Correlation, Regression and Time Series

Spotting patterns in data

A great deal of statistics is about spotting patterns and being careful with them. This topic looks at two kinds. The first is the relationship between two things, shown on a scatter graph: do they rise together, does one fall as the other rises, or is there no link at all? A line of best fit drawn through the points lets you make predictions, though you must be careful how far you trust it. The second is how a single measurement changes over time, such as sales month by month. Here a moving average smooths out the bumps so you can see the underlying direction, and you learn to separate a genuine long-term movement from the regular ups and downs of the seasons. Throughout, one warning runs like a thread: two things moving together is not proof that one causes the other. This module works through each idea and its careful use.

Correlation and time series words

Learn these terms before the ideas are matched up. They name the ideas used in this topic.

Match each idea to what it means

A link against a cause

The single most important habit in this topic is to tell a link between two things apart from one thing causing another.

What does this link really show?

Ice cream sales and cases of sunburn both rise at the same times of year. What does this link most likely show?

• A third factor such as hot weather affects both
• Eating ice cream causes sunburn
• Sunburn makes people buy ice cream
• The two things are completely unconnected

Smoothing out the bumps

When a measurement is taken over time, such as a shop takings each week, the raw figures often jump about so much that the real story is hard to see. A moving average is the tool that fixes this. Instead of looking at each single figure, you take a small group of them in a row, find their mean, then slide the group along one step and do it again. The string of means you get is far smoother than the raw data, because the highs and lows partly cancel out, and it lets the underlying direction show through clearly. This is especially useful when a measurement rises and falls in a regular yearly pattern, because the smoothing evens out those repeating swings. A moving average does not change the data; it simply helps you see the wood for the trees.

Pick the true facts about scatter graphs

Select every statement about correlation and scatter graphs that is true.

• Positive correlation means both rise together
• A line of best fit helps you make predictions
• A link does not prove one thing causes the other
• A link always proves cause
• A line of best fit must touch every point

Order how to use a scatter graph

Put the steps of using a scatter graph to make a prediction into a sensible order.

• Plot the pairs of values as points
• Look at the pattern the points make
• Draw a line of best fit
• Use the line to read off a prediction
• Judge how far the prediction can be trusted

Complete the correlation facts

When two things tend to rise together, a scatter graph shows positive _____. Using the line of best fit to make predictions is also known as _____. Reading a prediction from beyond the range of the data, which is risky, is called _____. The general direction a set of data moves in over time is called the _____.

Tap the two kinds of correlation

Read these four statistical terms. Tap the TWO that are kinds of correlation.

• positive correlation
• negative correlation
• the median
• a pie chart

A path through scattered stones

Picture a garden path laid as a scatter of stepping stones, none of them quite in a straight line. If someone asked you to lay a smooth ribbon of gravel that best followed the stones, you would not zigzag from stone to stone. You would lay a single steady line down the middle, close to most of the stones even though it touched few of them, following the overall direction they took. That gravel line is exactly a line of best fit. It does not have to pass through every point, and it should not try to; its job is to capture the general direction so that you can guess where the next stone would sit. And just as you would be far more confident guessing a stone within the laid path than one far off its end, a prediction made within your data is safer than one stretched well beyond it.

Work out the moving average

A shop sells 10, 12, 14 and 16 items on four days. Work out the four-point moving average by adding the four values and dividing by four. Give the number only.

Read the data

Read each situation and choose the best answer.

• On a scatter graph, as one value rises the other clearly falls. What does this show?
• A dataset stops at age eighteen, but you are asked to predict a value at age sixty. What is the risk?
• Weekly sales jump about wildly, but you want to see the underlying direction. What helps?

Build a statistics point

Choose the word for each gap to complete one point about this topic.

Explain correlation and time series

A friend is revising this topic. Using what you have learned, explain the main ideas and their careful use.

• Explain what positive and negative correlation mean
• Explain what a line of best fit is used for
• Explain the difference between interpolation and extrapolation
• Explain why a link between two things is not proof of cause
• Explain how a moving average helps with a time series