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📐 Mathematics  ·  Statistics  ·  JEE

In regression analysis, R² (coefficient of determination) measures:

Answer: Proportion of variance in Y explained by X.

  • A The correlation coefficient itself, without squaring it
  • B Proportion of variance in Y explained by X
  • C The slope of the fitted regression line
  • D The raw sum of squared residuals from the regression

Correct answer: B. Proportion of variance in Y explained by X

Explanation: SS_total = Σ(yᵢ−ȳ)², SS_residual = Σ(yᵢ−ŷᵢ)². R² = 1 − SS_residual/SS_total = SS_regression/SS_total. R² ∈ [0,1]; a value of 0.85 means 85% of variance in Y is explained by the regression model.

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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