Calibration with weighted LS regression

Introduction

Learning Goals

Tasks

Twin goals: estimate the calibration function for heteroscedastic measurements, and perform inverse regression to estimate the concentration of an unknown. The data is adapted from Thompson & Lowthian, “Notes on Statistics and Data Quality for Analytical Chemists,” 2011.

• Unfold and plot the raw data to see the heteroscedasticity (then delete)
• Calculate the average and standard error (SEM) of the signals and examine, and plot with error bars
• Perform weighted LS regression using WLS
• Smooth the SEM values with a best fit line and perform weighted LS regression using PolyLS and the smoothed standard deviations
• Use PolyPred to plot the prediction band using smoothed SEMs
• Use weighted PolyInv to predict $\hat{x}_u$, its standard error, and a 95% confidence interval (CI) for $x_u$
• Estimate the 95% CI from the prediction band
• Use the Inverse Regression procedure (with SOLVER) to get the exact inverse regression

When you finish, your spreadsheet should resemble the image below.