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

1.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.

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

3.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.

4.A scatter graph of the number of ice creams sold at a seaside kiosk in Bournemouth and the number of sunburn cases treated at a nearby pharmacy, recorded on the same 30 days, shows strong positive correlation. Which statement about this correlation is correct?

5.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.

6.A scatter graph shows the number of pages, x, in a chapter and the time, y minutes, a pupil took to read it, for 15 chapters. The line of best fit has equation y = 2x + 3. Use the line of best fit to estimate the time taken to read a chapter of 10 pages.

7.A straight line is drawn on a scatter graph to show the trend of the points. Write down the name given to this line.

8.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.

9.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.

10.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.

11.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.

12.For each of 30 fires in one county, the number of fire engines sent and the cost of the damage were recorded. The scatter graph of the data shows strong positive correlation. A newspaper prints the headline "Sending more fire engines causes more damage". Is the newspaper right? Give a reason for your answer.

13.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.

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

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.