id: 06000264
dt: j
an: 2012a.00679
au: Carr, James R.
ti: Orthogonal regression: a teaching perspective.
so: Int. J. Math. Educ. Sci. Technol. 43, No. 1, 134-143 (2012).
py: 2012
pu: Taylor \& Francis, Abingdon, Oxfordshire
la: EN
cc: K80 K90 M50
ut: orthogonal regression; least squares; major axis; reduced major axis;
errors-in-variables; data visualization; geyser eruption data
ci:
li: doi:10.1080/0020739X.2011.573876
ab: Summary: A well-known approach to linear least squares regression is that
which involves minimizing the sum of squared orthogonal projections of
data points onto the best fit line. This form of regression is known as
orthogonal regression, and the linear model that it yields is known as
the major axis. A similar method, reduced major axis regression, is
predicated on minimizing the total sum of triangular areas formed
between data points and the best fit line. Either of these methods is
appropriately applied when both $x$ and $y$ are measured, a typical
case in the natural sciences. In comparison to classical linear
regression, equation derivation for the slope of the major axis and
reduced major axis lines is a nontrivial process. For this reason,
derivations are presented herein drawing from previous literature with
as few steps as possible to enable an easily accessible understanding.
Application to eruption data for Old Faithful geyser, Yellowstone
National Park, Wyoming and Montana, USA enables a teaching opportunity
for choice of model.
rv: