IB Maths AI SL AI 4.2 Correlation and regression questions

Exam-style questions in the shape of Paper 1 and Paper 2, with full markschemes. Read the markscheme, or type, photograph or draw your answer and get it marked.

Paper

Paper 1 Paper 2

Difficulty

Easy Medium Hard

Question 1

Paper 2Easy6 marks

A technician records the volume of water in a container as it is filled. Let $t$ be the time, in minutes, after filling begins, and let $V$ be the volume of water, in litres.

$t$	0	2	4	6	8	10	12	14
$V$	10	17	27	30	44	46	60	64

(a)

Use a GDC to calculate Pearson’s product-moment correlation coefficient, $r$ to three significant figures. Describe the direction and strength of the linear correlation.

[2]

(b)

Use a GDC to find the equation of the regression line of $V$ on $t$ giving its coefficients to four significant figures.

[1]

(c)

Use your regression line to estimate the volume of water after 9 minutes. Give your answer in litres to three significant figures.

[1]

(d)

Interpret the gradient and the vertical intercept of the regression line in this context.

[2]

Question 2

Paper 1Easy7 marks

A fieldworker records the distance of seven sample plots from a road and the number of native plant species found in each plot.

Distance from road (m)	5	10	20	35	50	75	100
Number of native plant species	2	6	8	11	12	14	13

(a)

Use a graphic display calculator to find Spearman’s rank correlation coefficient, $r_s$ for these data. Give your answer to three significant figures.

[2]

(b)

Interpret your value of $r_s$ in the context of the fieldwork.

[1]

(c)

The scatter plot suggests an overall increasing, curved relationship between distance from the road and the number of native plant species. State which coefficient, Pearson’s product moment correlation coefficient or Spearman’s rank correlation coefficient, is more appropriate for describing this relationship. Give a reason.

[2]

(d)

If one additional observation is an extreme value, explain how Pearson’s product moment correlation coefficient and Spearman’s rank correlation coefficient are likely to differ in their sensitivity to it.

[2]

Question 3

Paper 1Easy5 marks

A fieldwork study records the daily hours of sunlight and the height of a plant in six plots.

Plot	A	B	C	D	E	F
Daily sunlight (hours)	2	4	6	8	10	12
Plant height (cm)	4	9	13	18	22	7

(a)

Use a graphic display calculator to find Spearman’s rank correlation coefficient, $r_s$ for these data. Give your answer to three significant figures.

[2]

(b)

State the direction of the association indicated by $r_s$

[1]

(c)

If the researchers want to assess a linear relationship, rather than a monotonic relationship in general, name the more appropriate coefficient: Pearson’s product-moment correlation coefficient or Spearman’s rank correlation coefficient.

[1]

(d)

Plot F appears to be an outlier. State which of these two coefficients is generally less sensitive to an outlier.

[1]

Question 4

Paper 2Hard16 marks

An environmental science team records water clarity and aquatic plant cover at eight ponds in one catchment. The team wants to investigate the association between these variables.

Pond	Water clarity (cm)	Aquatic plant cover (%)
A	10	12
B	20	18
C	30	25
D	30	31
E	40	39
F	50	45
G	60	52
H	200	10

Field notes state that pond H was recently dredged. Measurements at H were repeated and agreed.

(a)

Show that ponds C and D are each assigned a clarity rank of 3.5 when the clarity values are ranked from smallest to largest.

[2]

(b)

Using all eight ponds and your GDC, determine Pearson’s product moment correlation coefficient, $r$ and Spearman’s rank correlation coefficient, $r_s$ Give both coefficients to three significant figures.

[4]

(c)

Calculate $r$ and $r_s$ again, using the seven ponds other than H. Give both coefficients to three significant figures.

[4]

(d)

A researcher claims that the full-data Pearson coefficient proves there is no association between clarity and plant cover. The researcher also claims that H should be removed as an outlier and that the Pearson coefficient for the remaining ponds should be reported as the relationship.

Discuss these claims and recommend how the results should be reported. Refer to the coefficients and the field notes.

[6]

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