The girth of a tree is the circumference of the tree trunk measured $1$ metre above the ground. A

Question

The girth of a tree is the circumference of the tree trunk measured $1$ metre above the ground. A random sample of $9$ oak trees in a forest was taken and the age, $x$ years, and the girth, $y$ cm, of each tree was recorded. The data collected is shown in the following table. $x$$20$$23$$30$$38$$39$$45$$48$$55$$71$ $y$$35$$41$$59$$70$$67$$87$$91$$109$$124$ Give a sketch of the scatter diagram for the data, as shown on your calculator.[2] Find the value of the product moment correlation coefficient and comment on its value in the context of the data.[2] Find the equation of the regression line of $y$ on $x$, in the form $y = a + bx$, giving the values of $a$ and $b$ correct to $3$ significant figures. Sketch this line on your scatter diagram.[2] Use the equation of your regression line to calculate an estimate of the girth of a $50$-year-old oak tree, and comment on the reliability of your estimate.[2] Rewrite your equation in (c) so that it can be used to estimate the girth when the age is measured in months.[1]

Accepted Answer

(b)r=0.988 (c)$y=0.954+1.83x$ (d)estimated =92.3 cm (e)$y=0.954+0.152x$

2024 TJC H1 Q10

2024 TJC H1 Q10