statistik2

REGRESSION

1.1 Introduction

 

Regression analysis is one of the statistical methods to determine the causal relationship between the variables with the variable (-variable) to another. Variables "cause" is called with different terms: the explanatory variables, explanatory variables, independent variables, or freely, variable X (as is often depicted in the graph as the abscissa or X axis). Affected by variables known as a variable that is affected, the dependent variable, dependent variable, or the variable Y. Both of these variables can be a random variable (random), but the variable that is affected should always be a random variable.

Regression analysis is one of the most popular analysis and extensive use. Regression analysis is widely used to make predictions and forecasts, with the use of a complementary to the field of machine learning. This analysis was also used to understand which variables were associated with the dependent variable, and to determine the relationship forms.

1.2 Types of regression

The two basic types of regression are linear regression and multiple regression. Linear regression uses one independent variable to explain and/or predict the outcome of Y, while multiple regression uses two or more independent variables to predict the outcome. 

1.2.1 Simple Linear Regression

Linear regression is a method of organizing data.  Sometimes it is appropriate to show data as points on a graph, then try to draw a straight line through the data.  Linear regression is an algorithm for drawing such a line.  Linear regression typically uses the least squares method to determine which line best fits the data.  R-Squared is a measure of how well the data points match the resulting line.

Linear regression provides a deterministic way to this.  First, linear regression will provide an R-Squared value for the historical data.  If this value is too small, the data is not linear, so the original assumptions must change.  If R-Squared is large enough, then the linear regression will provide the best prediction of the second move each day based on the first move.

Linear Regression: Y = a + bX + u 

1.2.2 Multiple Regression

Multiple Regression is a statistical technique that uses several explanatory variables to predict the outcome of a response variable. The goal of multiple linear regression (MLR) is to model the relationship between the explanatory and response variables.

Multiple Regression: Y = a + b₁X₁ ⁺  b₂X₂ + B₃X₃ + ... + B_tX_t + u

Where:
Y= the variable that we are trying to predict

X= the variable that we are using to predict Y

a= the intercept 

b= the slope 

u= the regression residual. 

In multiple regression the separate variables are differentiated by using subscripted numbers. .

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1.3 Regression Coefficient

The strength of the linear relationship between the two variables in the regression equation is the correlation coefficient, r, and is always a value between -1 and 1, inclusive. The regression coefficient is the slope of the line of the regression equation.