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

1.A scatter graph shows the number of guests, x, at a wedding and the length of buffet table needed, y metres. The line of best fit is y = 0.5x + 2. Write down what the 2 in this equation tells you about the buffet table.

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

3.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.

4.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.

5.A scatter graph shows the midday temperature, x °C, and the number of ice creams sold at a seaside kiosk, y. The line of best fit is y = 3x − 20. Give a reason why the y-intercept of this line of best fit is not a sensible estimate of the number of ice creams sold.

6.A scatter graph shows the height, x cm, and the mass, y kg, of 20 pupils in Year 10. The heights on the graph run from 150 cm to 180 cm, and the line of best fit is y = 0.9x − 85. Nadia puts x = 90 into this equation to estimate the mass of a two-year-old child who is 90 cm tall. Is her estimate reliable? Give a reason for your answer.

7.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.

8.A scatter graph has 50 points. Most of them lie close to a rising line of best fit, but two of them lie a long way from that line. Write down how those two points should be treated.

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

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

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

12.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.

13.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.

14.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.

15.A gym in Cardiff has a scatter graph of the number of training sessions, x, attended by each member and the weight lost, y kg. The line of best fit is y = 0.4x + 1. Members want to lose at least 9 kg. Using the line of best fit, work out the least whole number of sessions needed to reach this target.