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
whereand
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, from the population model.
- 零条件均值假设
Assumption SLR.3 (ZERO CONDITIONAL MEAN)
- 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
whereare 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,, from the population model described by (3.31).
- 零条件均值假设
Assumption MLR.3 (ZERO CONDITIONAL MEAN)
The errorhas an expected value of zero, given any values of the independent variables. In other words,
- 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)
6.正态性
Assumption MLR.6 (NORMALITY)
The population errorand 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。
