A PE teacher is investigating the relationship between the height and the shoe size of students. The

Question

A PE teacher is investigating the relationship between the height and the shoe size of students. The height, $x$ cm, and the shoe size, $y$, for a random sample of $8$ students are given in the following table. StudentABCDEFGH $x$$150$$155$$160$$165$$170$$175$$180$$190$ $y$$6.5$$7.0$$8.0$$8.0$$9.0$$10.0$$9.5$$11.5$ Give a sketch of the scatter diagram for the data, as shown on your calculator.[2] Find 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 $y = mx + c$, giving the values of $m$ and $c$ correct to $3$ significant figures. Sketch this line on your scatter diagram.[2] Use the equation of your regression line to calculate an estimate for the shoe size of a student of height $171$ cm. State two reasons why you would expect this to be a reliable estimate.[2] The regression line of $y$ on $x$ changes to $y = 0.121x - 11.7$ when data from a new student is added. However, the shoe size data for the new student is missing, and only the height, which is $166$ cm, is available. Find the shoe size of the new student.[3]

Accepted Answer

(b)r=0.977 (c)$y=0.121x-11.6$ (d)estimated y = 9.03,reliable (e)8.03

2024 YIJC H1 Q10

2024 YIJC H1 Q10