IB SL – 2Markscheme
IB Packet – Correlation and Regression
1.(a)
(A1)for correct scales and labels
(A3)for all ten points plotted correctly
(A2)for eight or nine points plotted correctly
(A1)for six or seven points plotted correctly(A4)
Note: Award at most (A0)(A3)if axes reversed.
(b)(i) = 42(A1)
(ii) = 64(A1)
(c)plotted on graph and labelled, M(A1)(ft)(A1)
Note: Award (A1)(ft)for position, (A1)for label.
(d)–0.998(G2)
Note: Award (G1)for correct sign, (G1)for correct absolute value.
(e)line on graph(A1)(ft)(A1)
Notes: Award (A1)(ft)for line through their M, (A1)for approximately correct intercept (allow between 83 and 85). It is not necessary that the line is seen to intersect the y-axis. The line must be straight for any mark to be awarded.
(f)y = –0.470(25) + 83.7(M1)
Note: Award (Ml) for substitution into formula or some indication of method on their graph. y = –0.470(0.25) + 83.7 is incorrect.
= 72.0 (accept 71.95 and 72)(A1)(ft)(G2)
Note: Follow through from graph only if they show working on their graph.
Accept 72 ±0.5.
(g)Yes since 25 % lies within the data set and r is close to –1(R1)(A1)
Note: Accept Yes, since r is close to –1
Note: Do not award (R0)(A1).
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2.(a)
(A1)(A3)
Notes: Award (A1) for scales and labels (accept x/y).
Award (A3) for all points correct.
Award (A2) for 7 or 8 points correct.
Award (A1) for 5 or 6 points correct.
Award at most (A1)(A2) if points are joined up.
If axes are reversed award at most (A0)(A3)(ft).
(b)Negative(A1)
(c)(i)17(G1)
(ii)23(G1)
(d)Point correctly placed and labelled M(A1)(ft)(A1)
Note: Accept an error of ±0.5.
(e)y = –0.708x + 35.0(G1)(G1)
Note: Award at most (G1)(G0) if y = not seen. Accept 35.
(f)Regression line drawn that passes through M and (0, 35)(A1)(ft)(A1)(ft)
Note: Award (A1) for straight line that passes through M, (A1) for line (extrapolated if necessary) that passes through (0, 35) (accept error of ±1).
If ruler not used, award a maximum of (A1)(A0).
(g)y = –0.708(30) + 35.0(M1)
= 14 (Accept13)(A1)(ft)(G2)
OR
Using graph: (M1) for some indication on graph of point, (A1)(ft)(M1)
for answers. Final answer must be consistent with their graph.(A1)(ft)(G2)
Note: The final answer must be an integer.
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3.(a)
(A1)(A2)
Notes: Award (A1) for axes labelled with d and t and correct scale, (A2) for 6 or 7 points correctly plotted, (A1) for 4 or 5 points, (A0) for 3 or less points correctly plotted. Award at most (A1)(A1) if points are joined up.
If axes are reversed award at most (A0)(A2).
(b)(i)= 4(G1)
(ii)(G1)
Note: If answers are the wrong way around award in (i) (G0) and in (ii) (G1)(ft).
(c)Point marked and labelled with M or on their graph(A1)(ft)(A1)(ft)
(d)Line of best fit drawn that passes through their M and (0, 48)(A1)(ft)(A1)(ft)
Notes: Award (A1)(ft) for straight line that passes through their M, (A1) for line (extrapolated if necessary) that passes through (0, 48).
Accept error of ±3. If ruler not used award a maximum of (A1)(ft)(A0).
(e)4.5h (their answer ±0.2)(M1)(A1)(ft)(G2)
Note: Follow through from their graph. If method shown by some indication on graph of point but answer is incorrect, award (M1)(A0).
(f)d= 8.25t+ 48.1(G1)(G1)
Notes: Award (G1) for 8.25, (G1) for 48.1.
Award at most (G1)(G0) if d = (or y = ) is not seen.
Accept d – 81.1 = 8.25(t – 4) or equivalent.
(g)(i)d= 8.25 × 10.3 + 48.1(M1)
d= 133 km(A1)(ft)(G2)
(ii)No(A1)
Outside the set of values of t or equivalent.(R1)
Note: Do not award (A1)(R0).
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4.(a)
(A1)(A1)(A1)
Notes: (A1) for label and scales, (A2) for all
points correct, (A1) for 5 or 6 correct.
Award a maximum of (A2) if points are joined.
(b)r = −0.141(G2)
Note: If negative sign is missing award (G1)(G0).
(c)“The coefficient of correlation is too low, (very) weak
(linear) relationship”.(R1)
Not a sensible thing to do (accept “no”).(A1)
Note: Do not award (R0)(A1)
The correlation coefficient has to be mentioned in
their reasoning.
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5.(a)0.965(A1)(C1)
(b)y= 1.15x+ 0.976
(A1) for1.15x (A1) for+0.976(A1)(A1)(C2)
(c)y= 1.15 (7) + 0.976(M1)
Chemistry = 9.03 (accept9)(A1)(ft) (C2)
Note: Follow through from candidate’s answer to (b) even if no working is seen. Award (A2)(ft).
(d)the correlation coefficient is close to 1
OR strongly correlated variables
OR 7 lies within the range of physics marks.(R1)(C1)
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6.(a)r =
= (M1)
= 0.76(A1)2
(b)There is a fairly strong positive correlation between high school
grades and university grades.(A1) (A1)2
Note: Award (A1) for strong (or fairly strong) or high, (A1) for positive.
(c)y –
y – 3.04 = (x – 83.5)(M1)
y = 0.052x – 1.29 (3 s.f.)(A1)2
Note: Award (C2) for correct answer (from calculator).
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7.(a)For applying r = or any correct formulae.(M1)
For: Sx = 4.0034568… 4(M2)
Sy = 13.992456… 14(M2)
r = 0.6399706… 0.64 (2 d.p.)(A1)6
Note: Follow through with candidate’s Sx + Sy.
Accept solutions that use the unbiased estimates for the population standard deviations.
(b)This indicates that there is a degree of positive correlation between scores in Mathematics and scores in English.(R1)
Note: Follow through using candidate’s v,2
and (v) from table.
Therefore those who do well in Mathematics are likely to do well in English also. (Or equivalent statements.)(R1)2
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8.(a)II(A1)(C1)
(b)V(A1)(C1)
(c)III(A1)(C1)
(d)I(A1)(C1)
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