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A made-up clinic records the mean height of children at ages 2 to 8 years: 86, 95, 102, 109, 115…

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

A made-up clinic records the mean height of children at ages $2$ to $8$ years: $86$ , $95$ , $102$ , $109$ , $115$ , $121$ and $127$ cm. Find the least-squares line of height on age, with $b = \dfrac{S_{xy}}{S_{xx}}$ . Use it to predict the height at $6.5$ years and at $30$ years. Give answers to two decimal places. Which prediction should you trust, and why?

Need a reminder? The key ideaShow

The least-squares line $\hat{y} = a + bx$ has

\displaystyle b = r\,\dfrac{s_y}{s_x} = \dfrac{S_{xy}}{S_{xx}}, \qquad a = \bar{y} - b\bar{x}.

The slope is the change in $\hat{y}$ for each extra unit of $x$ . Predict inside the range of the data.

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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