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 = wx
where the variance of Y is assumed to be constant, and b and w are regression coefficients specifying the Y-intercept and slope of the line, respectively. the regression coefficients, w, and b can also be thought of as weight so that we can equivalently write,
y = w0 + w1x
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. Let D be a training set consisting of values of a predictor variable, x, for some population, and their associated values for the response variable,y. The training set contains |D|data points of the form (x1,y1), (x2,y2),............,(x|D|,y|D|). The regression coefficients can be estimated using this method with the following equations-
Multiple linear regression is 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, say, n predictor variables or attributes, A1, A2......., An, describing a tuple, X. Our training data set, D, contains data of the form (X1,y1),(X2,y2),...........(X|D|,y|D), where the Xi are the n-dimensional training tuples with associated class labels, Yi. An example of a multiple linear regression model based on two predictor attributes or variables, A1 and A2 is
y = w0 + w1x1 + w2x2,
Where x1 and x2 are the values of attributes A1 and A2, respectively, in X
y = wx
where the variance of Y is assumed to be constant, and b and w are regression coefficients specifying the Y-intercept and slope of the line, respectively. the regression coefficients, w, and b can also be thought of as weight so that we can equivalently write,
y = w0 + w1x
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. Let D be a training set consisting of values of a predictor variable, x, for some population, and their associated values for the response variable,y. The training set contains |D|data points of the form (x1,y1), (x2,y2),............,(x|D|,y|D|). The regression coefficients can be estimated using this method with the following equations-
y = w0 + w1x1 + w2x2,
Where x1 and x2 are the values of attributes A1 and A2, respectively, in X
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