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📐 Mathematics  ·  Statistics  ·  JEE

If byx × bxy = r², where byx and bxy are regression coefficients, then r =

Answer: sqrt(byx × bxy).

  • A byx × bxy
  • B sqrt(byx × bxy)
  • C (byx + bxy)/2
  • D byx/bxy

Correct answer: B. sqrt(byx × bxy)

Explanation: By definition byx = r·(σy/σx) and bxy = r·(σx/σy). Their product: byx × bxy = r²·(σy/σx)·(σx/σy) = r². Therefore r = ±√(byx × bxy), with sign matching that of both coefficients.

Normal Distribution: the 68-95-99.7 Rule68% within ±1σ95% within ±2σmean=median=mode (centre)

In a perfectly normal (bell-shaped) distribution, mean, median, and mode all coincide at the centre; about 68% of data falls within 1 standard deviation of the mean, 95% within 2, and 99.7% within 3 - the empirical rule used to judge how typical or extreme a value is.

Concept context

Mean, median, mode, standard deviation, and data interpretation

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