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Question 158992: I am having a problem understanding regression lines. One of my study questions is "use the equation of the regression line to predict y when x=20"
I am given a multiple choice answers of: 45.5, 50, 40 or 48.5.
Can somebody explain this to me?
Answer by gonzo(654)   (Show Source):
You can put this solution on YOUR website! a regression line is a line that expresses the average increase in the data in a linear fashion.
if you don't have one, then you need to create one.
if your problem states to use the equation of the regression line to predict y when x = 20 than i'm assuming you already have the equation.
if you don't already have the equation, then you must have some data points from which you can create the regression line.
an example would be as follows:
suppose you have x,y data points as shown below:
x,y
1,0
2,5
3,10
4,15
an equation of the regression line could be y = 5*x - 5
if x = 1, y = 5*1-5 = 5-5 = 0
if x = 2, y = 5*2-5 = 10-5 = 5
if x = 3, y = 5*3-5 = 15-5 = 10
etc........
your problems states to use the regression line to predict y when x = 20.
in the equation i provided for example above which states that y = 5*x-5, this would equate to y = (5*20)-5 which would equate to y = 50-5 = 45.
any resemblance to one of your answers is purely coincidental.
you need to use the equation you are given or the one you may have been asked to create.
please also take into account that in my example, the actual points of data all fall on the line.
in real life, the actual points of data will probably be somewhere in the vicinity of the line, but not actually on it since perfect alignment with the regression line is not usually encountered.
to give you an example of that, i will change the data but leave the equation the same.
the new data would be
x,y
1,3
2,4
3,7
4,18
now, if you use the equation y = 5*x-5 and plot for x = 3, you will get y = 5*3-5 = 10, but the actual point is 7.
this is ok because in real life, the actual data will be scattered around the regression line.
less scatter means a better fit of the regression line to the data.
more scatter with widely dispersed points means not so good a fit of the regression line to the data.
good luck.
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