A shop records the price x of an item in rupees tens, and the number sold y in a week, at six…

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A shop records the price $x$ of an item in rupees tens, and the number sold $y$ in a week, at six different prices: $x = 2, 4, 6, 8, 10, 12$ and $y = 14, 13, 10, 9, 6, 5$ . Find the means, the slope $b_{yx}$ of the line of sales on price and the intercept of that line, and the correlation coefficient $r$ .

Need a reminder? The key ideaShow

$b_{yx} = \dfrac{S_{xy}}{S_{xx}} = r\dfrac{\sigma_y}{\sigma_x}$ and $b_{xy} = \dfrac{S_{xy}}{S_{yy}} = r\dfrac{\sigma_x}{\sigma_y}$ . The line of $y$ on $x$ is $y - \bar{y} = b_{yx}(x - \bar{x})$ . Both lines pass through $(\bar{x}, \bar{y})$ , and $b_{yx}\,b_{xy} = r^2$ .

The worked solution

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