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1607Why Sample Covariance Can Be Rank DeficientWhy can a sample covariance matrix become rank deficient when the number of observations is smaller than the number of assets?数学中等essay未尝试免费1648Gaussian No-Intercept Regression as an MLE ProblemSuppose observations satisfy Y i = X i + \varepsilon i, \qquad \varepsilon i\stackrel iid \sim N(0, 2), with no intercept and known Gaussian errors. You are told that X iY i = 48, \qquad X i 2 = 16. Find the MLE of .统计中等derivation未尝试面试订阅1741Slope From Fitted Energy and Predictor EnergyIn a simple OLS regression with intercept, the centered predictor sum of squares is S xx = 20 and the fitted values have centered sum of squares 45. If the slope is known to be positive, what is the OLS slope?统计简单derivation未尝试免费1742Slope From Correlation and ScaleA simple OLS regression with intercept has sample correlation corr(x,y) = -0.6, sample standard deviation s x = 4, and sample standard deviation s y = 5. What is the slope coefficient on x?统计简单derivation未尝试免费1743Residual Sum of Squares From TSS and R-SquaredAn OLS fit with intercept has total sum of squares TSS = 250 and R 2 = 0.84. What is the residual sum of squares?统计简单derivation未尝试免费1744Why Centering a Regressor Changes the Intercept but Not the SlopeWhy does replacing x by x - x bar in a regression with intercept usually change the intercept interpretation while leaving the slope unchanged?统计简单essay未尝试免费1745Why Residuals Sum to Zero Only With an InterceptWhy does the property 'residuals sum to zero' depend on including an intercept in the design matrix?统计中等essay未尝试面试订阅1746Slope From Predictor Variance and Fitted VarianceIn a simple OLS regression with intercept, x has sample variance 9 and the fitted values have sample variance 4. If the slope is positive, what is the slope coefficient?统计简单derivation未尝试免费1747Why Duplicate Regressors Destabilize Coefficients but Not the SpanWhy does adding a regressor that is almost a copy of an existing regressor make the coefficient vector unstable even though the fitted values may barely change?统计中等essay未尝试面试订阅1748Fitted Variance From R-Squared and Response VarianceA regression with intercept has response variance 9 and R 2 = 4/9. What is the variance of the fitted values?统计简单derivation未尝试免费1749Intercept From Center of the CloudIn a simple OLS regression with intercept, x bar = 3, y bar = 5, and the slope estimate is -0.4. What is the intercept?统计中等derivation未尝试面试订阅1750Why High Leverage Is Not the Same Thing as a Big ResidualWhy can a data point have very high leverage without having a large residual, and why does that still make it influential?统计简单essay未尝试免费1751Slope and Intercept From Two Fitted BenchmarksA desk summarizes its fitted line by saying y hat = 2.4 when x = 1 and y hat = 0.9 when x = 6. What are the slope and intercept of the line?统计简单derivation未尝试免费1752Why OLS Hedging Is a Projection ProblemWhy is the OLS hedge ratio often described as projecting a cash-book return stream onto the span of hedge instruments?统计中等essay未尝试面试订阅1753Average Leverage and Average Residual-Maker DiagonalA regression uses n = 25 observations and three estimated parameters including the intercept. What are (i) the average leverage and (ii) the average diagonal entry of the residual-maker matrix I - H?统计中等derivation未尝试面试订阅1754Why Multicollinearity Can Leave Training Fit Looking FineWhy can a regression with severe multicollinearity still show a strong in-sample fit and a high R 2?统计简单essay未尝试免费1755Why the Prediction Problem Can Be Easier Than the Coefficient ProblemWhy can two very different coefficient vectors produce nearly the same predictions on the observed design points?统计简单essay未尝试免费1791Scaling Before Lasso on Mixed UnitsA signal library mixes raw prices, basis-point spreads, and z-scored microstructure features. Why should the team standardize features before running Lasso?统计简单derivation未尝试免费1833MA(1) Invertibility Check 3An MA(1) execution-noise model uses theta = -0.7. Is the model invertible?统计中等数值题未尝试面试订阅1843ARMA Identification or Simplification 3You observe the diagnostic statement: Both ACF and PACF tail off. What is the correct modeling conclusion?统计中等derivation未尝试面试订阅