**Correlation**is a way of describing the way two quantities are related to each other- You may see this referred to as
*linear*correlation - The word linear will not appear in an exam question

- You may see this referred to as
- Correlation can be one of three types
**Positive correlation**- This is where one quantity
**increases**as the other quantity**increases** - Examples

As the temperature increases, the sales of cold drinks increase

As the age of a tree increases, its height increases

- This is where one quantity
**Negative correlation**- This is where one quantity
**decreases**as the other quantity**increases** - Examples

The age of a car and its value

The amount of daylight hours and the time spent indoors

- This is where one quantity
**No correlation**- This is where there is no apparent relationship between the two quantities
- Examples

The batting average of a cricketer and the cost of a pint of milk

The amount of time spent playing computer games and the weight of an elephant

- For
**positive**and**negative**correlation, the strength of the correlation may be described**weak**correlation**strong**correlation- these terms should be self-explanatory!

- Note in some cases, a correlation might not be true all the time
- For example, a tree will reach an age where it is fully grown and it's height no longer increase

- There could also be exceptions to quantities that have correlation
- For example, an old, but rare, sports car may be worth a lot of money

- Correlation only refers to whether two quantities are linked by the way their values increase or decrease
- It does not necessarily mean they are linked in real-life
- One quantity increasing or decreasing does not
the other quantity to increase or decrease**cause** - e.g. the volume of cheese eaten by a population and the number of marriages in that population
- both could be increasing but an increase in the volume of cheese eaten does not
people to get married**cause**

- both could be increasing but an increase in the volume of cheese eaten does not

- One quantity increasing or decreasing does not
- It could be that the two quantities are not linked in real-life but can appear linked due to a third quantity - usually time
- e.g. the height of a sunflower and the weight of a puppy

- the height of a sunflower does not
the weight of a puppy to change!*cause* - but both generally increase with time

- the height of a sunflower does not

- e.g. the height of a sunflower and the weight of a puppy

**Scatter****graphs**are used to quickly see if there is a connection (correlation) between two pieces of data- For example a teacher may want to see if there is a link between grades in mathematics tests and grades in physics tests

- You may also come across scatter plots or scatter diagrams
- these are the same as scatter graphs

- For each data pair, points are plotted
- they are not joined up!
- points are 'scattered' around the diagram

- The general shape the points form indicate the type of correlation they are showing

- This is simply a matter of plotting points - usually from a table of values
- be very careful which way round you are plotting them
- this is particularly important when values are very similar

- If a
**scatter****graph**suggests there is a positive or negative correlation- a
**line of best fit**can be drawn on the scatter graph- this can then be used to predict one data value from the other

e.g. we can use the physics grade for a student to predict their maths grade

- this can then be used to predict one data value from the other

- a

- A
**line of best fit**can be drawn by eye- it does not have to pass through any particular point(s)
- however, in some cases it would make sense that it is drawn through the origin

e.g. the height and weight of a kitten

- however, in some cases it would make sense that it is drawn through the origin
- there should roughly be as many points on one side of the line as the other
- the spaces between the points and the line should roughly be the same on either side

- it does not have to pass through any particular point(s)
- The
*'closeness'*of the plotted points to a line of best fit can be described by the**strength**of the correlation- a
**weak correlation**would have many points with a fair amount of space between =them and the line of best fit - a
**strong correlation**would have many points close, or even on, the line of best fit

- a

- The line of best fit can be used to
**predict**the value of one**variable**from the other**variable**- Predictions should only be made for values that are within the range of the given data
- Making a prediction within the range of the given data is called
**interpolation** - Making a prediction outside of the range of the given data is called
**extrapolation**and is much less reliable - The prediction will be more reliable if the number of data values in the original sample set is bigger

- Watch out for
**outliers**on scatter graphs- these are rogue results or values that do not follow the general pattern of the data/graph
- you should ignore these points when judging where to draw your line of best fit
- you'll usually only see one of these in a question, if any

Sophie is investigating the price of computers to see if the more they cost, the quicker they are.

She tests 8 computers and runs the same program on each, measuring how many seconds each takes to complete the program. Sophie's results are shown in the table below.

Price (£) | 320 | 300 | 400 | 650 | 250 | 380 | 900 | 700 |

Time (secs) | 3.2 | 5.4 | 4.1 | 2.8 | 5.1 | 4.3 | 2.6 | 3.7 |

(a)

Draw a scatter graph to show this information.

Draw the points carefully and accurately as to not miss any out.

(b)

Describe the correlation and explain what this means in terms of the question.

As we are asked to explain what the correlation means in terms of the question we need to mention the connection between cost and speed.

**The graph shows negative correlation****This means that the more a computer costs, the quicker it is at running the program**

** **

(c)

Showing your method clearly, estimate the price of a computer that completes the task in 3.5 seconds.

First draw a line of best fit, by eye.

Draw a horizontal line from 3.5 on the time axis until it hits the line of best fit, then draw a vertical line down to the price axis and take a reading.

**The price of a computer taking 3.5 seconds to run the program should cost around £612**

Due to possible difficulties of reading an exact value a range of answers will be acceptable

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