linguistic:paraphrasing, information:filtering
Expanded formulas

The above equations are efficient to use if the mean of the x and y variables (x ¯ and y ¯ {\displaystyle {\bar {x}}{\text{ and }}{\bar {y}}}) are known. If the means are not known at the time of calculation, it may be more efficient to use the expanded version of the α ^ and β ^ {\displaystyle {\widehat {\alpha }}{\text{ and }}{\widehat {\beta }}} equations. These expanded equations may be derived from the more general polynomial regression equations by defining the regression polynomial to be of order 1, as follows.