Regression and correlation

Sample questions

Original practice questions written in the style of the exam.

1. Question 16 marks

   Two judges, P and Q, rank 8 contestants in a debating competition:

   Contestant	1	2	3	4	5	6	7	8
   Judge P	1	2	3	4	5	6	7	8
   Judge Q	3	1	4	2	7	5	8	6

   (a) Calculate Spearman's rank correlation coefficient between the two judges' rankings.

   (b) Test, at the 5% level of significance, whether there is positive agreement between the judges. The critical value for a one-tailed test with $n = 8$ at the 5% level is $0.6429$.

   Mark scheme

   • M1 Finds differences $d$ and $d^2$: $4, 1, 1, 4, 4, 1, 1, 4$ (1)
   • A1 $\sum d^2 = 20$ (1)
   • M1 $r_s = 1 - \dfrac{6 \times 20}{8 \times 63}$ (1)
   • A1 $r_s = 0.762$ (3 s.f.) (1)
   • B1 $H_0: \rho = 0$, $H_1: \rho > 0$ (1)
   • A1 $0.762 > 0.6429$, so reject $H_0$: there is evidence of positive agreement between the judges (1)