Mathematics · Oct / Nov 2023 · Paper 61 · Question 6
YMA01
As printed in the paper
The question as text
6. The variables x and y have the following regression equations based on the same 12 observations. Regression equation y on x y = 1.4x + 1.5 x on y x = 1.2 + 0.2y
Read automatically from the paper; the printed page above is exact.
Show the answer and mark scheme
6(a)[4]
x
=
1.2
+
0.2 1.4
x
+
1.5
o.e or
y
=
+
y
+
o.e
25
53
x
=
y
=
12
12
25
[
]
(ii)
=
×
12
=
25
x
12
53
y
=
'
' 12
×
=
53
12
(
)
25 '53'
×
6961
=
−
=
5.6
S
xy
60
12
'5.6'
'5.6'
and '5.6'
S
S
0.2
=
1.4
=
xy
=
1.4 and
xy
=
0.2
'5.6'
'5.6'
S
S
×
S
S
xx
yy
1.4
0.2
xx
yy
5.6
=
4
and
=
28
5.6
S
S
r =
2
1.4 0.2
×
xx
yy
1.4 0.2
×
'5.6'
r =
=
0.5291...
1.4 0.2
×
=
0.5291
'4' '28'
×
awrt 0.529
Notes
For either of the two equations o.e or an attempt to solve the two equations simultaneously.
25
53
(a)(i)
M1
/ 2.08 or better or
/ 4.42 or better
May be implied by
x
=
y
=
12
12
25
53
For either
x
=
/ 2.08 or better or
y
=
/ 4.42 or better
A1
12
12
25
53
For both
x
=
/ 2.08 or better and
y
=
/ 4.42 or better
(May be written as a coordinate)
A1
12
12
NB This is M1 on EPEN
For 25
(
12 ×
12
14.4
0.2 1.4
18
Allow use of
x
rather than x e.g.
x
=
+
x
+
(ii)
A1*
As the answer is given no incorrect working must be seen. NB Working must be shown
53
×
'
' 12
ft their y coordinate.
For
12
(b)
M1
(
)
Allow use of
y
rather than y e.g.
y
=
1.4 14.4
+
0.2
y
+
18
oe
y =
53
A1ft
For
or ft their y coordinate × 12 (An answer of exactly 5.6 implies M1A1)
6961
25 '
×
'
y
M1
Use of
=
−
ft their
y
If
y
is not stated then M0 is awarded
S
xy
60
12
5.6 (Allow awrt 5.6)
A1
For use of the gradient to find
S
and
S
ft their
S
or use of
S
xy
xx
yy
xy
S
S
xy
×
xy
(c)
1.4
0.2
M1
S
S
or setting both
xy
and
xy
equal to their respective gradients
S
S
xx
yy
or (
)
2
S
S
=
4
and
=
28
or
xy
xy
=
1.4 0.2
×
S
S
A1
xx
yy
S
×
S
S
xy
xx
yy
1.4 0.2
×
For a correct expression for r ft their
S
,
S
and
S
or 1.4 0.2
×
If answer is incorrect then
xy
xx
yy
M1
you must see their stated values substituted into a correct expression for r. An answer of
implies M1A1M1 only
dA1
Dependant on all previous marks being awarded. awrt 0.529
Pearson Education Limited. Registered company number 872828
with its registered office at 80 Strand, London, WC2R 0RL, United Kingdom
6(b)[4]
y
=
'
' 12
×
=
53
12
(
)
25 '53'
×
6961
=
−
=
5.6
S
xy
60
12
'5.6'
'5.6'
and '5.6'
S
S
0.2
6(c)[4]
=
1.4
=
xy
=
1.4 and
xy
=
0.2
'5.6'
'5.6'
S
S
×
S
S
xx
yy
1.4
0.2
xx
yy
5.6
=
4
and
=
28
5.6
S
S
r =
2
1.4 0.2
×
xx
yy
1.4 0.2
×
'5.6'
r =
=
0.5291...
1.4 0.2
×
=
0.5291
'4' '28'
×
awrt 0.529
Notes
For either of the two equations o.e or an attempt to solve the two equations simultaneously.
25
53
(a)(i)
M1
/ 2.08 or better or
/ 4.42 or better
May be implied by
x
=
y
=
12
12
25
53
For either
x
=
/ 2.08 or better or
y
=
/ 4.42 or better
A1
12
12
25
53
For both
x
=
/ 2.08 or better and
y
=
/ 4.42 or better
(May be written as a coordinate)
A1
12
12
NB This is M1 on EPEN
For 25
(
12 ×
12
14.4
0.2 1.4
18
Allow use of
x
rather than x e.g.
x
=
+
x
+
(ii)
A1*
As the answer is given no incorrect working must be seen. NB Working must be shown
53
×
'
' 12
ft their y coordinate.
For
12
(b)
M1
(
)
Allow use of
y
rather than y e.g.
y
=
1.4 14.4
+
0.2
y
+
18
oe
y =
53
A1ft
For
or ft their y coordinate × 12 (An answer of exactly 5.6 implies M1A1)
6961
25 '
×
'
y
M1
Use of
=
−
ft their
y
If
y
is not stated then M0 is awarded
S
xy
60
12
5.6 (Allow awrt 5.6)
A1
For use of the gradient to find
S
and
S
ft their
S
or use of
S
xy
xx
yy
xy
S
S
xy
×
xy
(c)
1.4
0.2
M1
S
S
or setting both
xy
and
xy
equal to their respective gradients
S
S
xx
yy
or (
)
2
S
S
=
4
and
=
28
or
xy
xy
=
1.4 0.2
×
S
S
A1
xx
yy
S
×
S
S
xy
xx
yy
1.4 0.2
×
For a correct expression for r ft their
S
,
S
and
S
or 1.4 0.2
×
If answer is incorrect then
xy
xx
yy
M1
you must see their stated values substituted into a correct expression for r. An answer of
implies M1A1M1 only
dA1
Dependant on all previous marks being awarded. awrt 0.529
Pearson Education Limited. Registered company number 872828
with its registered office at 80 Strand, London, WC2R 0RL, United Kingdom
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