What Is The Difference Between Linear Regression And Multiple Regression

What is the difference between linear regression and multiple regression? By Andriy Blokhin SHARE

A: In statistics, linear regression models the relationship between a dependent variable and one or more explanatory variables using a linear function. If two or more explanatory variables have a linear relationship with the dependent variable, the regression is called a multiple linear regression. Multiple regression, on the other hand, is a broader class of regressions that encompasses linear and nonlinear regressions with multiple explanatory variables. Regression analysis is a common way to discover a relationship between dependent and explanatory variables. However, this statistical relationship does not mean that the explanatory variables cause the dependent variable; it rather speaks of some significant association in the data. Linear regression attempts to draw a line that comes closest to the data by finding the slope and intercept that define the line and minimize regression errors. However, many relationships in data do not follow a straight line, so statisticians use nonlinear regression instead. It is rare that a dependent variable is explained by only one variable. In this case, an analyst uses multiple regression, which attempts to explain dependent

variable using more than one independent variable. Multiple regressions can be linear and nonlinear. Consider an analyst who wishes to establish linear relationship between the daily change in a company's stock prices and other explanatory variables such as the daily change in trading volumeand the daily change in market returns. If he runs a regression with the daily change in the company's stock prices as a dependent variable and the daily change in trading volume as an independent variable, this would be an example of a simple linear regression with one explanatory variable. If the analyst adds the daily change in market returns into the regression, it would be a multiple linear regression.

The Linear Regression of Time and Price By Emily Norris | Updated March 30, 2018 — 8:15 AM EDT

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Technical and quantitative analysts have applied statistical principles to the financial market since its inception. Some attempts have been very successful, while others have been anything but. The key is to find a way to identify price trends without the fallibility and bias of the human mind. One

approach that can be successful for investors and is available in most charting tools is linear regression. Linear regression analyzes two separate variables in order to define a single relationship. In chart analysis, this refers to the variables of price and time. Investors and traders who use charts recognize the ups and downs of price printed horizontally from day-to-day, minute-to-minute or week-to-week, depending on the evaluated time frame. The different market approaches are what make linear regression analysis so attractive. (Learn more about quantitative analysis in Quantitative Analysis of Hedge Funds.)

Bell Curve Basics Statisticians have used the bell curve method, also known as a normal distribution, to evaluate a particular set of data points. Figure 1 is an example of a bell curve, which is denoted by the dark blue line. The bell curve represents the form of the various data point occurrences. The bulk of the points normally take place toward the middle of the bell curve, but over time, the points stray, or deviate, from the population. Unusual or rare points are sometimes well outside of the "normal" population.

Figure 1: A bell curve, normal distribution. Source: ProphetCharts

As a reference point, it is common to average the values to create a mean score. The mean doesn't necessarily represent the middle of the data, and instead represents the average score, including all outlying data points. After a mean is established, analysts determine how often price deviates from the mean. A standard deviation to one side of the average is usually 34% of the data, or 68% of the data points if we look at one positive and one negative standard deviation, which is represented by the orange arrow section in Figure 1. Two standard deviations include approximately 95% of the data points and are the orange and pink arrow sections added together. The very rare occurrences, represented by purple arrows, occur at the tails of the bell curve. Because any data point that appears outside two standard deviations is very rare, it is often assumed that the data points will move back toward the average, or regress. (See also: Standard Deviation and Variance.)