Linear Models & Regression
55 questions across 3 topics. Also examined in CNET, ISS, GATE ST.
Simple and Multiple Linear Regression, Logistic Regression
- 151Variance of a prediction in simple linear regressionMSET June 2025Simple and Multiple Linear Regression, Logistic RegressionHard
- 152Which mean squares are unbiased for sigma^2MSET June 2025Simple and Multiple Linear Regression, Logistic RegressionHard
- 153What the adjusted R^2 adjusts forMSET June 2025Simple and Multiple Linear Regression, Logistic RegressionHard
- 154Degrees of freedom for the deviance goodness-of-fit testMSET June 2025Simple and Multiple Linear Regression, Logistic RegressionHard
- 102Correlation — geometric vs. arithmetic mean of the regression coefficientsMSET April 2024Simple and Multiple Linear Regression, Logistic RegressionHard
- 151Regression residuals — correlated and heteroscedastic even when the errors aren'tMSET April 2024Simple and Multiple Linear Regression, Logistic RegressionHard
- 152Covariance of y and hat y under least squaresMSET April 2024Simple and Multiple Linear Regression, Logistic RegressionEasy
- 154Logistic regression — odds ratio for a pm1-coded covariateMSET April 2024Simple and Multiple Linear Regression, Logistic RegressionEasy
- 151What the least-squares regression line can and cannot claimMSET March 2023Simple and Multiple Linear Regression, Logistic RegressionMedium
- 152Unbiasedness of the three mean squares in multiple regressionMSET March 2023Simple and Multiple Linear Regression, Logistic RegressionHard
- 153sum yi=sumhat yi holds precisely when there's an interceptMSET March 2023Simple and Multiple Linear Regression, Logistic RegressionMedium
- 154The logistic regression response is binaryMSET March 2023Simple and Multiple Linear Regression, Logistic RegressionEasy
- 162Prediction variance grows with distance from the mean of the regressorsMSET September 2021Simple and Multiple Linear Regression, Logistic RegressionMedium
- 163Regression residuals are correlated and heteroscedastic, againMSET September 2021Simple and Multiple Linear Regression, Logistic RegressionHard
- 164Regression SS and Error SS — uncorrelated by orthogonal projectionsMSET September 2021Simple and Multiple Linear Regression, Logistic RegressionHard
- 102Correlation as the geometric mean of the two regression slopes, sign includedMSET December 2020Simple and Multiple Linear Regression, Logistic RegressionEasy
- 162The least-squares line passes through (bar x,bar y) exactly when an intercept is fittedMSET December 2020Simple and Multiple Linear Regression, Logistic RegressionMedium
- 163Uncorrelated errors give non-identical, uncorrelated responsesMSET December 2020Simple and Multiple Linear Regression, Logistic RegressionMedium
- 162Residuals sum to zero whenever the model has an interceptMSET June 2019Simple and Multiple Linear Regression, Logistic RegressionEasy
- 163A fitted regression predicts; it neither proves causation nor needs a good fit to existMSET June 2019Simple and Multiple Linear Regression, Logistic RegressionEasy
- 164Only the error mean square is unbiased for sigma^2 in generalMSET June 2019Simple and Multiple Linear Regression, Logistic RegressionHard
- 52Adding a regressor can never increase the residual sum of squaresMSET January 2018 Paper IISimple and Multiple Linear Regression, Logistic RegressionEasy
- 99Regression through the origin: hatalpha=sum xizi/sum zi^2MSET January 2018 Paper IIISimple and Multiple Linear Regression, Logistic RegressionEasy
- 115Adjusted R^2=1-(1-R^2)n-1/n-k-1approx0.960 — not among the optionsMSET January 2018 Paper IIISimple and Multiple Linear Regression, Logistic RegressionEasy
- 119The Box–Cox family is continuous in lambda, with log Y as its lambda=0 limitMSET January 2018 Paper IIISimple and Multiple Linear Regression, Logistic RegressionMedium
- 120A tiny R^2 rules out only a linear relationMSET January 2018 Paper IIISimple and Multiple Linear Regression, Logistic RegressionEasy
- 51Regression coefficients: c/a=sigmaX^2/sigmaY^2, ac=r^2, and the lines meet at the meansMSET April 2017 Paper IISimple and Multiple Linear Regression, Logistic RegressionMedium
- 52r^2=bYXbXY=2ale1 with a of the same sign as 2MSET April 2017 Paper IISimple and Multiple Linear Regression, Logistic RegressionEasy
