Line of Best Fit Question/Opinions

Hey all, quick question (or rather opinion) on line of best fit. Here are the figures from the data table:

http://imgur.com/5y8QU

The answer is, in fact, B; y = 1.1x + 3.8

Well, by hand I took averages of slopes and y-intercepts, and came up with; y = 1.333x + 2.602

Just want your opinions, which line (if you can graph it) do you like better? I graphed both on the TI-84, and mine was pretty much square down the middle between plotted points, whereas the other line passed through the very first point and almost grazed the fourth but was still a ways off.

In any case, it doesn't make any difference. Both would give a fairly good approximation, and it's not graded or tested, I've just never done line of best fit by hand before (I just use regression).

The regression line is specifically designed to minimize the error between the actual values (data points) and the approximation, and hence why it's called a least-squares regression. So even though the equation you derived is very similar to the model, the actual regression model of y ≈ 1.1x + 3.8 is ever-so-slightly better because it reduces the amount of error as much as possible, and is therefore slightly more accurate. Although it doesn't really matter here, if you were using those two possible regression lines to extrapolate the data for a much larger value, say, x = 10000, then the first equation is more likely to predict the data value at that point than yours would.

And since I couldn't fit it in, thank you very much for your response! It was most helpful!

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