题目2494 · 机器学习
Centered Simple Regression Through the Origin 24
After centering x and y in simple regression with an intercept, what optimization problem remains for the slope?
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中文题目题目2276 · 数理金融
LSM Regression Interpretation 1
An LSM continuation regression is fit linearly from two in-the-money paths: (S,C)=(70,24) and (90,10). What continuation estimate does that line give at S = 80?
打开 →题目2524 · 机器学习
Why No Closed Form in Logistic Regression 5
Why does logistic regression usually require iterative optimization rather than a normal-equation-style closed form?
打开 →题目2277 · 数理金融
LSM Regression Interpretation 2
Two in-the-money paths used in an LSM fit are (S,C)=(65,22) and (95,13). If the desk uses a linear continuation fit, what slope is implied?
打开 →题目2278 · 数理金融
LSM Regression Interpretation 3
A linear LSM continuation fit passes through (S,C)=(85,16) and (100,7). What intercept a in C(S)=a+bS is implied?
打开 →题目2279 · 数理金融
LSM Regression Interpretation 4
An LSM continuation fit is C(S) = a + 0.2S and passes through (S,C)=(72,20). At what spot S would the continuation estimate equal 15.6?
打开 →题目2280 · 数理金融
LSM Regression Interpretation 5
A linear LSM continuation fit passes through (75,18) and gives continuation 14 at S = 90. If another in-the-money path is at S = 105, what continuation value must it have to stay on the same fitted line?
打开 →题目1817 · 统计
Spurious Regression Warning
Why can regressing one drifting series on another produce a large R-squared and tiny p-values even when there is no economic relation?
打开 →题目2549 · 机器学习
Penalized Split Decision on a Regression Node 18
A regression leaf has SSE 260. Splitting it would reduce child SSE to 230. If the complexity penalty is 12 per extra leaf, should you keep the split?
打开 →题目2581 · 机器学习
Why Random-Forest Regression Extrapolates Poorly 16
Why does random-forest regression usually fail to extrapolate a trend far beyond the training range?
打开 →题目1648 · 统计
Gaussian No-Intercept Regression as an MLE Problem
Suppose observations satisfy $$Y_i = \beta X_i + \varepsilon_i, \qquad \varepsilon_i\stackrel{iid}{\sim}N(0,\sigma^2),$$ with no intercept and known Gaussian errors. You are told that $$\sum X_iY_i = 48, \qquad \sum X_i^2 = 16.$$ Find the MLE of $\beta$.
打开 →题目2489 · 机器学习
A Constant Shift in One Feature 19
If a feature x is replaced by x+k in a regression that already includes an intercept, what happens to the slope on x and the intercept?
打开 →题目1768 · 统计
A Lagged Variable Is Not Automatically a Valid Instrument
Someone proposes using yesterday's order-flow imbalance as an instrument for today's imbalance in a return-impact regression. Why is this not automatically a valid instrument in financial data?
打开 →题目1753 · 统计
Average Leverage and Average Residual-Maker Diagonal
A 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?
打开 →题目1761 · 统计
Direct and Total Effect After a Routing Channel Split
A routing signal X increases child-order fragmentation M by 2 units on average. The outcome obeys Y = 1.3 X + 0.4 M + noise, with X otherwise exogenous. What coefficient on X would you expect in a regression that controls for M, and what total effect of a one-unit increase in X w
打开 →题目1748 · 统计
Fitted Variance From R-Squared and Response Variance
A regression with intercept has response variance 9 and R^2 = 4/9. What is the variance of the fitted values?
打开 →题目2476 · 机器学习
Infer the Slope From Covariance and Variance 6
In a simple regression with an intercept, Cov(x,y)=12 and Var(x)=16. What is the OLS slope beta_hat?
打开 →题目1749 · 统计
Intercept From Center of the Cloud
In a simple OLS regression with intercept, x_bar = 3, y_bar = 5, and the slope estimate is -0.4. What is the intercept?
打开 →题目2486 · 机器学习
Intercept From Means 17
In a simple regression with intercept, xbar = 3, ybar = 11, and beta_hat = 2. What is alpha_hat?
打开 →题目2472 · 机器学习
Intercept From Sample Means and Slope 2
Derive the OLS intercept in simple regression with an intercept once beta_hat is known.
打开 →题目2291 · 数理金融
LSM Implementation Judgment 11
Why is filtering to in-the-money paths often reasonable for regression design, but not a theorem that it must always help?
打开 →题目2284 · 数理金融
LSM Implementation Judgment 4
Why is an out-of-sample valuation pass valuable even after the continuation regression looks fine in-sample?
打开 →题目2285 · 数理金融
LSM Implementation Judgment 5
Why can reusing exactly the same simulation paths for regression design and valuation make the option look too good?
打开 →题目1742 · 统计
Slope From Correlation and Scale
A 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?
打开 →题目1741 · 统计
Slope From Fitted Energy and Predictor Energy
In 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?
打开 →题目1746 · 统计
Slope From Predictor Variance and Fitted Variance
In 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?
打开 →题目2491 · 机器学习
Solve a Two-Feature No-Intercept OLS System 21
For a no-intercept regression with X^T X = [[4, 1], [1, 9]] and X^T y = [10, 19], what is beta_hat?
打开 →题目1744 · 统计
Why Centering a Regressor Changes the Intercept but Not the Slope
Why does replacing x by x - x_bar in a regression with intercept usually change the intercept interpretation while leaving the slope unchanged?
打开 →题目1754 · 统计
Why Multicollinearity Can Leave Training Fit Looking Fine
Why can a regression with severe multicollinearity still show a strong in-sample fit and a high R^2?
打开 →题目2526 · 机器学习
Why Separable Data Pushes Coefficients Outward 7
Why do logistic-regression coefficients tend to diverge on perfectly linearly separable data if no regularization is used?
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