单词	regression analysis
释义	regression analysis(least-squares method) A method for calculating the best straight line for a linear equation with two variables x and y, for which x can be measured accurately and y has a random error associated with its measurement. The linear equation is written in the form y = α + ßx , where α and ß are constants. The error is associated with a mean (see average) and variance. For a given xi, the true value of yi is given by yi = α + ßxi . The measured value Yi of yi is given by Yi = yi + εii , where εii is a random error. The relation between x and y is a straight line together with a random error. If the line y = a + bx is considered then the quantity di = a + bxi - Yi is the difference between the value of yi on the line at xi and Yi. The method of least squares is used to find a and b, which minimize S, defined by This is done using partial derivatives. b is given by: where x̄ and ȳ denote the mean values. a can be worked out from b by a = ȳ - bx̄ . The line y = a + bx , with the values of a and b obtained by the method of least squares, is called the regression line
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