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For a made-up data set of sale prices and ages of second-hand bicycles, the total sum of squares of…

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Try it on paper first. A hint, the key idea and the worked solution are here when you need them.

For a made-up data set of sale prices and ages of second-hand bicycles, the total sum of squares of the prices about their mean is $S_{yy} = 250$ , in units of thousand rupees squared. The least-squares line slopes downwards, and its sum of squared residuals is $40$ . Find $r^2$ and $r$ , to four decimal places.

Need a reminder? The key ideaShow

$r^2 = 1 - \dfrac{\text{SSE}}{S_{yy}}$ is the share of the variation in $y$ that the line accounts for; $r = \pm\sqrt{r^2}$ with the sign of the slope. A residual plot with a pattern (a curve, a fan) shows that a straight line is not the right model.

The worked solution

Have you tried it?

Work it out on paper first. It is fine to get stuck or make a mistake: that is how we learn. When you are ready, go through the solution one step at a time, and check each step against your own.

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