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2276LSM Regression Interpretation 1An 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?数理金融中等数值题未尝试面试订阅2277LSM Regression Interpretation 2Two 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?数理金融中等数值题未尝试面试订阅2278LSM Regression Interpretation 3A linear LSM continuation fit passes through (S,C)=(85,16) and (100,7). What intercept a in C(S)=a+bS is implied?数理金融中等数值题未尝试面试订阅2279LSM Regression Interpretation 4An 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?数理金融中等数值题未尝试面试订阅2280LSM Regression Interpretation 5A 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?数理金融中等数值题未尝试面试订阅2471Slope From Centered Sufficient Statistics 1In simple OLS with an intercept, if the centered sufficient statistics satisfy sum i (x i-xbar)(y i-ybar)=S xy and sum i (x i-xbar) 2=S xx, derive beta hat.机器学习简单derivation未尝试免费2472Intercept From Sample Means and Slope 2Derive the OLS intercept in simple regression with an intercept once beta hat is known.机器学习简单derivation未尝试免费2473Scaling One Feature Rescales Its Coefficient 3If a feature x is replaced by x new = c x in an OLS model with an intercept, how does its fitted coefficient change when all fitted values are kept identical?机器学习中等derivation未尝试面试订阅2474Shifting the Response by a Constant 4If every target value is replaced by y i + k in an OLS model with an intercept, what happens to the fitted slope and intercept?机器学习中等derivation未尝试面试订阅2475Why Duplicate Features Cause Non-Unique Coefficients 5Why do two perfectly duplicated features make the OLS coefficient vector non-unique even though fitted predictions can stay unique?机器学习困难essay未尝试面试订阅2476Infer the Slope From Covariance and Variance 6In a simple regression with an intercept, Cov(x,y)=12 and Var(x)=16. What is the OLS slope beta hat?机器学习简单数值题未尝试免费2477Why Centering Can Simplify OLS Algebra 7Why does centering features and targets often make OLS derivations cleaner when an intercept is present?机器学习中等essay未尝试免费2478Residual Orthogonality to Features 8Why must the OLS residual vector be orthogonal to every column of the design matrix at the optimum?机器学习中等derivation未尝试面试订阅2479Why Multicollinearity Hurts Coefficient Stability More Than Fit 10Why can severe multicollinearity make coefficients unstable even when training predictions barely change?机器学习中等essay未尝试面试订阅2480Orthogonal Features Give Coordinatewise Coefficients 9Suppose two features x1 and x2 are centered and orthogonal. Derive the OLS coefficients in terms of x1 T y, x2 T y, ||x1|| 2, and ||x2|| 2.机器学习困难derivation未尝试面试订阅2481Adding an Orthogonal Zero-Signal Feature 11If a new centered feature z is orthogonal to both the existing centered design and the response y, what coefficient does OLS assign to z?机器学习简单derivation未尝试免费2482Projection Interpretation of the Fitted Vector 12In one sentence, what geometric object is X beta hat in OLS?机器学习简单derivation未尝试免费2483Why Centering Leaves Slopes Unchanged 13Why does centering x and y leave the fitted slope unchanged in simple OLS with an intercept?机器学习中等derivation未尝试面试订阅2484Response Scaling 14If every target is multiplied by c, what happens to the OLS coefficient vector and intercept?机器学习困难derivation未尝试面试订阅2485Why Gradient Descent and Closed Form Agree 15Why do exact gradient descent convergence and the normal-equation solution agree for OLS?机器学习困难derivation未尝试面试订阅