what is the simple linear regression equation

So, this is the finally derived Normal Equation with θ giving the minimum cost value. So, now getting the value of θ using the partial derivative In fact, everything you know about the simple linear regression modeling extends (with a slight modification) to the multiple linear regression models. It is used to show the relationship between one dependent variable and two or more independent variables. So to get the squared value, multiply the vector/matrix with its transpose. Multiple linear regression model is the most popular type of linear regression analysis. As the square of a vector/matrix is not equal to the square of each of its values. We cannot simply square the above expression. X i j: value of j ih feature in i ih training example.īut each residual value is squared. It was used for mathematical convenience while calculating gradient descent. We have ignored 1/2m here as it will not make any difference in the working. Let us represent the cost function in a vector form. Y i: the expected result of i th instance X i: the input value of i ih training example. The motive in Linear Regression is to minimize the cost function: So for the convenience to solve we can write it as: Notice that this is a dot product between θ and x values.

Θ: hypothesis parameters that define it the best. So, in Normal Equation method, we get the minimum value of the Cost function by finding its partial derivative w.r.t to each weight and equating it to zero. Following this approach is an effective and time-saving option when working with a dataset with small features. Normal Equation method is based on the mathematical concept of Maxima & Minima in which the derivative and partial derivative of any function would be zero at the minima and maxima point. We can directly find out the value of θ without using Gradient Descent. Normal Equation is an analytical approach to Linear Regression with a Least Square Cost Function. Decision Tree Introduction with example.Removing stop words with NLTK in Python.Regression and Classification | Supervised Machine Learning.Basic Concept of Classification (Data Mining).Gradient Descent algorithm and its variants.ML | Momentum-based Gradient Optimizer introduction.Optimization techniques for Gradient Descent.ML | Mini-Batch Gradient Descent with Python.Difference between Batch Gradient Descent and Stochastic Gradient Descent.Difference between Gradient descent and Normal equation.ML | Normal Equation in Linear Regression.Mathematical explanation for Linear Regression working.Linear Regression (Python Implementation).

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What is the simple linear regression equation