Financial Terms least squares regression analysis

# Definition of least squares regression analysis

## 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

# Related Terms:

## dispersion

the degree of variability or difference; it is measured
as the vertical distance of an actual point from the
estimated regression line in least squares regression analysis

## method of least squares

see least squares regression analysis

## activity analysis

the process of detailing the various repetitive actions that are performed in making a product or
providing a service, classifying them as value-added and
non-value-added, and devising ways of minimizing or eliminating

## BARRA's performance analysis (PERFAN)

A method developed by BARRA, a consulting firm in
Berkeley, Calif. It is commonly used by institutional investors applying performance attribution analysis to
evaluate their money managers' performances.

## Break-even analysis

An analysis of the level of sales at which a project would make zero profit.

## break-even analysis

analysis of the level of sales at which the company breaks even.

## Break-Even Analysis

An analytical technique for studying the relationships between fixed cost, variable cost, and profits. A breakeven chart graphically depicts the nature of breakeven analysis. The breakeven point represents the volume of sales at which total costs equal total revenues (that is, profits equal zero).

## capital investment analysis

Refers to various techniques and procedures
used to determine or to analyze future returns from an investment
of capital in order to evaluate the capital recovery pattern and the
periodic earnings from the investment. The two basic tools for capital
investment analysis are (1) spreadsheet models (which I strongly prefer)
and (2) mathematical equations for calculating the present value or
internal rate of return of an investment. Mathematical methods suffer
from a lack of information that the decision maker ought to consider. A
spreadsheet model supplies all the needed information and has other

## Cluster analysis

A statistical technique that identifies clusters of stocks whose returns are highly correlated
within each cluster and relatively uncorrelated between clusters. Cluster analysis has identified groupings
such as growth, cyclical, stable and energy stocks.

## Common-base-year analysis

The representing of accounting information over multiple years as percentages
of amounts in an initial year.
Common-size analysis The representing of balance sheet items as percentages of assets and of income
statement items as percentages of sales.

## Comparative credit analysis

A method of analysis in which a firm is compared to others that have a desired
target debt rating in order to infer an appropriate financial ratio target.

## correlation analysis

an analytical technique that uses statistical
measures of dispersion to reveal the strength of the
relationship between variables

## Cost-Benefit Analysis

The calculation and comparison of the costs and benefits of a policy or project.

## cost-benefit analysis the analytical process of comparing the

relative costs and benefits that result from a specific course
of action (such as providing information or investing in a
project)

## cost driver analysis

the process of investigating, quantifying,
and explaining the relationships of cost drivers and
their related costs

## Cost–volume–profit analysis (CVP)

A method for understanding the relationship between revenue, cost and sales volume.

## Credit analysis

The process of analyzing information on companies and bond issues in order to estimate the
ability of the issuer to live up to its future contractual obligations. Related: default risk

## credit analysis

Procedure to determine the likelihood a customer will pay its bills.

## Discriminant analysis

A statistical process that links the probability of default to a specified set of financial ratios.

## Factor analysis

A statistical procedure that seeks to explain a certain phenomenon, such as the return on a
common stock, in terms of the behavior of a set of predictive factors.

## Failure analysis

The examination of failure incidents to identify components
with poor performance profiles.

## Financial Trend Analysis

Process of analyzing financial statements of a company for any continuing relationship.

## First-pass regression

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

## Fundamental analysis

Security analysis that seeks to detect misvalued securities by an analysis of the firm's
business prospects. Research analysis often focuses on earnings, dividend prospects, expectations for future
interest rates, and risk evaluation of the firm.

## Horizon analysis

An analysis of returns using total return to assess performance over some investment horizon.

## Horizontal analysis

The process of dividing each expense item of a given year by the same expense item in
the base year. This allows for the exploration of changes in the relative importance of expense items over time
and the behavior of expense items as sales change.

## incremental analysis

a process of evaluating changes that
focuses only on the factors that differ from one course of
action or decision to another

## Linear regression

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

## Log-linear least-squares method

A statistical technique for fitting a curve to a set of data points. One of the
variables is transformed by taking its logarithm, and then a straight line is fitted to the transformed set of data
points.

## Mean-variance analysis

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

## Multiple-discriminant analysis (MDA)

Statistical technique for distinguishing between two groups on the
basis of their observed characteristics.

## Multiple regression

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

## multiple regression

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

## Ordinary least squares (OLS)

regression analysis a statistical technique that minimizes the sum of the squared deviations between a dependent variable and one or more independent variables and provides the user
with a y-intercept and x-coefficients, as well as feedback such as R2 (explained
variation/total variation) t-statistics, p-values, etc.

## Pareto analysis

a method of ranking the causes of variation
in a process according to the impact on an objective
Pareto inventory analysis an analysis that separates inventory
into three groups based on annual cost-to-volume usage

## Pareto analysis

The 80:20 ratio that states that 20% of the variables included in an
analysis are responsible for 80% of the results. For example, 20% of all customers
are responsible for 80% of all customer service activity, or 20% of all inventory
items comprise 80% of the inventory value.

The decomposition of a money manager's performance results to explain
the reasons why those results were achieved. This analysis seeks to answer the following questions: (1) What
were the major sources of added value? (2) Was short-term factor timing statistically significant? (3) Was
market timing statistically significant? And (4), Was security selection statistically significant?

## Pro forma capital structure analysis

A method of analyzing the impact of alternative capital structure
choices on a firm's credit statistics and reported financial results, especially to determine whether the firm will
be able to use projected tax shield benefits fully.

## Ratio analysis

A method of analysing financial reports to interpret trends and make comparisons by using ratios – two numbers, with one generally expressed as a percentage of the other.

## Ratio analysis

A method of relating numbers from the various financial statements to one another in order to get meaningful information for comparison.

## Ratio Analysis

The process of using financial ratios, calculated from key accounts
found in a company's financial statements, to make judgements
concerning the finances and operations of the firm

## Regression analysis

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

## 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.

## Regression equation

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

## 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

## Regression toward the mean

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

## Scenario analysis

The use of horizon analysis to project bond total returns under different reinvestment rates
and future market yields.

## scenario analysis

Project analysis given a particular combination of assumptions.

## 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.

## Sensitivity analysis

analysis of the effect on a project's profitability due to changes in sales, cost, and so on.

## Sensitivity analysis

An approach to understanding how changes in one variable of cost–volume–profit analysis are affected by changes in the other variables.

## sensitivity analysis

a process of determining the amount of change that must occur in a variable before a different decision would be made

## sensitivity analysis

analysis of the effects of changes in sales, costs, and so on, on project profitability.

## Simple linear regression

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

## simple regression

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

## simulation analysis

Estimation of the probabilities of different possible outcomes, e.g., from an investment project.

## Technical analysis

Security analysis that seeks to detect and interpret patterns in past security prices.

## Variance analysis

A method of budgetary control that compares actual performance against plan, investigates the causes of the variance and takes corrective action to ensure that targets are achieved.

## variance analysis

the process of categorizing the nature (favorable or unfavorable) of the differences between standard and actual costs and determining the reasons for those differences

## Vertical analysis

The process of dividing each expense item in the income statement of a given year by net
sales to identify expense items that rise faster or slower than a change in sales.

## VERTICAL ANALYSIS

A financial analysis technique that relates key amounts on the income statement and balance sheet to a 100 percent or base figure for the present and previous year.
It shows the percentage change from last year to this year, making it easier to spot problems that require analysis.