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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✓ Correct
  4. D.20

You have the answer. Trap Analysis is why the other three were written.

Not a worked solution repeated four times — the specific reasoning error each wrong option was built to reward, and why this one tests execution slip.

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The trap it tests

Execution slip

The idea was right. The computation was not.

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Related counterexample: OLS is the BLUE in every linear model

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The chapter behind this: Linear models, Gauss–Markov and ANOVA — free to read

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

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