Parish R C
Department of Pharmacy Practice, College of Pharmacy, University of Georgia, Athens 30602.
DICP. 1989 Nov;23(11):891-98. doi: 10.1177/106002808902301111.
Five common linear regression methods were evaluated for their ability to determine the correct values of slope and intercept of a known function after random errors were added to x and y. The error variances were controlled to simulate research problems commonly studied by linear regression. The total error of each method was assessed by the absolute value of the bias in the estimate of slope. Whenever differences among methods were observed, the mean of the slope determined by two reciprocal techniques performed as well as or better than orthogonal regression, regression of y upon x, or x upon y. All the methods studied appeared to perform equally well when x and y errors were heteroscedastic or when the data set was small (n = 7). Regression of y upon x was equal or superior to other methods when n = 7 or n = 20 and y and x errors were homoscedastic. When the data set was large (n = 50) and the error in x greater than that in y, the standard method (regression of y upon x) was inferior to all other methods. It is suggested that linear regression by the traditional method of y upon x (a method present in many hand-held calculators) is appropriate in the majority of clinical situations, but when n is large and errors in x are much larger than those in y, orthogonal regression or the averaging method may be preferable.
对五种常见的线性回归方法进行了评估，以确定在x和y中添加随机误差后，它们确定已知函数斜率和截距正确值的能力。控制误差方差以模拟线性回归通常研究的研究问题。通过斜率估计偏差的绝对值评估每种方法的总误差。每当观察到方法之间的差异时，由两种倒数技术确定的斜率均值与正交回归、y对x的回归或x对y的回归表现得一样好或更好。当x和y误差为异方差或数据集较小时（n = 7），所有研究的方法似乎表现同样良好。当n = 7或n = 20且y和x误差为同方差时，y对x的回归等于或优于其他方法。当数据集较大（n = 50）且x中的误差大于y中的误差时，标准方法（y对x的回归）不如所有其他方法。建议在大多数临床情况下，采用传统的y对x的方法进行线性回归（许多手持计算器中都有的一种方法）是合适的，但当n较大且x中的误差远大于y中的误差时，正交回归或平均方法可能更可取。
