Posted by kamilla on Monday, October 26, 2009 at 5:07pm.
OK, so you've plotted your points.
The linear model assumption is that a straight line will go through them. It won't, of course, because they're not perfectly in a line, but the idea is to create a line that comes as close as possible to them, usually with the idea of predicting future numbers from it.
Having plotted your points, you can see that a straight line directly between the first point and the last is not a fit, but it is something like a fit. 1996 messes it up, but the other years aren't too far off. That, then, is one possible linear model. There are others, but this one is simple, so let's follow it for a minute.
We are essentially creating a standard straight line y = mx + c (or Profit = m * Year + c in this case) from the points (1994, 250000) and (1998, 310000). Or, what might make a little more sense, depending, subtract 1994 from the year before starting, so that you're plotting (0, 250000) through (4, 310000). Any of these would be a linear model. Wikipedia has more than you'll ever want to know about this on its Linear_regression page.
Anyway, as one possible approach, let's model (0, 250000) through (4, 310000).
We want y=mx+c
y = (60000/4)x + 250000
Translating it into your graph, we get:
P = 15000(Y-1994) + 250000
which gves us, as we expect, 250000 in 1994 and 310000 in 1998. You can calculate the predicted P for the points inbetween to see that it is sane for the other years, and you should see that those numbers are where the straight line would pass through on your graph.
This is not the best fit line for this graph, and in general, joining up the start and end points probably won't be the best fit, but it's a first estimate, and I figure if your course required one of the specific methods for linear regression, they'd have said so.
Now, for number 2, I think the question must intend: "Use your linear model to
estimate the profit in 2002."
So we have, in Y = 2002,
P = 15000(Y-1994) + 250000
P = 15000(2002-1994) + 250000
P = 120000 + 250000 = 370000.
I'm conscious, writing this, that it's a very simplistic answer. If you need more depth - and boy, there's a lot of material on linear regression! - do ask again.