Basics of Generally Accepted Accounting Principles (GAAP)

Basic objectives
Financial reporting should be rich with information that is;

• Useful to provide information to potential investors and creditors and other financial market users in making rational investment, credit, and other financial decisions.

• Helpful to assess the amounts, timing, and uncertainty of prospective cash receipts.

• About economic resources, the claims and the changes in those resources.

• Key to make financial decisions.

• Provide information to make long-term decisions.

• Improving the performance of the business

• Useful in maintaining records

Basic concepts
GAAP has four basic assumptions, four basic principles, and four basic constraints to achieve its basic objectives and implement fundamental qualities.

Assumptions

• Accounting Entity: Business has a separate existence from its owners and revenue and expense should be kept separate from personal expenses.

• Going Concern: Business will be in operation indefinitely.

• Monetary Unit principle: Assumes a stable currency is going to be the unit of record.

• Time-period principle: Economic activities of a business can be divided into artificial time periods.

Principles

• Historical cost principle - Companies to account and report based on acquisition costs rather than fair market value for most assets and liabilities.

• Revenue recognition principle - Requires companies to record in accrual basis accounting.

• Matching principle - Expenses have to be matched with revenues.

• Full Disclosure principle - Information disclosed should be enough to make decisions.

Constraints

• Objectivity principle: The financial statements should be based on objective evidence.

• Materiality principle: The significance of an item should be reported when considering.

• Consistency principle: The company uses the same accounting principles and methods from year to year.

• Conservatism principle: When choosing between two solutions, the one that will be least likely to overstate assets and income should be picked.

A Quick Guide to Least Squares Regression Method..

Carl Friedrich Gauss’s method of least squares is a standard approach for sets of equations in which there are more equations than unknowns. Least squares problems fall into two main categories. Linear also know as ordinary least squares and non-linear least squares. The linear least-squares problem pops up in statistical regression analysis and it has a closed-form solution while the non-linear problem has no closed-form solution. Thus the core calculation is similar in both cases.

In a least squares calculation with unit weights, or in linear regression, the variance on the jth parameter, denoted is usually estimated with

Weighted least squares

When that the errors are uncorrelated with each other and with the independent variables and have equal variance, is a best linear unbiased estimator (BLUE). If, however, the measurements are uncorrelated but have different uncertainties, a modified approach might be adopted. When a weighted sum of squared residuals is minimized, is BLUE if each weight is equal to the reciprocal of the variance of the measurement.

The gradient equations for this sum of squares are

Which, in a linear least squares system give the modified normal equations

When the observational errors are uncorrelated and the weight matrix, W, is diagonal, these may be written as

Where

For non-linear least squares systems a similar argument shows that the normal equations should be modified as follows.

Least-squares regression is a method for finding a line that summarizes the relationship between the two variables.

Regression Line: A straight line that describes how a response variable y changes as an explanatory variable x changes.

A residual is a difference between an observed y and a predicted y.

Important facts about the least squares regression line.

• The point (x,y) is on the line, where x is the mean of the x values, and y is the mean of the y values.
• Its form is y(hat) = a + bx. (Note that b is slope and a is the y-intercept.)
• a = y - bx.
• The slope b is the approximate change in y when x increases by 1.
• The y-intercept is the predicted value of y when x = 0

r² in regression: The coefficient of determination, r² is the fraction of the variation in the values of y that is explained the least squares regression of y on x.

Calculation of r² for a simple example:

r² = (SSM-SSE)/SSM, where

SSM = sum(y-y)² (Sum of squares about the mean y)
SSM = sum(y-y(hat))² (Sum of squares of residuals)

Calculating the regression slope and intercept

The terms in the table are used to derive the straight line formula for regression: y = bx + a, also called the regression equation. The slope or b is calculated from the Y's associated with particular X's in the data. The slope coefficient (by/x) equals

THINGS TO NOTE:

· Sum of deviations from mean = 0.

· Sum of residuals = 0.

· r² > 0 does not mean r > 0. If x and y are negatively associated, then r < 0.