State whether each pair of variables would most likely show positive correlation, negative correlation or no correlation. (a) The number of pages printed by a printer and the amount of ink remaining in its cartridge.
(Total for Question 1 is 1 mark)
2
State whether this pair of variables would most likely show positive correlation, negative correlation or no correlation. The number of hours a candle has been burning and the height of the candle remaining.
(Total for Question 2 is 1 mark)
3
State whether this pair of variables would most likely show positive correlation, negative correlation or no correlation. The number of goals a football team scores in a season and the shirt number of their goalkeeper.
(Total for Question 3 is 1 mark)
4
For each statement about correlation, write down True or False. (i) A strong correlation means the points on a scatter graph lie close to a straight line.
(Total for Question 4 is 1 mark)
5
Complete the sentence with the correct word. A sample of 8 towns shows a correlation between the number of umbrella shops and the number of raincoat shops, but neither business causes the other to exist; both are affected by how often it _______ in that area.
(Total for Question 5 is 2 marks)
6
Give the missing word. Just because two variables are correlated, this does not mean that a change in one _______ a change in the other.
(Total for Question 6 is 2 marks)
7
A survey of 9 households finds a strong positive correlation between the number of pets owned and the amount spent on pet food each month. Describe the strength and type of this correlation.
(Total for Question 7 is 2 marks)
8
A study of 10 cars finds a weak negative correlation between the age of the tyres, in months, and the tyre's grip rating out of 10. Describe what this tells you about the relationship between tyre age and grip rating.
(Total for Question 8 is 2 marks)
9
A gardener records the amount of fertiliser used, in grams, and the height of 8 sunflowers, in cm, at the end of the season. The data shows a clear upward trend, with the points lying close to a straight line rising from (10, 40) to (80, 190). Describe the correlation shown by this data.
(Total for Question 9 is 2 marks)
10
For each statement about lines of best fit, write down True or False. (i) A line of best fit is always drawn so it touches every point on the scatter graph. (ii) Estimating a value that lies inside the range of the collected data is called interpolation.
(Total for Question 10 is 2 marks)
11
For each statement about lines of best fit, write down True or False. (i) Estimating a value well beyond the range of the collected data (extrapolation) is generally less reliable than interpolation. (ii) A line of best fit must have a positive gradient.
(Total for Question 11 is 2 marks)
12
A line of best fit for a set of data is y = 4x + 6, where x is the number of hours a heater is used and y is the electricity used, in units. Work out the estimated electricity used when the heater is used for 5 hours.
(Total for Question 12 is 2 marks)
13
A scientist plants 9 identical bean seeds and records the amount of water given each week, in ml, and the height of each plant after one month, in cm. The line of best fit is h = 0.6w + 2, valid for values of w between 20 and 100. (a) Use the line of best fit to estimate the height of a plant given 60 ml of water per week. (b) Explain why using this line to estimate the height for a plant given 250 ml of water per week would not be reliable.
(Total for Question 13 is 3 marks)
14
A researcher collects data from 10 towns and finds a strong positive correlation between the number of coffee shops in a town and the number of dentists in the town. A blogger claims: 'Opening more coffee shops causes more dentists to set up business.' Explain why the blogger's claim is not a valid conclusion, suggesting a more likely explanation for the correlation.
(Total for Question 14 is 3 marks)
15
An airline notices that in months when sales of sun cream are higher, the number of long-haul flight bookings is also higher. Suggest a factor, other than one directly causing the other, that could explain this correlation, and explain how it affects both variables.
(Total for Question 15 is 3 marks)
16
A health website reports that towns with more gyms tend to have lower rates of a certain illness, and concludes that 'building more gyms in a town directly reduces illness rates.' A student disagrees. Explain why the website's conclusion is not fully justified, and suggest one confounding variable that might explain the pattern instead.
(Total for Question 16 is 3 marks)
17
A student investigates the statement: 'Students who spend longer travelling to school tend to arrive with lower energy levels for their first lesson.' She plans to survey 30 students at her school, recording their journey time in minutes and a self-rated energy score out of 10. (a) Give one reason why she should survey students from a range of year groups, rather than only her own form group. (b) The completed scatter graph shows a moderate negative correlation. State what this suggests, and explain why she should not conclude that a longer journey directly causes lower energy, suggesting one other possible factor.
(Total for Question 17 is 4 marks)
18
A council collects data from 12 streets and finds a strong positive correlation between the number of streetlights on a street and the number of evening dog walkers seen there. It also finds a strong positive correlation between the number of evening dog walkers and the number of houses with a dog. Comment on whether this second correlation is more likely to reflect a genuine direct relationship than the first, giving a reason.
