2013 RI P2 Q9
The data below shows the average height, measured in feet, of cherry trees from age $1$ year to age $11$ years.
(i)
Calculate $r$, the value of the product moment correlation coefficient between $x$ and $y$. State, with a reason, whether the value of $r$ would be different if the average height is measured in meters instead.
[2]
(ii)
Give a sketch of the scatter diagram for the data.
[1]
(iii)
It is desired to predict the average height of cheery trees beyond age $11$ years. Explain why neither a linear nor a quadratic model is likely to be appropriate.
[2]
It is suggested that the average height $y$ can be modelled by the formula $y=a+b\ln x$.
(iv)
Find the equation of the regression line for the suggested model, and the product moment correlation coefficient between $\ln x$ and $y$. Estimate the average height of cherry trees age $5.5$ years, and comment on the reliability of your answer.
[4]
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