What Correlation Would You Expect Between These Two Variables?

Scatter Diagrams

Question 1

What correlation would you expect between these two variables?

a) Between distance from London and house prices. ______

b) Between cigarette smoked a day and risk of cancer. ______

c) Between favourite colour and annual earnings. ______

d) Between the weight of 24-carot gold bar and its value. ______

Question 2

a) Describe the correlation between age and annual salary.
______

b) Draw a line of best fit.

c) Directly use your line and the chart to estimate what someone earns when they’re 50:
______

d) Similarly, give an estimate for someone’s age if their salary is £40,000.
______

e) Determine the equation of your line of best fit.
______

f) Use your equation to estimate the salary of a 90-year-old. Why is this not a good estimate?
______

Question 3

a) Describe the correlation between distance and archery score.
______

b) Draw a line of best fit.

c) Directly use your line and the chart to estimate an archery score at 55m:
______

d) Similarly, if a score was 90, how far away might someone be from the target?
______

e) Determine the equation of your line of best fit.
______

f) Use your equation to estimate the score at 100m.
______

Scatter Diagrams - Answers

Question 1

What correlation would you expect between these two variables?

a) Between distance from London and house prices. Medium negative correlation.

b) Between cigarettes smoked a day and risk of cancer. Weak positive correlation.

c) Between favourite colour and annual earnings. No correlation.

d) Between the weight of 24-carot gold bar and its value. Strong positive correlation.

Question 2

a) Describe the correlation between age and annual salary.
Weak positive correlation

b) Draw a line of best fit.

c) Directly use your line and the chart to estimate what someone earns when they’re 50:
~£54400

d) Similarly, give an estimate for someone’s age if their salary is £40,000.
~35 years

e) Determine the equation of your line of best fit.
(Courtesy of Excel) y = 978x + 5566

f) Use your equation to estimate the salary of a 90-year-old. Why is this not a good estimate?
£93586. Not a good estimate because (i) the actual relationship between age and salary is not likely to be linear (i.e. we expect salaries to ‘peak’) and (ii) the retirement age is considerably less than 90!

Question 3

a) Describe the correlation between distance and archery score.
Strong negative correlation.

b) Draw a line of best fit.

c) Directly use your line and the chart to estimate an archery score at 55m:
~65.4

d) Similarly, if a score was 90, how far away might someone be from the target?
~14.8m

e) Determine the equation of your line of best fit.
y = -0.6107x + 99.017

f) Use your equation to estimate the score at 100m.
37.9