REGRESSION EQUATIONS DO NOT PROVIDE THE BEST-FIT-LINE RELATING TWO DEPENDENT VARIABLES

Title REGRESSION EQUATIONS DO NOT PROVIDE THE BEST-FIT-LINE RELATING TWO DEPENDENT VARIABLES
Author, Co-Author Frank Thorn
Topic
Year
1992
Day
Sunday
Program Number
1:30 pm
Room
Ireland B
Affiliation
Abstract Though widely used for this purpose, linear regression equations do not accurately describe the mathematical relationship between two measured dependent variables. The slope of the regression line differs dramatically depending on which variable is chosen for the X-axis, the correlation between the two variables, and the true slope of the data cloud in a scatterplot. A regression equation will often underestimate the true slope of the data in a scatterplot by a factor of two or three. Principal axis analysis based on eigenvalue calculations is the appropriate method for calculating the best- fit-line. I will describe this obscure line fitting technique and show how simple linear regressions have mislead numerous researchers with examples from articles in Optometry and Vision Science (including some of my own work). Principal axis analysis provides best-fit-lines around which the scatterplot data clouds in these articles are symmetrically balanced.
Affiliation of Co-Authors
Outline