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对回归分析进行参数估计时，有三种估计方法，最小二乘法（OLS， ordinary least squares），广义矩估计（GMM， general moment method）以及最大似然估计（MLE, maximum likelihood estimation），最为常用的方法即是最小二乘法，即采用的是高斯马尔科夫定理。
参考伍德里奇的计量经济学导论，但在采用最小二乘法进行估计时，针对SLR（一元线性回归），其变量需要满足如下的条件假设
模型的线性
Assumption SLR.1 (LINEAR IN PARAMETERS)
In the population model, the dependent variable y is related to the independent variable x and the error (or disturbance) u as
where  and  are the population intercept and slope parameters, respectively.
变量的随机性
Assumption SLR.2 (RANDOM SAMPLING)
We can use a random sample of size%3A%20i%20%3D1%2C2%2C%E2%80%A6%2Cn%7D) , from the population model.
零条件均值假设
Assumption SLR.3 (ZERO CONDITIONAL MEAN)
%20%3D%200)
自变量方差不为零
Assumption SLR.4 (SAMPLE VARIATION IN THE INDEPENDENT VARIABLE)
In the sample, the independent variables  , are not all equal to the same constant. This requires some variation in x in the population.
而如果进行的是 MLR（多元线性回归），其假设条件为：
模型的线性
Assumption MLR.1 (LINEAR IN PARAMETERS)
The model in the population can be written as
where  are are the unknown parameters (constants) of interest, and u is an unobservable random error or random disturbance term.
变量的随机性
Assumption MLR.2 (RANDOM SAMPLING)
We have a random sample of n observations, %3A%20i%20%3D1%2C2%2C%E2%80%A6%2Cn%7D) , from the population model described by (3.31).
零条件均值假设
Assumption MLR.3 (ZERO CONDITIONAL MEAN)
The error  has an expected value of zero, given any values of the independent variables. In other words,
%20%3D%200)
变量无完美共线性
Assumption MLR.4 (NO PERFECT COLLINEARITY )
In the sample (and therefore in the population), none of the independent variables is constant, and there are no exact linear relationships among the independent variables.
方差齐性
Assumption MLR.5 (HOMOSKEDASTICITY)
%20%3D%20%5Csigma%5E2)
6.正态性
Assumption MLR.6 (NORMALITY)
The population error is independent of the explanatory variables  and is normally distributed with zero mean and variance  : u ~ Normal(0, )
以上是对模型运用中的基本假设进行解读，具体到应用中，涉及到回归模型的诊断、统计检验、绘图及模型解释可以参考文章回归分析诊断、统计检验、绘图及模型解释。
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