## NIST Handbook Load Cell Calibration Case Study

Walks through analysis and modeling of a load cell output data with the goal of being able to understand performance characteristics of the cell and be able to predict future load output levels. exploratory data analysis, model fitting, heteroskedasticity tests and corrections, and interpretation of analysis results.

NIST Handbook Load Cell Calibration Case Study

## Serial Correlation Gauss-Markov Assumption

Having no serial correlation of errors is stating that the dependent variable in the sample observations from a population don’t affect or depend on each other.

## Weighted Least Squares – General Intuition and Usage

Weighted Least Squares adjusts the line of best fit plotting points taking into account a variable variance as the observation plot progresses. I.e. the regression in an area where there is lower variance will be “weighted” lower than an area where there’s a higher variance.

The weight is derived by taking the residual errors of the regression model and deriving a separate model of regression for that residual error, which describes a function of movement of how the error varies throughout the observations.
The derived weight is then applied as a multiplier to the regressor coefficients in the model.

## Heteroskedasticity – General Intuition and Usage

Description:
Systematic variance in our model error relative to one of the independent variables in the regression model.

2 Types:
Population Heteroskedasticity
– There is heteroskedasticity in the actual population data.

Omitted Variable Bias Heteroskedasticity (Model Heteroskedasticity)
– Error is linked to one of the independent variables in the regression model.

Investigation Approach
When analyzing model we should assume that we have omitted variable bias heteroskedasticity (if patterned error variance is visible in scatter-plot) and try to prove existence with tests. If model heteroskedasticity tests fail then we should explore tests for population heteroskedasticity.

Problems Caused:
Standard errors will be wrong. Any inference done using bad standard errors will be wrong.
OLS is no longer BLUE. Another type of regression model would better describe the population process.

Solutions:
Use White and/or Newey-west methods to correct the erratic standard errors produced in a heteroskedastic model.
– We can then use for inference techniques.
– Problem is that the heteroskedasticity in the model still exists.
Use fGLS regression model to produce a regression model with a homoskedastic error variance.
– Solves the root problem of heteroskedasticity in the population data.