- 113Reading "se(hatbeta,hatgamma)" as the s.e. of hatbetahatgamma (delta method)MSET April 2017 Paper IIISimple and Multiple Linear Regression, Logistic RegressionHard
- 114Varhatbeta=sigma^2/sum(Xi-bar X)^2, not sigma^2/sum Xi^2MSET April 2017 Paper IIISimple and Multiple Linear Regression, Logistic RegressionEasy
- 115Positive errors with mean theta: the slope is still unbiased, the intercept absorbs thetaMSET April 2017 Paper IIISimple and Multiple Linear Regression, Logistic RegressionMedium
Gauss-Markov Models, Estimability, Best Linear Unbiased Estimators
- 147Estimability in the general linear model — the row-space characterisationMSET April 2024Gauss-Markov Models, Estimability, Best Linear Unbiased EstimatorsHard
- 148Estimability from a partial set of linear relationsMSET March 2023Gauss-Markov Models, Estimability, Best Linear Unbiased EstimatorsMedium
- 161Estimability with four linked expectations — identify the one genuinely non-estimable combinationMSET September 2021Gauss-Markov Models, Estimability, Best Linear Unbiased EstimatorsHard
- 128Estimability in one-way ANOVA: the coefficient of mu must equal the sum of the alpha coefficientsMSET December 2020Gauss-Markov Models, Estimability, Best Linear Unbiased EstimatorsMedium
- 129In one-way ANOVA, cmu+sum dialphai is estimable iff sum di=cMSET June 2019Gauss-Markov Models, Estimability, Best Linear Unbiased EstimatorsMedium
- 161Estimable functions are the combinations of theta2-theta1 and theta2+theta3MSET June 2019Gauss-Markov Models, Estimability, Best Linear Unbiased EstimatorsEasy
- 165Centred regressor values make the least-squares estimators uncorrelatedMSET June 2019Gauss-Markov Models, Estimability, Best Linear Unbiased EstimatorsEasy
- 116Fitted values are centred at Xbeta, not at betaMSET January 2018 Paper IIIGauss-Markov Models, Estimability, Best Linear Unbiased EstimatorsEasy
- 117Under sigma^2Omega, the fitted values do not have covariance sigma^2OmegaMSET January 2018 Paper IIIGauss-Markov Models, Estimability, Best Linear Unbiased EstimatorsMedium
- 118hatbeta is unique exactly when X has full column rankMSET January 2018 Paper IIIGauss-Markov Models, Estimability, Best Linear Unbiased EstimatorsMedium
- 72Divide the residual sum of squares by its n-K degrees of freedomMSET April 2017 Paper IIGauss-Markov Models, Estimability, Best Linear Unbiased EstimatorsEasy
- 116A true linear restriction keeps the restricted estimator unbiased and more preciseMSET April 2017 Paper IIIGauss-Markov Models, Estimability, Best Linear Unbiased EstimatorsMedium
- 117Unbiasedness, sigma^2(X'X)^-1 and BLUE are exact; consistency needs conditions on XMSET April 2017 Paper IIIGauss-Markov Models, Estimability, Best Linear Unbiased EstimatorsMedium
- 118GLS weights by Omega^-1, not OmegaMSET April 2017 Paper IIIGauss-Markov Models, Estimability, Best Linear Unbiased EstimatorsEasy
Analysis of Variance and Covariance, Fixed/Random/Mixed Effects
- 149Completing a two-way ANOVA tableMSET June 2025Analysis of Variance and Covariance, Fixed/Random/Mixed EffectsHard
- 150What ANOVA actually testsMSET June 2025Analysis of Variance and Covariance, Fixed/Random/Mixed EffectsHard
- 149Reading a partially filled ANOVA tableMSET April 2024Analysis of Variance and Covariance, Fixed/Random/Mixed EffectsMedium
- 150Overparametrised one-way ANOVA — what is and isn't estimableMSET April 2024Analysis of Variance and Covariance, Fixed/Random/Mixed EffectsHard
- 170Two-level ANOVA — equivalent to a two-sided t-testMSET April 2024Analysis of Variance and Covariance, Fixed/Random/Mixed EffectsHard
- 149Filling in a two-way ANOVA table from its own consistency constraintsMSET March 2023Analysis of Variance and Covariance, Fixed/Random/Mixed EffectsMedium
- 129The full assumption set behind the one-way ANOVA F-testMSET September 2021Analysis of Variance and Covariance, Fixed/Random/Mixed EffectsMedium
- 165Testing a variance component's insignificance, not a mean-equality hypothesis, for random effectsMSET December 2020Analysis of Variance and Covariance, Fixed/Random/Mixed EffectsMedium
- 74Error variance =SSE/(N-k)=399.6/27MSET January 2018 Paper IIAnalysis of Variance and Covariance, Fixed/Random/Mixed EffectsEasy
- 126OC-curve parameter for factor A: Phi^2=nbsumtaui^2/(asigma^2)MSET January 2018 Paper IIIAnalysis of Variance and Covariance, Fixed/Random/Mixed EffectsHard