Definition of Regression equation

Regression equation

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

Alpha equation

The alpha of a fund is determined as follows:
[ (sum of y) -((b)(sum of x)) ] / n
where:
n =number of observations (36 months)
b = beta of the fund
x = rate of return for the S&P 500
y = rate of return for the fund

Beta equation (Mutual Funds)

The beta of a fund is determined as follows:
[(n) (sum of (xy)) ]-[ (sum of x) (sum of y)]
[(n) (sum of (xx)) ]-[ (sum of x) (sum of x)]
where: n = # of observations (36 months)
x = rate of return for the S&P 500 Index
y = rate of return for the fund

Beta equation (Stocks)

The beta of a stock is determined as follows:
[(n) (sum of (xy)) ]-[(sum of x) (sum of y)]
[(n) (sum of (xx)) ]-[(sum of x) (sum of x)]
where: n = # of observations (24-60 months)
x = rate of return for the S&P 500 Index
y = rate of return for the stock

First-pass regression

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

Linear regression

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

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 toward the mean

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

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.

Accounting equation

The representation of the double-entry system of accounting such that assets are equal to liabilities plus capital.

Accounting equation

The formula Assets = Liabilities + Equity.

accounting equation

An equation that reflects the two-sided nature of a
business entity, assets on the one side and the sources of assets on the
other side (assets = liabilities + owners’ equity). The assets of a business
entity are subject to two types of claims that arise from its two basic
sources of capital—liabilities and owners’ equity. The accounting equation
is the foundation for double-entry bookkeeping, which uses a
scheme for recording changes in these basic types of accounts as either
debits or credits such that the total of accounts with debit balances
equals the total of accounts with credit balances. The accounting equation
also serves as the framework for the statement of financial condition,
or balance sheet, which is one of the three fundamental financial
statements reported by a business.

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

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.

Equation of Exchange

The quantity theory equation Mv = PQ.

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