Projection

Projection, projector, or projective may refer to:

Demand

In economics, demand is the utility for a good or service of an economic agent, relative to his/her income. (Note: This distinguishes "demand" from "quantity demanded", where demand is a listing or graphing of quantity demanded at each possible price. In contrast to demand, quantity demanded is the exact quantity demanded at a certain price. Changing the actual price will change the quantity demanded, but it will not change the demand, because demand is a listing of quantities that would be bought at various prices, not just the actual price.)

Demand is a buyer's willingness and ability to pay a price for a specific quantity of a good or service. Demand refers to how much (quantity) of a product or service is desired by buyers at various prices. The quantity demanded is the amount of a product people are willing or able to buy at a certain price; the relationship between price and quantity demanded is known as the demand. (see also supply and demand). The term demand signifies the ability or the willingness to buy a particular commodity at a given point of time, ceteris paribus. Utility preferences and choices underlying demand can be represented as functions of cost, benefit, odds and other variables.

Linear regression

In statistics, linear regression is an approach for modeling the relationship between a scalar dependent variable y and one or more explanatory variables (or independent variables) denoted X. The case of one explanatory variable is called simple linear regression. For more than one explanatory variable, the process is called multiple linear regression. (This term should be distinguished from multivariate linear regression, where multiple correlated dependent variables are predicted, rather than a single scalar variable.)

In linear regression, the relationships are modeled using linear predictor functions whose unknown model parameters are estimated from the data. Such models are called linear models. Most commonly, the conditional mean of y given the value of X is assumed to be an affine function of X; less commonly, the median or some other quantile of the conditional distribution of y given X is expressed as a linear function of X. Like all forms of regression analysis, linear regression focuses on the conditional probability distribution of y given X, rather than on the joint probability distribution of y and X, which is the domain of multivariate analysis.

Time series

A time series is a sequence of data points that

1) Consists of successive measurements made over a time interval

2) The time interval is continuous

3) The distance in this time interval between any two consecutive data point is the same

4) Each time unit in the time interval has at most one data point

Examples of time series are ocean tides, counts of sunspots, and the daily closing value of the Dow Jones Industrial Average.

Non-Examples: The height measurements of a group of people where each height is recorded over a period of time and each person has only one record in the data set.

Panel data set is sometimes difficult to be differentiated from time series data set. One data set may exhibit both characteristics of panel data set and time series data set. One way to differentiate is to ask: what makes one data record unique from the other records? If the answer is the time data field, then this is a time series data set candidate. If determining a unique records requires a time data field and an additional identifier which is unrelated to time (student ID, stock symbol, country code), then it is a panel data candidate. If the differentiation lies on the non time identifier, then the data set is a cross sectional data set candidate.

Approximation error

The approximation error in some data is the discrepancy between an exact value and some approximation to it. An approximation error can occur because

In the mathematical field of numerical analysis, the numerical stability of an algorithm in numerical analysis indicates how the error is propagated by the algorithm.

Formal Definition

One commonly distinguishes between the relative error and the absolute error.

Given some value v and its approximation v_approx, the absolute error is

where the vertical bars denote the absolute value. If the relative error is

and the percent error is

In words, the absolute error is the magnitude of the difference between the exact value and the approximation. The relative error is the absolute error divided by the magnitude of the exact value. The percent error is the relative error expressed in terms of per 100.