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bivariate

Bivariate refers to phenomena, data, or distributions that involve two variables. The term derives from Latin bi-, meaning two, and varius, variable.

In statistics, bivariate data consist of paired observations of two random variables X and Y. Analysts study

Bivariate distributions describe the joint behavior of two random variables. The joint distribution defines marginal distributions

Bivariate normal distribution is a central model in statistics. It specifies a two-variable normal distribution characterized

Common measures and models include Pearson correlation coefficient for linear relationships, Spearman's rho and Kendall's tau

Applications: any field dealing with two related measurements, such as biology, economics, psychology, and social sciences,

the
relationship
between
the
variables
using
descriptive
and
inferential
techniques,
including
scatter
plots,
correlation,
and
regression.
A
key
distinction
is
between
association
and
causation;
correlation
measures
the
strength
and
direction
of
a
linear
relationship,
while
regression
models
the
conditional
expectation
of
one
variable
given
the
other.
of
each
variable
and
conditional
distributions
of
one
variable
given
the
other.
If
the
joint
distribution
factors
into
a
product
of
marginals,
the
variables
are
independent.
by
means,
variances,
and
a
covariance.
Its
contours
are
ellipses
in
the
plane,
and
independence
occurs
when
the
covariance
is
zero.
for
monotonic
relationships,
simple
linear
regression,
and
the
coefficient
of
determination
(R^2).
For
categorical
data,
chi-squared
tests
assess
independence
in
a
contingency
table.
use
bivariate
analyses
to
understand
associations,
predict
outcomes,
and
explore
underlying
mechanisms.