# Optimal designs for estimating individual coefficients in polynomial regression with no intercept

## TL;DR

This paper determines the optimal experimental design for estimating individual coefficients in polynomial regression models without intercepts, extending previous work that relied on Chebyshev system properties.

## Contribution

It explicitly identifies the optimal design for coefficient estimation in polynomial regression models lacking an intercept, where previous methods do not apply.

## Key findings

- Explicit optimal design for no-intercept polynomial regression
- Extension of classical results to non-Chebyshev systems
- Improved efficiency in coefficient estimation

## Abstract

In a seminal paper \cite{studden1968} characterized $c$-optimal designs in regression models, where the regression functions form a Chebyshev system. He used these results to determine the optimal design for estimating the individual coefficients in a polynomial regression model on the interval $[-1,1]$ explicitly. In this note we identify the optimal design for estimating the individual coefficients in a polynomial regression model with no intercept (here the regression functions do not form a Chebyshev system).