伍德里奇计量经济学英文版第三版中关于回归模型交叉项引入的说明：其实就是因为一个变量固定的时候，其对因变量的影响还要与另外一个自变量有关。比如出行费用对出行方式选择行为的影响，还和人的收入水平有关系。以下为原文（pp207-209）

Models with Interaction Terms

Sometimes, it is natural for the partial effect, elasticity, or semi-elasticity of the dependent

variable with respect to an explanatory variable to depend on the magnitude of yet another explanatory variable. For example, in the model

the partial effect of bdrms on price (holding all other variables fixed) is(6.17)

If<IMG alt="beta{}_3{} , then (6.17) implies that an additional bedroom yields a higher increase in hous-

ing price for larger houses. In other words, there is an interaction effect between square

footage and number of bedrooms. In summarizing the effect of bdrms on price, we must

evaluate (6.17) at interesting values of sqrft, such as the mean value, or the lower and upper quartiles in the sample. Whether or not <IMG alt="beta{}_3{} is zero is something we can easily test.

The parameters on the original variables can be tricky to interpret when we include an

Interaction term.  For example, in the previous housing price equation, equation  (6.17)

shows that  is the effect of bdrms on price for a price with zero square feet! This effect is clearly not of much interest. Instead, we must be careful to put interesting values of sqrft, such as the mean or median values in the sample, into the estimated version of equation (6.17).

Often, it is useful to reparameterize a model so that the coefficients on the original variables have an interesting meaning. Consider a model with two explanatory variables and an interaction:

As just mentioned, is the partial effect of on  when . Often, this is not of

interest. Instead, we can reparameterize the model as

Where is the population mean of and  is the population mean of  . We can easily see that now the coefficient on  , , is the partial effect of  on at the mean value of . (By multiplying out the interaction in the second equation and comparing the coefficients, we can easily show that (此公式有错，该死的科学网公式编辑器) . The parameter has a similar interpretation.) Therefore, if we subtract the means of the variables—in practice, these would typically be the sample means—before creating the interaction term, the coefficients on the original variables have a useful interpretation. Plus, we immediately obtain standard errors for the partial effects at the mean values. Nothing prevents us from replacing  or  with other values of the explanatory variables that may be of interest. The following example illustrates how we can use interaction terms.