AS June 2018 Q1

EdexcelAS paperCurrent spec11 marksCorrelationLinear Regression

1. The scores achieved on a maths test, \(m\), and the scores achieved on a physics test, \(p\), by 16 students are summarised below.

\[\sum m = 392 \qquad \sum p = 254 \qquad \sum p^2 = 4748 \qquad \mathrm{S}_{mm} = 1846 \qquad \mathrm{S}_{mp} = 1115\]
(a) Find the product moment correlation coefficient between \(m\) and \(p\) (2)
(b) Find the equation of the linear regression line of \(p\) on \(m\) (3)

Figure 1 shows a plot of the residuals.

Figure 1: residual (from –6 to 6) against maths test score (from 0 to 40) for 16 students; the point at maths score 20 has residual about –5.1, the others lie between about –1.2 and 2
Figure 1
(c) Calculate the residual sum of squares (RSS). (2)

For the person who scored 30 marks on the maths test,

(d) find the score on the physics test. (2)

The data for the person who scored 20 on the maths test is removed from the data set.

(e) Suggest a reason why. (1)

The product moment correlation coefficient between \(m\) and \(p\) is now recalculated for the remaining 15 students.

(f) Without carrying out any further calculations, suggest how you would expect this recalculated value to compare with your answer to part (a).
Give a reason for your answer. (1)
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