Editing Linear trend estimation (section)

==Goodness of fit (''r''-squared) and trend==
[[Image:Random-data-plus-trend-r2.png|thumb|right|Illustration of the effect of filtering on ''r''<sup>2</sup>. Black&nbsp;=&nbsp;unfiltered data; red&nbsp;=&nbsp;data averaged every 10 points; blue&nbsp;=&nbsp;data averaged every 100 points. All have the same trend, but more filtering leads to higher ''r''<sup>2</sup> of fitted trend line.]]

The least-squares fitting process produces a value, [[Coefficient of determination|r-squared]] (''r''<sup>2</sup>), which is 1 minus the ratio of the variance of the [[Errors and residuals|residuals]] to the variance of the dependent variable. It says what fraction of the variance of the data is explained by the fitted trend line. It does '''not''' relate to the [[statistical significance]] of the trend line (see graph); the statistical significance of the trend is determined by its [[t-statistic]]. Often, filtering a series increases ''r''<sup>2</sup> while making little difference to the fitted trend.