the sum of the residuals is always 0(zero) because its how far they are away from the LSRL. that's what makes them residuals in the first place :P
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When given a set of data where the independent variable is time, it is possible to use statistical techniques to find a line (or curve) of best fit. One of the ways to do this is to minimise the square of the the differences between the actual values which are observed and the values that are predicted by such a curve (fitted values). The slope of this line or of the tangent to the curve at any point, is the least squares trend.A statistical explanation of the theory or the calculations required are too much for the pathetic browser that we are required to use.
It is often called the "Least Squares" line.
No, it is not resistant.It can be pulled toward influential points.
Whenever you are given a series of data points, you make a linear regression by estimating a line that comes as close to running through the points as possible. To maximize the accuracy of this line, it is constructed as a Least Square Regression Line (LSRL for short). The regression is the difference between the actual y value of a data point and the y value predicted by your line, and the LSRL minimizes the sum of all the squares of your regression on the line. A Correlation is a number between -1 and 1 that indicates how well a straight line represents a series of points. A value greater than one means it shows a positive slope; a value less than one, a negative slope. The farther away the correlation is from 0, the less accurately a straight line describes the data.
Least Squares method