2024 RVHS H1 Q10

Mr Tan wants to determine the correlation between the number of hours, \(x\), a student spent on revision per day and the University Admission Score (UAS), \(y\), obtained by the student for the school’s Preliminary Examination. The data of a random sample of \(9\) students from a particular class taught by him are given in the following table.

1. Give a sketch of the scatter diagram of the data.[2]
2. Find the product moment correlation coefficient and comment on its value in the context of the data.[2]
3. Mr Tan claims that higher number of hours spent on revision per day will result in higher UAS for students. Comment on the validity of his claim.[1]
4. Find the equation of the regression line of \(y\) on \(x\) in the form of \(y=a+bx\), giving the value of \(a\) and \(b\) correct to \(3\) significant figures. Sketch this line on your scatter diagram in part (i).[2]
5. Student \(J\) from the same class missed the school’s Preliminary Examination. He claims that he spent \(8\) hours on revision per day. Mr Tan uses the equation of the regression line found in part (iv) to calculate an estimate for his UAS. Find this estimated value and comment on its reliability.[3]