Edexcel A-Level Mathematics A2 S3.5 Regression and Correlation Questions

Athlete & A & B & C & D & E & F & G & H

Rank SBT & 4 & 2 & 1 & 3 & 5 & 6 & 8 & 7

FP & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8
d^2=9+0+4+1+0+0+1+1[=16]}
r_s=1-6(" 16^")8(63) =0.8095.

awrt 0.81

H_0: =0, H_1: >0}
Critical Value r_s=0.8333 or CR: r_s 0.8333}
Do not reject H_0 or not significant or does not lie in the critical region or there is no
evidence of a positive correlation}
There is no evidence of a positive correlation between season's best time and finishing
position for these athletes

A1ft

Critical value r=0.7887 or critical region r>0.7887.
M1
There is evidence of a positive correlation between season's best time and finishing time for these athletes.
A1 ft

& 200 m & 400 m & d & $d^{2}$

A & 3 & 1 & 2 & 4

B & 2 & 2 & 0 & 0

C & 1 & 4 & -3 & 9

D & 4 & 5 & -1 & 1

E & 7 & 7 & 0 & 0

F & 6 & 6 & 0 & 0

G & 5 & 3 & 2 & 4

$\sum d^{2}=18$$r_{s}=1-\frac{6 \times 18}{7 \times 48}=\frac{19}{28}=$ awrt $\underline{\mathbf{0. 6 7 9}}$

(5)

M1 A1 A1 dM1 A1

$$\mathrm{H}_{0}: \rho=0$$$\mathrm{H}_{1}: \rho>0$

Critical value 0.7143

( 0.679<0.7143 ) so insufficient evidence to reject $\mathrm{H}_{0}$

There is insufficient evidence to suggest a positive correlation between the
finishing order in the 200 metre race and the finishing order in the 400 metre
race.

(4)

B1 B1 M1 A1ft

There are tied lengths so use average ranks

Then use $r_{s}=\frac{\mathrm{S}_{x y}}{\sqrt{\mathrm{~S}_{x x} \mathrm{~S}_{y y}}}$

B1 B1