Lattice Designs in Standard and Simple Implicit Multi-linear Regression

TL;DR

This paper introduces lattice design methods for simple and implicit multi-linear regression, emphasizing non-response analysis and rotational analysis as alternatives to traditional fixed-effects models, with a focus on variance and covariance measures.

Contribution

It presents novel lattice design techniques for regression analysis, including non-response and rotational analysis, to better evaluate parameter estimates through variance and covariance measures.

Findings

Non-response analysis outperforms traditional methods in certain regression contexts.

Lattice designs provide new insights into variance and covariance in regression models.

Implications for improved parameter estimation in simple linear regression.

Abstract

Statisticians generally use ordinary least squares to minimize the random error in a subject response with respect to independent explanatory variable. However, Wooten shows illustrates how ordinary least squares can be used to minimize the random error in the system without defining a subject response. Using lattice design Wooten shows that non-response analysis is a superior alternative rotation of the pyramidal relationship between random variables and parameter estimates in multi-linear regression. Non-Response Analysis for simple linear co-linearity and Rotational Analysis in Simple Linear Regression challenge the notion of fixed effects; unity is included as a random measure (variable). The illustrations using lattice designs a mean operator that generates the standard mean and the self-weighing mean, among other point estimates with random weights; and a join that illustrates variance and covariance; and develops the measures of variance referred to as internal co-variance and base variance. These concepts are used to illustrate how these measures are used to evaluate parameter estimates in standard simple linear regression and simple implicit regression (non-response and rotational). The resulting analysis of these lattice designs show standard simple linear regression limits the relationship by consider the variance in one direction as relating to the two adjacent co-variances (standard and internal) whereas non-response analysis defines the relationship in terms of the internal co-variances and the base variance.