Mathematics · Oct / Nov 2024 · Paper 61 · Question 2
YMA01
As printed in the paper
The question as text
2. A biologist records the length, y cm, and the weight, w kg, of 50 rabbits. The following summary statistics are calculated from these data. y 2015 y 2 81938 5 . w 125 S 72 25 . S 219 55 . ww yw
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2(a)[3]
S
=
81938.5
−
=
734
*
yy
50
219.55
r =
=
0.95338...
awrt 0.953 M1 A1
(ii)
734 72.25
×
e.g. [In general] the longer the rabbit the greater the weight
Consistent/Yes as r/PMCC is close to 1
219.55
b =
=
0.2991...
734
125
2015
[
]
a
=
−
' '
b
= −
9.554...
50
50
= −
9.55
+
0.299
w
y
' 9.55' '0.299' 45
−
+
×
=
3.905
awrt 3.91 M1 A1ft
Notes
(a)(i)
B1*
Answer is given so a correct numerical expression and no incorrect working seen
S
For use of
yw
May be implied by awrt 0.953
(ii)
M1
×
S
S
yy
ww
A1
awrt 0.953
A correct interpretation ft their r value (provided that
r <
1
) e.g as length/y increases the
(b)
B1ft
weight/w increases Ignore any figures quoted. Do not accept comments about correlation on their
own
A correct statement with a correct reason ft their r value (provided that
r <
1
) Allow 0.953 ≈ 1
(c)
B1ft
Allow ‘my value’ to imply r
(d)
M1
A correct method to find the gradient (May be implied by awrt 0.299 or 4391
14680 )
awrt 0.299 (Condone awrt 0.3 if M1 scored) May be implied by a correct gradient in the
A1
regression line.
M1
A correct method to find the intercept ft their b (May be implied by awrt –9.55)
A1
For
w
=
(awrt)
−
9.55
+
(awrt)0.299
y
Must be seen in part (d)
(e)
M1
For substitution of 45 into their regression equation
For awrt 3.91 or ft their regression line, provided their final answer is > 0. If regression line is
A1ft
not correct, then you will need to check their answer
2(b)[1]
e.g. [In general] the longer the rabbit the greater the weight
2(c)[1]
Consistent/Yes as r/PMCC is close to 1
219.55
2(d)[4]
b =
=
0.2991...
734
125
2015
[
]
a
=
−
' '
b
= −
9.554...
50
50
= −
9.55
+
0.299
w
y
2(e)[2]
' 9.55' '0.299' 45
−
+
×
=
3.905
awrt 3.91 M1 A1ft
Notes
(a)(i)
B1*
Answer is given so a correct numerical expression and no incorrect working seen
S
For use of
yw
May be implied by awrt 0.953
(ii)
M1
×
S
S
yy
ww
A1
awrt 0.953
A correct interpretation ft their r value (provided that
r <
1
) e.g as length/y increases the
(b)
B1ft
weight/w increases Ignore any figures quoted. Do not accept comments about correlation on their
own
A correct statement with a correct reason ft their r value (provided that
r <
1
) Allow 0.953 ≈ 1
(c)
B1ft
Allow ‘my value’ to imply r
(d)
M1
A correct method to find the gradient (May be implied by awrt 0.299 or 4391
14680 )
awrt 0.299 (Condone awrt 0.3 if M1 scored) May be implied by a correct gradient in the
A1
regression line.
M1
A correct method to find the intercept ft their b (May be implied by awrt –9.55)
A1
For
w
=
(awrt)
−
9.55
+
(awrt)0.299
y
Must be seen in part (d)
(e)
M1
For substitution of 45 into their regression equation
For awrt 3.91 or ft their regression line, provided their final answer is > 0. If regression line is
A1ft
not correct, then you will need to check their answer
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