Lecture Note
University
Stanford UniversityCourse
CS229 | Machine LearningPages
2
Academic year
2023
anon
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47
Multiple Features' Inο¬uence on Linear Regression Data scientists can utilize the potent tool of linear regression to forecast the connectionbetween a dependent variable and one or more independent variables. The original form oflinear regression, however, only takes one independent variable into account, which canmake it harder to forecast the dependent variable with precision. This is where linearregression can beneο¬t from using several characteristics. We can acquire a more thorough understanding of the link between the dependent variableand these independent factors, improving prediction accuracy, by integrating severalindependent variables in the regression analysis. This article will examine how and why it isadvantageous to add several characteristics into linear regression. Multiple Features in Linear Regression Notation When linear regression was ο¬rst developed, the model was written as , π π€,π (π₯) = π€π₯ + π where x stood for the size of the house and was used to forecast its price. The notation usedin linear regression alters when there are many characteristics. To keep things simple, we refer to the four features as , , , and . The total number of π 1 π 2 π 3 π 4 features is denoted by the lowercase n, which in this case is equal to 4. A list of fournumbers or a vector that contains all the attributes of the ith training example is used torepresent the ith training example, which is denoted as . π π In the ith training example, we write , where j ranges from one to four, to refer to a given π (π,π) feature. For instance, in the second training example, represents the value of the third π (2,3) feature, the number of storeys. The Linear Regression Model with Multiple Features The linear regression model is speciο¬ed differently from its basic form when manycharacteristics are present. is the deο¬nition of the π π€,π (π₯) = π€ 1 π₯ 1 + π€ 2 π₯ 2 + π€ 3 π₯ 3 + π€ 4 π₯ 4 + π new model. One such model, for instance, may be that the price of the property is calculated as beingequal to 0.1 times the size of the house, 0.05 times the number of bedrooms, 0.03 times thenumber of storeys, and 0.02 times the age of the home, plus a constant b. We may better understand the link between the dependent variable and these factors byincluding a variety of features in the model, which will enable us to make predictions that aremore accurate.
Multiple Features' Favorable Effects in Linear Regression Using numerous features in linear regression has a number of beneο¬ts, such as: Increased Prediction Accuracy: By including several independent factors in the regressionanalysis, we can acquire a deeper understanding of the connections between the dependentvariable and these independent variables, increasing the precision of our predictions. Having several features allows us to better understand the relationships between thevariables, including which ones have the biggest effects on the dependent variable and howthey interact. This may help to clarify how the variables are related to one another. Better Handling of Complex Data: Linear regression can handle complex data, such as datawith non-linear connections or data with several confounding variables, better when it hasmultiple features. Improved Model Interpretability: When a linear regression model has numerous features, it issimpler to understand because it is clear how each feature affects the prediction of thedependent variable.
Multiple Features' Influence on Linear Regression
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