Answer: (x̄, ȳ) - the means.
- A The origin point specifically, regardless of the data
- B (x̄, ȳ) - the means
- C All of the individual data points at once
- D Just the first and last data point in the set
Correct answer: B. (x̄, ȳ) - the means
Explanation: The regression line y on x is ȳ = b·x̄ + a, derived by minimising Σ(yᵢ - ŷᵢ)². Setting partial derivatives to zero gives the normal equations, whose solution always passes through the point of means (x̄, ȳ). Both regression lines share this point.
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