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 gradient of the regression line of $y$ upon $x$ , to 3 decimal places?

Model answer

0.126

Also accepted: 0.1263, 0.13

Explanation

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

and

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

. The gradient is

b=S_{xy}/S_{xx}=1810/14336\approx0.126

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

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