‹ Back to the paper
Answer the following on regression and correlation.
If two lines of regression are and , find the correlation coefficient between and .
If two lines of regression are $4x + 2y - 3 = 0$ and $3x + 6y + 5 = 0$, find the correlation coefficient between $x$ and $y$.
Answer
Answer
AIRegression coefficient of y on x: -1/2
Regression coefficient of x on y: -1/2
Correlation coefficient r: -1/2
Line of y on x: y = -0.5x - 5/6
Line of x on y: x = -0.5y + 3/4
Take $4x + 2y - 3 = 0$ as the line of $x$ on $y$ and $3x + 6y + 5 = 0$ as the line of $y$ on $x$ (the other choice gives $b_{xy}b_{yx} = 4 > 1$, impossible).
$x = -\frac{1}{2}y + \frac{3}{4}$, so $b_{xy} = -\frac{1}{2}$.
$y = -\frac{1}{2}x - \frac{5}{6}$, so $b_{yx} = -\frac{1}{2}$.
$r^2 = b_{xy}b_{yx} = \frac{1}{4}$; both coefficients are negative, so $r$ is negative.
Hence $r = -\frac{1}{2}$.
From ISC 2018 Specimen Mathematics Paper 1, question 19(b).
Check your working with the Regression lines calculator: both regression lines, b_yx, b_xy and r from data, summary sums or the two lines; with estimates.