A social scientist recorded ARD rate ( $X\%$ ) and divorce rate ( $Y\%$ ) over 6 periods, with $n=6$ , $\sum X=684$ , $\sum Y=64$ , $\sum X^2=92312$ , $\sum Y^2=926$ , $\sum XY=9106$ . What is the product moment correlation coefficient, to 3 decimal places?

Model answer

0.969

Also accepted: 0.97

Explanation

S_{xx}=92312-684^2/6=14336

;

S_{yy}=926-64^2/6\approx243.333

;

S_{xy}=9106-684(64)/6=1810

r=\dfrac{S_{xy}}{\sqrt{S_{xx}S_{yy}}}=\dfrac{1810}{\sqrt{14336\times243.333}}\approx0.969

, indicating a strong positive correlation.

Derived from ZIMSEC Maths Paper 1, June 2007, Q9 (Statistics)

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