Trend Estimation - Goodness of Fit (R-squared) and Trend

Goodness of Fit (R-squared) and Trend

The least-squares fitting process produces a value – r-squared (r2) – which is the square of the residuals of the data after the fit. 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); statistical significance of the trend is determined by its t-statistic. Often, filtering a series increases r2 while making little difference to the fitted trend.