Scatter graphs, correlation and lines of best fit worksheet — GCSE Foundation

1.Write down what a scatter graph is used to show.

2.On a scatter graph of the age of a car, in years, and its value, in pounds, the points fall from left to right. Write down the type of correlation shown.

3.On a scatter graph of the arm span and the height of some pupils, the points rise from left to right. Write down the type of correlation this shows.

4.A scatter graph plots the shoe size and the spelling test score of 25 pupils. The points are scattered with no pattern across the graph. Write down the type of correlation shown.

5.Four pairs of variables are listed below. Write down the pair that you would expect to show no correlation.

6.Write down the statement that correctly describes the difference between correlation and causation.

7.Four pairs of variables are listed below. Write down the pair that you would expect to show negative correlation.

8.A study found that people who drink more coffee tend to concentrate better at work. A coffee company says that this shows that drinking coffee improves concentration. Give the reason why this conclusion cannot be drawn.

9.A café owner in Brighton records the midday temperature, x °C, and the number of hot chocolates sold, y, on 12 days. The temperatures recorded run from 4 °C to 18 °C, and the line of best fit is y = −3x + 74. The forecast for tomorrow gives a midday temperature of 12 °C. Work out the number the line of best fit predicts, and write down how much confidence the owner can have in it.

10.A scatter graph of taxi journeys in Bristol shows the distance, x miles, and the fare, y pounds. The line of best fit is y = 2x + 3.50. Work out the estimated fare for a journey of 6 miles, using the line of best fit.

11.In a scatter graph of the age, in years, and the wingspan, in cm, of 20 birds of the same species, all the points lie close to a rising line of best fit except one, which lies a long way below the line. That bird was later found to have a damaged wing. Give a reason why this point should not be used when drawing the line of best fit.

12.A scatter graph shows the number of years of experience, x, of 18 sales assistants and their monthly sales, y hundred pounds. The plotted points run from x = 1 to x = 12 years, and the line of best fit is y = 4x + 20. A new assistant has 25 years of experience. Use the line of best fit to estimate a value of y for this assistant, and decide whether the estimate would be reliable.

13.A scatter graph of the number of hours, x, that pupils revised against their test score, y, has the line of best fit y = 2.5x + 15. Amelia wants a score of at least 80. Work out the least whole number of hours of revision the line of best fit suggests she needs.

14.A scatter graph shows the number of hours of sunshine, x, and the number of visitors, y, at an outdoor swimming pool in Torquay on each of 15 days. The line of best fit passes through the points (5, 150) and (15, 350). Work out the estimated number of visitors on a day with 8 hours of sunshine, using the line of best fit.

15.A scatter graph shows the number of days, x, that each of 16 tomato plants was watered and its height, y cm. The line of best fit has equation y = 1.5x + 4. Write down what the 1.5 in this equation tells you about the plants.