Understand and use = and = − to determine the equation of a least-squares line, where is slope (gradient), is correlation coefficient, is (sample) standard deviation of values, is (sample) standard deviation of values, is -intercept, is mean of values and is mean of values.

gm-u3-t2-s1-d2

Interactive

Least-squares slope from r, sₓ, sᵧ

manipulative

The fitted slope is b = r (sᵧ / sₓ). Correlation is not the gradient — lock r and stretch the sᵧ/sₓ ratio to watch b move.

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