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The goal of multiple linear regression is to find a linear relationship between several independent factors and a dependent variable. Researchers can use multiple regression to look at the effect of multiple independent variables on response at the same time. Regression can be used to see how much a specific set of independent variables can explain an outcome for various research issues. In other circumstances, multiple regression is used to look at the effect of an outcome while taking into consideration several factors that could influence it.
Assume we have data on baby birth weights as well as a range of other characteristics about the baby, the birth, or the mother. Assume we wish to predict a baby's birth weight based on a collection of these characteristics. This is precisely what multiple regression entails. To predict a response variable, we use a set of explanatory variables. Our explanation will be limited to the case where the response variable is numerical. The explanatory variables, on the other hand, can be numerical or categorical.
We'll learn about multiple linear regression in particular, which is a strategy for analyzing specific types of multivariate data. This can help us comprehend the relationship between a response variable and one or more predictor variables, show how a change in one of the predictor variables affects the response variable, and estimate or predict the response variable's value based on the predictor variables' values.
The data are made up of n observations on the dependent or response variable Y and p predictor or explanatory factors, XI, X2,..., Xp. The relationship between Y and XI, X2, . . . , Xp, is formulated as a linear model
where β0, β1, β2, . . . , βp,, are constants referred to as the model partial regression coefficients (or simply as the regression coeficients) and e is a random disturbance or error.
A generalization (extension) of simple linear regression is multiple linear regression. When the number of predictor variables p = 1, simple linear regression can be thought of as a special case of multiple regression because all simple linear regression findings can be derived using the multiple regression results.
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