Definition of Regression toward the mean

Regression toward the mean

The tendency for subsequent observations of a random variable to be closer to its mean.

Arithmetic average (mean) rate of return

Arithmetic mean return.

Arithmetic mean return

An average of the subperiod returns, calculated by summing the subperiod returns
and dividing by he number of subperiods.

First-pass regression

A time series regression to estimate the betas of securities portfolios.

Geometric mean return

Also called the time weighted rate of return, a measure of the compounded rate of
growth of the initial portfolio market value during the evaluation period, assuming that all cash distributions
are reinvested in the portfolio. It is computed by taking the geometric average of the portfolio subperiod
returns.

Linear regression

A statistical technique for fitting a straight line to a set of data points.

Mean

The expected value of a random variable.

Mean of the sample

The arithmetic average; that is, the sum of the observations divided by the number of
observations.

Mean-variance analysis

Evaluation of risky prospects based on the expected value and variance of possible outcomes.

Mean-variance criterion

The selection of portfolios based on the means and variances of their returns. The
choice of the higher expected return portfolio for a given level of variance or the lower variance portfolio for
a given expected return.

Mean-variance efficient portfolio

Related: Markowitz efficient portfolio

Multiple regression

The estimated relationship between a dependent variable and more than one explanatory variable.

Regression analysis

A statistical technique that can be used to estimate relationships between variables.

Regression equation

An equation that describes the average relationship between a dependent variable and a
set of explanatory variables.

Second pass regression

A cross-sectional regression of portfolio returns on betas. The estimated slope is the
measurement of the reward for bearing systematic risk during the period analyzed.

Simple linear regression

A regression analysis between only two variables, one dependent and the other explanatory.

least squares regression analysis

a statistical technique that investigates the association between dependent and independent variables; it determines the line of "best fit" for a set of observations by minimizing the sum of the squares
of the vertical deviations between actual points and the
regression line; it can be used to determine the fixed and
variable portions of a mixed cost

multiple regression

a statistical technique that uses two or
more independent variables to predict a dependent variable

regression line

any line that goes through the means (or averages) of the set of observations for an independent variable and its dependent variables; mathematically, there is a line of “best fit,” which is the least squares regression line

simple regression

a statistical technique that uses only one independent variable to predict a dependent variable

Mean

a. A number that typifies a set of numbers, such as a geometric mean
or an arithmetic mean.
b. The average value of a set of numbers.

Regression analysis

Statistical analysis techniques that quantify the
relationship between two or more variables. The intent is quantitative
prediction or forecasting, particularly using a small population to forecast the
behavior of a large population.

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