Lecture Note
University
Stanford UniversityCourse
CS229 | Machine LearningPages
2
Academic year
2023
anon
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21
A Guide to Non-Linear Data Modeling: UnderstandingPolynomial Regression A common statistical technique for determining the relationship between a dependentvariable and one or more independent variables is linear regression. The relationshipbetween variables, however, may not always be linear. Polynomial regression is advised incertain circumstances. In this post, we'll go through polynomial regression's deﬁnition,beneﬁts, and practical implementation. Polynomial Regression: What Is It? Regression analysis that analyzes the link between the dependent variable and one or moreindependent variables is known as polynomial regression. Polynomial regression and linearregression vary in that the independent variable in the former is changed into a polynomialfunction of one or more degrees. In contrast to linear regression, which ﬁts data to a straightline, this enables us to ﬁt a curve, or nonlinear functions, to our data. Consider the following home dataset as an illustration, where feature x represents size insquare feet. A straight line might not adequately match the dataset in this situation. In suchcases, the data can be ﬁtted to a curve, such a quadratic function. Size x and size squared,
which is size raised to the power of two, are both components of a quadratic function. Youmay be able to obtain a signiﬁcantly better model for your data by utilizing polynomialregression. Polynomial Regression's beneﬁts When compared to linear regression, polynomial regression has a number of beneﬁts.Among them are: 1. Flexibility: When modeling the relationship between variables, polynomial regression offers more ﬂexibility. You can use it to record non-linear correlationsbetween variables and ﬁt curves to your data. 2. Accuracy gain: When there is a non-linear relationship between the variables, polynomial regression can produce results that are more accurate than those oflinear regression. 3. Simplicity: When compared to other sophisticated regression techniques, polynomial regression is quite straightforward to use and comprehend. Application of Polynomial Regression Polynomial regression is simple to implement and may be done in a few stages. Here is adetailed procedure for carrying out polynomial regression: 1. Preprocessing: The data must ﬁrst be cleaned and transformed as the ﬁrst stage in the preprocessing process. This entails handling outliers, ﬁlling in any missingvalues, and normalizing the features. 2. In this stage of feature engineering, you must turn the independent variable into a polynomial function with one or more degrees. For instance, if the independentvariable is size, you can square it, cube it, and so forth. 3. Model construction: Using the converted data, the model construction process is the following step. To develop the model, you can use a variety of algorithms, includingsupport vector machines, decision trees, and linear regression. 4. Evaluation of the model: The model's performance is assessed in the ﬁnal stage using metrics like mean squared error, R-squared, or adjusted R-squared.
Non-Linear Data Modeling: Understanding Polynomial Regression
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