4 mistakes learners make with scatter graphs and correlation, each one named and explained.
A scatter graph shows that two things move together, which is not the same as one of them causing the other.
You extend the line well past the last point and read off an answer with full confidence.
The line carries on just as easily off the end of the data as it does across it.
Question. The data covers ages 5 to 11. You use the line to predict for age 30. How reliable is that?
A common answer. just as reliable, the line is the same line
The answer. not reliable. Nothing was measured out there and the pattern may not continue
Why. Reading inside the data is interpolation and is reasonable; going beyond it is extrapolation.
Check where the last point is before you read anything off the line.
You check the biggest and smallest values and report no outliers, missing the point sitting well away from the line.
Outlier has been taught with lists of numbers, where the odd one out really is at one end.
Question. On a scatter graph, where can an outlier be?
A common answer. only at the highest or lowest values
The answer. anywhere that sits far from the pattern of the other points
Why. On a scatter graph it is distance from the trend that makes a point an outlier, not its size.
Look for the point that the line had to ignore, wherever it sits.
Ice cream sales and sunburn rise together, and you write that ice cream causes sunburn.
The two really do move together, and a cause is the first explanation that comes to mind for that.
Question. Ice cream sales and sunburn both rise in the same months. What can you conclude?
A common answer. ice cream causes sunburn
The answer. they are correlated, most likely because hot weather raises both
Why. A third thing affecting both explains the pattern without either causing the other.
Look for a third thing that could move both before claiming a cause.
You start the line at (0, 0) because that is where lines start.
Straight-line graphs in algebra are usually drawn from the origin, and it looks like a natural anchor.
Question. Where should a line of best fit begin?
A common answer. at the origin
The answer. wherever it best follows the points
Why. The line is there to follow the data, and nothing says the data passes through zero.
Draw it through the middle of the points. Ignore the origin unless the points go there.
WAJD spots these patterns in your child's answers and names the one behind their wrong answers, instead of just marking them wrong.