(Total for Question 18 is 4 marks)
Mark scheme · F02D Correlation and Causation (Foundation): Fluency and Exam Drill
Question 1
B1 negative correlation cao
Answer: Negative correlation
Question 2
B1 negative correlation cao
Answer: Negative correlation
Question 3
B1 no correlation cao
Answer: No correlation
Question 4
B1 True cao
Answer: True
Question 5
M1 recognises the missing word describes local weather/climate oe
A1 rains cao
Answer: rains
Question 6
M1 identifies the sentence is stating the correlation/causation rule oe
A1 causes oe (e.g. causing)
Answer: causes
Question 7
B1 positive correlation
B1 strong (correlation)
Answer: Strong positive correlation
Question 8
B1 as tyre age increases, grip rating tends to decrease, oe (stated in context)
B1 identifies the relationship as weak, i.e. there is a lot of scatter/it is not a strong pattern oe
Answer: As the tyres get older, their grip rating tends to fall slightly, but the relationship is weak, so there is a lot of variation and the pattern is not strong.
Question 9
B1 positive correlation
B1 strong (correlation), since the points lie close to a straight line
Answer: Strong positive correlation.
Question 10
B1 (i) False cao
B1 (ii) True cao
Answer: (i) False (ii) True
Question 11
B1 (i) True cao
B1 (ii) False cao
Answer: (i) True (ii) False
Question 12
M1 4(5) + 6 oe
A1 26 cao
Answer: 26 units
Question 13
M1 0.6(60) + 2 oe
A1 38 cao
B1 250 ml is well outside the range of data collected (20 to 100 ml), so this would be extrapolation and is unreliable oe
Answer: Estimated height at 60 ml = 38 cm; using the line at 250 ml would not be reliable because 250 ml is far outside the range of data collected (extrapolation).
Question 14
B1 correlation does not prove causation
B1 identifies population/town size as a plausible confounding variable oe
B1 explains that a larger town supports more of both types of business, rather than one causing the other oe
Answer: The correlation does not prove causation. A likely confounding variable is the size of the town's population: a larger town can support more coffee shops and more dentists simply because it has more customers for both, rather than coffee shops causing dentists to open.
Question 15
B1 identifies a plausible common cause, e.g. the summer holiday season oe
B1 explains that this factor increases both variables, e.g. more people go on holiday and buy sun cream during the summer months oe
B1 states that neither variable directly causes the other oe
Answer: The summer holiday season is a likely confounding factor: more people go abroad and buy sun cream during the summer months, so the season affects both variables rather than one causing the other.
Question 16
B1 correlation does not prove causation
B1 suggests a plausible confounding variable, e.g. average household income oe
B1 explains that this variable could affect both the number of gyms and the illness rate, e.g. wealthier towns can afford more gyms and also better healthcare/diet oe
Answer: The website's conclusion is not justified because correlation does not prove causation. Average household income is a plausible confounding variable: wealthier towns can afford more gyms and also tend to have better healthcare and diet, which could lower illness rates without the gyms themselves being the direct cause.
Question 17
B1 surveying a range of year groups makes the sample more representative of the whole school, since her form group may share similar journeys/habits oe
B1 as journey time increases, energy score tends to decrease, oe
B1 correlation does not prove causation
B1 suggests a plausible other factor, e.g. how late the student goes to bed, or how much they eat for breakfast, oe
Answer: Surveying several year groups avoids her own form group's shared habits biasing the sample. Longer journeys are associated with lower energy scores, but correlation does not prove causation; a factor such as how late a student goes to bed, or whether they eat breakfast, could affect energy levels independently of journey time.
Question 18
B1 recognises the streetlights/dog walkers correlation is likely explained by a confounding variable, e.g. safer/busier streets attract both more streetlights and more walkers oe
B1 recognises the dog walkers/houses with a dog correlation is more likely to reflect a genuine direct relationship oe
B1 gives a reason, e.g. a household needing to walk its dog directly explains an evening dog walker being seen there oe
B1 notes that neither correlation on its own proves causation without further investigation oe
Answer: The second correlation (dog walkers and houses with a dog) is more likely to reflect a genuine direct relationship, since owning a dog is a direct reason someone would be seen walking it; the streetlights/dog walkers link is more likely explained by a confounding variable such as how safe or busy a street feels. Neither correlation alone proves causation without further investigation.