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Part BCSIR NET June 2024standardized-slope-is-the-covariance

Standardized slope is the covariance

An analyst considers standardized values of observations on three variables, consumption (C), saving (S) and total income (TI) so that they have zero means and unit variances. She further considers disposable income (DI) where DI = C + S. In the simple linear regressions of DI on TI, DI on C and S on TI, the regression coefficients are 0.8, 0.5 and 0.4, respectively. There are 21 sample observations. Sample covariances and variances are calculated with divisor 20. Then, the value of sum of squared residuals in the regression of DI on S is

  1. A.5
  2. B.10
  3. C.15✓
  4. D.20

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Related counterexample: OLS is the BLUE in every linear model

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From Linear Models and Multivariate › Gauss–Markov, regression, ANOVA basics

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