Regression Analysis for Forecast Improvement
Regression Analysis is a causal / econometric forecasting method that is widely used for prediction and forecasting improvement.
Learning Objective

Explain how regression analysis works
Key Points
 Regression Analysis is a causal / econometric forecasting method. Some forecasting methods use the assumption that it is possible to identify the underlying factors that might influence the variable that is being forecast.
 Regression analysis includes several classical assumptions.
 Regression analysis includes many techniques for modeling and analyzing several variables when the focus is on the relationship between a dependent variable and one or more independent variables.
 A large body of techniques for carrying out regression analysis has been developed. Familiar methods, such as linear regression and ordinary least squares regression, are parametric.
Terms

Ordinary least squares regression
In statistics, ordinary least squares (OLS) or linear least squares is a method for estimating the unknown parameters in a linear regression model. This method minimizes the sum of squared vertical distances between the observed responses in the dataset and the responses predicted by the linear approximation.

linear regression
In statistics, linear regression is an approach to modeling the relationship between a scalar dependent variable y and one or more explanatory variables denoted X.

independent
not contingent or depending on something else
Example
 One can forecast based on linear relationships. If one variable is linearly related to the other for a long enough period of time, it may be beneficial to predict such a relationship in the future.
Full Text
Regression Analysis
Regression Analysis is a causal / econometric forecasting method. Some forecasting methods are based on the assumption that it is possible to identify underlying factors that might influence a variable that is being forecast. For example, including information about weather conditions might improve the ability of a model to predict umbrella sales. This is a model of seasonality that shows a regular pattern of up and down fluctuations. In addition to weather, seasonality can also result from holidays and customs such as predicting that sales in college football apparel will be higher during football season as opposed to the off season.
Regression analysis includes a large group of methods that can be used to predict future values of a variable using information about other variables. These methods include both parametric (linear or nonlinear) and nonparametric techniques.
Classical assumptions for regression analysis include:
 The sample is representative of the population for the inference prediction.
 The error is a random variable with a mean of zero conditional on the explanatory variables.
 The independent variables are measured with no error. (Note: If this is not so, modeling may be performed instead, using errorsinvariables model techniques).
 The predictors are linearly independent, i.e. it is not possible to express any predictor as a linear combination of the others.
 The errors are uncorrelated, that is, the variance– covariance matrix of the errors is diagonal, and each nonzero element is the variance of the error.
 The variance of the error is constant across observations (homoscedasticity). (Note: If not, weighted least squares or other methods might instead be used).
In statistics, regression analysis includes many techniques for modeling and analyzing several variables, when the focus is on the relationship between a dependent variable and one or more independent variables. More specifically, regression analysis helps one understand how the typical value of the dependent variable changes when any one of the independent variables is varied, while the other independent variables are held fixed.
Regression analysis
Regression analysis shows the relationship between a dependent variable and one or more independent variables.
Most commonly, regression analysis estimates the conditional expectation of the dependent variable given the independent variables — that is, the average value of the dependent variable when the independent variables are fixed. Less commonly, the focus is on a quantile, or other location parameter of the conditional distribution of the dependent variable given the independent variables. In all cases, the estimation target is a function of the independent variables called the regression function. In regression analysis, it is also of interest to characterize the variation of the dependent variable around the regression function, which can be described by a probability distribution.
Forecast Improvement
Regression analysis is widely used for prediction and forecasting, where its use has substantial overlap with the field of machine learning. Regression analysis is also used to understand which among the independent variables is related to the dependent variable, and to explore the forms of these relationships. In restricted circumstances, regression analysis can be used to infer causal relationships between the independent and dependent variables. However, this can lead to illusions or false relationships, so caution is advisable.
A large body of techniques for carrying out regression analysis has been developed. Familiar methods, such as linear regression and ordinary least squares regression, are parametric, in that the regression function is defined in terms of a finite number of unknown parameters that are estimated from the data. Nonparametric regression refers to techniques that allow the regression function to lie in a specified set of functions, which may be infinitedimensional.
The performance of regression analysis methods in practice depends on the form of the data generating process and how it relates to the regression approach being used. Since the true form of the datagenerating process is generally not known, regression analysis often depends to some extent on making assumptions about this process. These assumptions are sometimes testable if a large amount of data is available. Regression models for prediction are often useful even when the assumptions are moderately violated, although they may not perform optimally. However, in many applications, especially with small effects or questions of causality based on observational data, regression methods give misleading results.
Key Term Reference
 CoVariance
 Appears in this related concept: Portfolio Risk
 Future Value
 Appears in these related concepts: Calculating Values for Different Durations of Compounding Periods, The Valuation of Stocks, and Future Value of Annuity
 Interest
 Appears in these related concepts: Interest Compounded Continuously, Accounting for Interest Earned and Principal at Maturity, and Tax Considerations
 analysis
 Appears in these related concepts: The Impact of External and Internal Factors on Strategy, Scenario Analysis, and Writing in Different Academic Disciplines
 distribution
 Appears in these related concepts: Application of Knowledge, Monte Carlo Simulation, and Selling to Consumers
 forecast
 Appears in these related concepts: Forecasting, Impact of Modifying Inputs on Business Operations, and Problems in Forecasting Population Growth
 parameter
 Appears in these related concepts: Sensitivity Analysis, Cash Flow Factors, and Basic Inferential Statistics
 period
 Appears in these related concepts: Frequency of Sound Waves, Sine and Cosine as Functions, and Tangent as a Function
 probability distribution
 Appears in these related concepts: Probability Distributions for Discrete Random Variables, Recognizing and Using a Histogram, and Overview of How to Assess StandAlone Risk
 sales
 Appears in these related concepts: Additional Funds Needed (AFN), Repurchasing Stock, and Seasoned Equity Offering
 seasonality
 Appears in these related concepts: Dangers Involved in Inventory Management and Seasonal Production
 variable
 Appears in these related concepts: What is a Linear Function?, Math Review, and Introduction to Variables
 variance
 Appears in these related concepts: Mean, Variance, and Standard Deviation of the Binomial Distribution, Variance, and Variance Estimates
Sources
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