الأسبوع 1 · الارتباط: العلاقة الطردية والعكسية بين متغيرين وأشكال الانتشار ومقياس معامل الارتباط r من −1 إلى 1 · 3 دروس
2
Scatter diagrams: plotting pairs (x, y) and reading the type and the strength of the relation from the dots
Statistics Sec 3 Term 1, Unit 1, Lesson 1
GoalPlot pairs (x, y) as dots and read the type and the strength of the relation from the shape of the dots.
New words
scatter diagram · a graph in which each pair (x, y) is one dotordered pair (x, y) · x tells how far to go along, y how far to go uplinear correlation · the dots lie near a straight line
Explanation
A scatter diagram shows every case as one dot. For the pair (x, y) we go x units along the horizontal axis and y units up. When all the dots are drawn, we look at the shape of the cloud. A strip of dots rising from the lower left to the upper right shows a direct correlation; a strip falling from the upper left to the lower right shows an inverse correlation; a shapeless cloud means there is no correlation. The narrower the strip, the stronger the relation, because dots close to one line mean that x predicts y well. When the dots lie near a straight line we call the relation linear. The axes do not have to start at 0: if all the marks lie between 7 and 18, we may start the vertical axis at 4, so that the dots fill the picture. The diagram below shows eight pupils: revision hours (x) and quiz mark out of 20 (y). The strip rises narrowly, so the correlation is direct and strong.
Worked examples
Reading one dot: the dot at (3, 13) is a pupil who revised 3 hours and scored 13. There are two dots above x = 3 (scores 11 and 13) and two above x = 1 (scores 7 and 9): two pupils can share an x-value, so the dots stay separate.
Six towns: altitude x in hundreds of metres, evening temperature y in °C: (1, 27), (2, 30), (4, 23), (5, 25), (7, 19), (9, 20). The dots fall from the upper left to the lower right in a fairly narrow strip: inverse and fairly strong.
Eight pupils: seat number x and quiz mark y: (1, 12), (2, 4), (3, 9), (4, 15), (5, 6), (6, 13), (7, 5), (8, 10). The dots form a cloud that neither rises nor falls: no correlation, as we expected.
Class activity
On squared paper draw the two axes and plot the six pairs (1, 6), (2, 5), (4, 5), (5, 3), (7, 2), (8, 1) for a bicycle’s age in years and its price in thousands of LE. Say the type of correlation, then lay a ruler over the dots and say whether a straight line fits well.
Practice
1
The diagram shows the number of weekly trips (x) of a delivery van against the petrol left in the tank in litres (y). Which type of correlation is it?
Inverse and strong: the dots fall in a narrow strip.
2
Describe the diagram: direct, inverse or none?
None: a cloud without a direction.
3
Where do you draw the dot for the pair (5, 15)?
Go 5 along the horizontal axis (x), then 15 up (y).
4
Why may the vertical axis of a scatter diagram start at 4 and not at 0?
The axis only has to show the values that occur. If all marks are between 7 and 18, starting at 4 uses the whole picture and makes the shape easier to read.
5
Two dot-strips both rise from left to right. Strip A is wide, strip B is narrow. Which correlation is stronger?
B: the narrower the strip, the closer the dots are to a line and the better x predicts y.
