Regression: Regression can be used to smooth the data by fitting the data to a function.
Linear regression involves finding the “best” line to fit two attributes (or variables), so that one attribute can be used to predict the other.
- 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 areregression 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:
- 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 .