Graph & Formulas to View Variable Relationships
A simple way that researchers often write variables out mathematically is:
y = a0 + a1x
It’s much simpler than writing out:
Depression = a0 + a1Bullying
Let’s say kid A reported depression at a level of 3.5 and bullying at a level of 2.5, his score can be plotted onto the x-y graph here.
We do this for all kids, and we get quite a few dots on our graph.
If we were to draw a line that was as close to as many of the dots as we could possible get, it could look like the graph here.
If we were to extend this line backwards to hit the y-axis (i.e. when y = 0), this is the value a0.
How steep the slope of this line is can be calculated, and this is the value a1.
y = a0 + a1x
It’s much simpler than writing out:
Depression = a0 + a1Bullying
Let’s say kid A reported depression at a level of 3.5 and bullying at a level of 2.5, his score can be plotted onto the x-y graph here.
We do this for all kids, and we get quite a few dots on our graph.
If we were to draw a line that was as close to as many of the dots as we could possible get, it could look like the graph here.
If we were to extend this line backwards to hit the y-axis (i.e. when y = 0), this is the value a0.
How steep the slope of this line is can be calculated, and this is the value a1.
Scatterplots and using Excel
Some advanced learning on how you could use Microsoft Excel to create some cool scatterplots.
Click on image to view Video
Click on image to view Video
Maths helps us visualize relationships
Why would such a plot and such a mathematical formula be useful to us?
The plot helps us see visually the relationship between depression and bullying.
The mathematical formula helps us make predictions for values of depression that aren’t represented in the sample. The formula is also useful in many other statistical ways of understanding the relationship between variables of interest.
The plot helps us see visually the relationship between depression and bullying.
The mathematical formula helps us make predictions for values of depression that aren’t represented in the sample. The formula is also useful in many other statistical ways of understanding the relationship between variables of interest.