2013 IJC P2 Q9
John is training for National Shooting Championship and he practices shooting each week. His percentage score, $y\%$ in week $x$, are as follows.
(i)
Draw a scatter diagram to illustrate the data.
[2]
(ii)
Calculate the value of the product moment correlation coefficient, and explain why its value does not necessarily mean that a linear model is an appropriate model for the relationship between $x$ and $y$.
[2]
It is decided to fit a model of the form $\text{ln}\left( 95-y \right)=a+bx$.
(iii)
Find, correct to $4$ decimal places, the value of the product moment correlation coefficient between $\text{ln}\left( 95-y \right)$ and $x$ and comment on its value.
[2]
(iv)
Calculate the values of $a$ and $b$ correct to $4$ decimal places. Use them to predict, to the nearest whole number, the percentage score John will obtain for week $8$. Comment on the reliability of the estimate.
[4]
(v)
Give an interpretation, in context, of the value $95$ in the model $\text{ln}\left( 95-y \right)=a+bx$.
[1]
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