1. Year 8 Scatter Diagrams Dr J Frost (jfrost@tiffin.kingston.sch.uk) Last modified: 24 th November 2013 Objectives: Understand the purpose of a scatter diagram, spotting correlation in data, and how to draw a line of best fit.

2. They display data involving two variables. For example, we might collect compare students’ test performance in English and Maths. EnglishMaths 4055 6557 4192 6880 9997 7578 5867 8675 6672 90100 3245 What are Scatter Diagrams?

3. They can help us identify if there is any relationship between the two variables. The relationship between two variables is known as correlation. ? How are English and Maths test scores related? If someone’s English test score is higher, their Maths score tends to be higher. We call this relationship: Positive correlation ? ? Schoolboy Error TM : “A higher English score means their Maths score will be higher.” How can they help us interpret data?

4. There’s 3 types you should be able to identify. Type of correlation: Weak positive correlation ?? strengthtype Weak negative correlation ?? Strong positive correlation ?? No correlation ? Different Types of Correlation

5. Line of best fit We can add a line of best fit to the scatter diagram. This allows us to estimate one variable’s value given the other. (I used Excel to generate this trendline.) If a boy gets 50% in his English test, what score might we expect him to get in his Maths test? 65% ?

6. We can add a line of best fit to the scatter diagram. This allows us to estimate one variable’s value given the other. Here’s a more interesting question... Can you come up with an equation that could estimate a Maths Score (y) from an English score (x)? y = 0.55x + 38.5 ? The y-intercept seems to be about 39. We can find the gradient by picking two random points on the line suitably far apart. (0, 39) and (80, 82) Change in y is 43 Change in x is 80 m = = = 0.54 43 80 ΔyΔxΔyΔx Line of Best Fit

7. y-intercept: 17Gradient: -0.18 Equation of line: -0.18x + 17 ?? ? Line of Best Fit

8. (-0.18 x 50) + 17 = 8 y = -0.18x + 17 ? If someone’s age is 50, how many hours would we therefore expect them to be on the internet? Line of Best Fit

9. Calculator Fun! We can actually use our calculator to input data and find a line of best fit. Distance from Kingston (x)0.2km2.5km3.6km0.8km House Price (y)£560,000£470,000£365,000£580,000 Reference: Use the ‘Casio Calculator’ interactive slides for instructions!

10. Age Earnings 0 10 20 30 40 50 60 70 80 90 £80000 £70000 £60000 £50000 £40000 £30000 £20000 £10000 When we use our line of best fit to estimate a value inside the range of our data, this is known as: interpolation When we use our line of best fit to estimate a value outside the range of our data, this is known as: extrapolation ? ? In general, we should be wary of making estimates using values outside the range of our data. Estimating for this age is bad because: The person may have retired. Estimating for this age is bad because: Children don’t have full- time jobs. ? ?

11. The Dangers of Extrapolation