Simple Linear Regression - Regression Through the Origin

$In\; some\; situations\; prior\; knowledge\; of\; the\; relationship\; between\; Y\; and\; X\; may\; suggest\; that\; b$₀ is exactly zero. For the equation

Y = c₁ X

the least squares estimate of c₁ (c is used rather than b to emphasize a different equation) is

An estimate of the variability of the data about the regression line is given by

Variance of a prediction for X^* may be estimated by

Regression through the origin should not be used indiscriminately. The variability of the data about the regression line should be compared to that for the equation including b₀ (that is, compare corresponding s_y.xs). A plot of studentized residuals versus X should be made as well. If a non-horizontal linear trend is apparent, a nonzero intercept should be suspected.