What is the line of best fit mean in algebra?

Answer 1

The line of best fit is a concept in statistics rather than algebra. Given two variables, X and Y, they can be plotted (a scatter plot). Before going any further, it is good practise to look at the scatter plot and see if the points look like they are approximately in a straight line. If not, a line of best fit is not appropriate: you may need to transform one or both variable.

For each observed value, xi, there will be a value yi where i ranges over all the observations: that is, your data comprises the set of ordered pairs (xi, yi). You can then draw a line over the scatter plot. Many points will not lie on the line but some distance above or below it. If the value on the line. corresponding to xi is yi-fitted, then ei = (yi-fitted - yi) is the error between the fitted and observed values. Then the line of best fit is the one which minimises the sum of (ei)2.

It is not easy to explain this in plain text, and more so when you are handicapped by a rubbish browser. Although the calculations may look daunting, they are not that bad, and there packages which will do away with the drudgery.