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Part CCSIR NET June 2025a-symmetric-x-grid-and-an-even-y-give-zero-correlation-despite-exact-dependence

A symmetric x grid and an even y give zero correlation despite exact dependence

Consider a paired data , where and for all i = 1, 2, 3, 4, 5. On this data, a simple linear regression model with an intercept term and a simple linear regression model without an intercept term are fitted using the method of least squares. Which of the following statements are true?

  1. A.The two fitted lines have the same slope✓
  2. B.The two fitted models have the same intercept
  3. C.The model with intercept passes through at least one of the observed data points
  4. D.The model without intercept passes through at lesast one of the observed data points✓

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 dependence misread.

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50 are analysed free — try those first.

The trap it tests

Dependence misread

Independence, pairwise vs mutual, or correlation vs dependence.

Drill statements like this

Related counterexample: OLS is the BLUE in every linear model

More on this topic

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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