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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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更新时间:2025/6/23 3:34:37