The goal in any data analysis is to extract from raw information the accurate estimation. One of the most important and common questions concerning is if there is a statistical relationship between a response variable (Y) and explanatory variables (Xi). An option to answer this question is to employ regression analysis in order to model its relationship.

Multiple linear regression is used to determine a mathematical relationship among a number of random variables. In other terms, it examines how multiple independent variables are related to one dependent variable.

Uses

Once each of the independent factors has been determined to predict the dependent variable, the information on the multiple variables can be used to create an accurate prediction on the level of effect they have on the outcome variable.

Interpretation

Yi=β0+β1Xi1+β2Xi2+...+βpXip+ϵ

where, for i=n observations

Yi=dependent variable

Xi=explanatory variables

β0=y-intercept (constant term)

βp=slope coefficients for each explanatory variable

ϵ=the model’s error term (also known as the residuals)

Example

The sugars in the body (dependent variable) depends on many factors like

lifestyle(food,exercise.etc) ,stress and hereditary(independent variables).We can use a Multi linear regression model to build the quantitative relation between these variables and predict the amount of sugars in the body.

Conclusion

Though there are chances for false conclusions,Multi linear regression is widely used for its two main advantages of being able to find the relative influence of predictor variables to criterion value and being able to identify anomalies.

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