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Write a short note on linear regression.
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Linear regression involves finding the “best” line to fit two attributes (or variables), so that one attribute can be used to predict the other.

Linear Regression

1. Straight-line regression:

• Straight-line regression analysis involves a response variable, y, and a single predictor variable, x.
• It is the simplest form of regression, and models y as a linear function of x.
• That is, y = b+wx;

where the variance of y is assumed to be constant,

band w are regression coefficients specifying the Y-intercept and slope of the line, respectively. - These coefficients can be solved by the method of least squares, which estimates the best-fitting straight line as the one that minimizes the error between the actual data and the estimate of the line. - The regression coefficients can be estimated using this method with the following equations:

2. Multiple linear regression:

• Multiple linear regressionis an extension of straight-line regression so as to involve more than one predictor variable.
• It allows response variable y to be modeled as a linear function of n predictor variables or attributes.
• The equations(obtained from the method of least squares ), become long and are tedious to solve by hand.
• Multiple regression problems are instead commonly solved with the use of statistical software packages, such as SAS, SPSS, and S-Plus
• Speed and Scalability: Time to construct the model and also time to use the model.
• Robustness: This is the ability of the classifier to make correct predictions given noisy data or data with missing values
• Scalability: This refers to the ability to construct the classifier efficiently given large amounts of data.
• Interpretability: This refers to the level of understanding and insight that is provided by the classifier
• Goodness of rules: Decision tree size compactness of classification rules.