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Regression lines
By James Furness (P2986) on Saturday, September 30, 2000 - 08:51 pm:

I am having trouble with the following question,
I seem to be going round in circles obtaining the same value for both x and x-bar, also y and y-bar
respectively.

Ques.-Two Variables, x and y, are plotted against each other on a scatter diagram. The regression line of y on x has equation y=2x-3, whilst x on y has equation x=0.4y+3. Find x-bar and y-bar.

Thankyou for your answer.

By Alex Barnard (Agb21) on Sunday, October 1, 2000 - 10:38 pm:

James,

The point here is that regression lines always go through the point (x-bar, y-bar). This is basically because regression lines are chosen to be as close it is possible for a straight line to be to the data and so you'd expect it to hit the averages. Then you sit down and do some calculations to see that you are actually right. So all this question is really asking you to do is to intersect these two lines. The point where the lines intersect will be (x-bar, y-bar).

I'll leave you to do the algebra, but I think the answer is x-bar = 9, y-bar = 15.

AlexB.

By James Furness (P2986) on Wednesday, October 4, 2000 - 07:53 pm:

Thanks very much Alex, it was the intersection at (x-bar,y-bar) which was the clue I was missing.
p.s. your answers are right.