2.6.5.2.1.

Weighted fit

Weights Proportional to the Variance

We can use weighting to improve the fit where the weights are proportional to the variance. The weights are estimated using the power function. That is, we fit

where are the variances from each set of replicates in the data. We then calculate the weights as

Plot of the Power Function

The following is the plot of the power function with the corresponding linear fit for this data set.

Note that for this data, the plot is dominated by the flux=90 group. Also, the plot does not demonstrate a clear linear pattern. Instead, the variances are basically flat for the first five values, and then there is a rise for the last three values. Based on this plot, it is reasonable to conclude that weighting the fit with this method may do more harm than good.