Multiple regression is a statistical technique that can be used to analyze the relationship between a single dependent variable and several independent variables. The objective of multiple regression analysis is to use the independent variables whose values are known to predict the value of the single dependent value.
Multiple regression analysis allows researchers to assess the strength of the relationship between an outcome (the dependent variable) and several predictor variables as well as the importance of each of the predictors to the relationship, often with the effect of other predictors statistically eliminated.
Multiple linear regression assumes that the amount of error in the residuals is similar at each point of the linear model. This scenario is known as homoscedasticity.
Multiple linear regression allows the investigator to account for all of these potentially important factors in one model. The advantages of this approach are that this may lead to a more accurate and precise understanding of the association of each individual factor with the outcome.
There are several types of multiple regression analyses (e.g. standard, hierarchical, setwise, stepwise) only two of which will be presented here (standard and stepwise). Which type of analysis is conducted depends on the question of interest to the researcher.
Multiple linear regression requires at least two independent variables, which can be nominal, ordinal, or interval/ratio level variables. A rule of thumb for the sample size is that regression analysis requires at least 20 cases per independent variable in the analysis.
Specifically, we will discuss the assumptions of linearity, reliability of measurement, homoscedasticity, and normality.
There is a linear relationship between the dependent variables and the independent variables. The independent variables are not too highly correlated with each other. yi observations are selected independently and randomly from the population. Residuals should be normally distributed with a mean of 0 and variance σ
Regression analysis is a common statistical method used in finance and investing. Linear regression is one of the most common techniques of regression analysis. Multiple regression is a broader class of regressions that encompasses linear and nonlinear regressions with multiple explanatory variables.
In Linear regression the sample size rule of thumb is that the regression analysis requires at least 20 cases per independent variable in the analysis.
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The regression has five key assumptions:
- Linear relationship.
- Multivariate normality.
- No or little multicollinearity.
- No auto-correlation.
- Homoscedasticity.
What is difference between simple linear and multiple linear regressions? Simple linear regression has only one x and one y variable. Multiple linear regression has one y and two or more x variables. For instance, when we predict rent based on square feet alone that is simple linear regression.
It is also widely used for predicting the value of one dependent variable from the values of two or more independent variables. When there are two or more independent variables, it is called multiple regression.
Polynomial regression models a non-linear dataset using a linear model. It is the equivalent of making a square peg fit into a round hole. It works in a similar way to multiple linear regression (which is just linear regression but with multiple independent variables), but uses a non-linear curve.
Linearity: The relationship between X and the mean of Y is linear. Homoscedasticity: The variance of residual is the same for any value of X. Independence: Observations are independent of each other. Normality: For any fixed value of X, Y is normally distributed.
