14/11/2018 CORRELATION

14/11/2018 Correlation Correlation tells us about the relationship between two variables It can be… positive (going up ↗, so as one increases the other increases) negative (going down ↘, so as one increases the other decreases) no correlation (no direction) It can also be… strong (points nearly on a straight line) weak (points have a clear direction but not nearly on a straight line)

14/11/2018 Example What does this scatter graph show about the relationship between the height and weight of twenty Year 10 boys? 40 45 50 55 60 140 150 160 170 180 190 Height (cm) Weight (kg) As height increases, weight increases. This is called a strong positive correlation.

What does this scatter graph show? 14/11/2018 Example What does this scatter graph show? 50 55 60 65 70 75 80 85 20 40 100 120 Number of cigarettes smoked in a week Life expectancy It shows that life expectancy decreases as the number of cigarettes smoked increases. This is called a weak negative correlation.

14/11/2018 Task Decide whether each of the following graphs shows, strong positive correlation strong negative correlation zero correlation weak positive correlation weak negative correlation

Petrol consumption (mpg) 14/11/2018 Task – State the type of correlation for each graph. Extension – Write a sentence to describe the relationship for each one 1 Positive 2 Negative 3 None Physics test scores Petrol consumption (mpg) Height Maths test scores Car engine size (cc) KS 3 Results There is no relationship between KS 3 results and the height of students. People with higher maths scores tend to get higher physics scores. As the engine size of cars increase, they use more petrol. (Less mpg) People tend to buy more sun cream when the weather is sunnier. The older the car the less its value. As the outside air temperature increases, heating bills will be lower. 4 Sales of Sun cream 5 6 Negative Positive Negative Heating bill (£) Value of car (£) Outside air temperature Daily hours of sunshine Age of car (years)

PLOTTING SCATTER GRAPHS 14/11/2018 PLOTTING SCATTER GRAPHS

14/11/2018 Spot the errors! What is wrong with each of these sets of axes?

14/11/2018 Examples – Fill this in on your sheet as we go through it. Then try the second one yourself… 4 5 6 7 8 9 10 11 12 13 Shoe Size 60 65 70 75 80 85 90 95 100 Mass (kg) 74 88 76 78 92 68 97 Mass Size

14/11/2018 USING SCATTER GRAPHS

14/11/2018 Line of best fit Is a straight line which is supposed to be a good representation of the pattern / trend of the data Method Try to get roughly the same amount of points above the line as below Experiment by using your ruler as your line, and only draw the line in when you are happy Your line does NOT have to start at the origin (0, 0)

14/11/2018 Complete the worksheet for plotting scatter graphs and drawing lines of best fit.

14/11/2018 Estimating using the line of best fit Question 1: If 7 pupils forget to hand in their homework, how many minutes of yoga might Mr Barton do? Question 2: If Mr Barton does 28 minutes of yoga, how many pupils might have forgotten their homework? Following the green line up and across gives… 16 minutes Following the purple line across and down… 14.5 pupils

14/11/2018 Solutions 1)

14/11/2018 Solutions 2)