- #1
tom8
- 19
- 0
I am trying to use Weighted Least Squares with a linear model: Y = Xβ + ε, where Y are some observed measurements and β is a vector of estimates. For example, in this case β has two terms: intercept and slope.
The weighted least squares solution, as shown here, involves a weight matrix, W, defined as a diagonal matrix whose elements are inverse of the variance of the measurements Y (here we assume the measurements are uncorrelated so the matrix is diagonal). But this mean that, if I just keep W as an identity matrix, then I am assuming a measurement with errors / variances equal to 1 unit. So if my measurements are in meters, then I am assuming 1 m of variance. So it is unclear to me how this matrix W is used to represent measurement error in real life.
The weighted least squares solution, as shown here, involves a weight matrix, W, defined as a diagonal matrix whose elements are inverse of the variance of the measurements Y (here we assume the measurements are uncorrelated so the matrix is diagonal). But this mean that, if I just keep W as an identity matrix, then I am assuming a measurement with errors / variances equal to 1 unit. So if my measurements are in meters, then I am assuming 1 m of variance. So it is unclear to me how this matrix W is used to represent measurement error in real life.