Hyperplan in linear regression3/2/2023 The scatter plot of the two variables (dependent and independent variables) in a 2 dimensional space is as shown below:įrom the scatter plot above, we can see a fairly linear relationship between variable x and y i.e. Since m (the number of feature) is 1, the data can therefore be represented in a 2 dimensional space. Since the number of feature is 1, we can therefore represent this data in a m+1 dimensional space. For example, consider a randomly generated data with one independent variable x and dependent variable y as shown below: The “ +1” in the m+1 number of dimensions of the space mathematically represent the addition of the dependent variable as a dimension in the space. Independent variables are sometimes called features or attributes, while dependent variables are sometimes called target variables or labels (often used when the values are categorical). As a result, dependent variables depend on the independent variables. On the other hand, dependent variables are the variables we want to use the independent variables to predict. They are called independent variables because they can assume any values. Independent variables are variables we want to use to predict or model the dependent variable. Linear regression model is a type of supervised machine learning model because its variables can be broadly classified into categories. For example, a 2 dimensional plane is a hyperplane for a 3 dimensional space, while a 1 dimensional plane (a line) is a hyperplane for a 2 dimensional space. A hyperplane is a plane whose number of dimension is one less than its ambient space. Linear regression is a machine learning model that fits a hyperplane on data points in an m+1 dimensional space for a data with m number of features. In this article, I will be explaining linear regression in simple terms, and showing you how it is used to model data with a continuous response variable.
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