.
C) for unbiased estimators.
D) robust standard errors.
E) None of the above (A, B, C, D) is close to be correct.

Heteroskedasticity-robust/White SEs are used so t-tests and confidence intervals remain valid under heteroskedasticity. OLS coefficients themselves do not change.

Rule: Training data estimates/selects; hold-out data evaluates. Lower RMSE = better prediction.