Linear trend estimation

Statistical technique to aid interpretation of data Linear trend estimation is a statistical technique used to analyze data patterns. Data patterns, or trends, occur when the information gathered tends to increase or decrease over time or is influenced by changes in an external factor. Linear trend estimation essentially creates a straight line on a graph of data that models the general direction that the data is heading. Fitting a trend: Least-squares Given a set of data, there are a variety of functions that can be chosen to fit the data. The simplest function is a straight line with the dependent variable (typically the measured data) on the vertical axis and the independent variable (often time) on the horizontal axis. The least-squares fit is a common method to fit a straight line through the data. This method minimizes the sum of the squared errors in the data series y {\displaystyle y} . Given a set of points in time t {\displaystyle t} and data values y t {\displaystyle y_{t}} observed for those points in time, values of a ^ {\displaystyle {\hat {a}}} and b ^ {\displaystyle {\hat {b}}} are chosen to minimize the sum of squared errors ∑ t [ y t − ( a ^ t + b ^ ) ] 2 {\di