Multiple Regression Analysis
Multiple Regression Analysis
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DOI：
10.1007/978-3-642-03383-4_4
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发表时间：
2019-12
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影响因子：
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通讯作者：
B. Baltagi
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作者：
B. Baltagi
到目前为止，除了回归方程中的常量外，我们只考虑了一个回归方程X。经济关系通常包括不止一个回归因素。例如，一种产品的需求方程通常会包括该产品的实际价格，以及竞争产品的实际价格和该产品的广告支出。在这种情况下，$$Y_i=\α+\beta_2 X_{2i}+\beta_3 X_{3i}+..+\beta_K X_{ki}+u_i\quad i=1，2，ldots，n$$其中Y表示对因变量Y的第1次观察，在这种情况下表示该产品的销售额。X表示对自变量Xkfork=2，…的第1次观察，在这种情况下，是自己的价格，竞争对手的价格和广告支出。α是截取，β2，β3，…，βK为(K−1)斜率系数。Theui满足第三章中给出的经典假设1-4。假设4被修改为包括回归中出现的所有X，即每个Xkfork=2，‘，K，与定理ui无关，具有以下性质：$$\sum\NoLimits^{n}_{i=1}(X_{ki}-\bar{X}_k)^2/n\\Hbox{where}\\bar{X}_k=\sum\NoLimits^{n}_{i=1}X_{ki}/n$$具有不为零的有限概率极限。
So far we have considered only one regressorXbesides the constant in the regression equation. Economic relationships usually include more than one regressor. For example, a demand equation for a product will usually include real price of that product in addition to real income as well as real price of a competitive product and the advertising expenditures on this product. In this case $$Y_i = \alpha + \beta_2 X_{2i} + \beta_3 X_{3i} + .. + \beta_K X_{Ki} + u_i \quad i= 1,2, \ldots, n$$ whereYidenotes thei-th observation on the dependent variableY, in this case the sales of this product.Xkidenotes thei-th observation on the independent variableXkfork= 2, … ,Kin this case, own price, the competitor’s price and advertising expenditures.αis the intercept andβ2,β3, … ,βKare the (K− 1) slope coefficients. Theui’s satisfy the classical assumptions 1–4 given in Chapter 3. Assumption 4 is modified to include all theX’s appearing in the regression, i.e., everyXkfork= 2, ’ ,K, is uncorrelated with theui’s with the property that $$\sum\nolimits^{n}_{i=1} (X_{ki} - \bar{X}_k)^2/n \ \hbox{where} \ \bar{X}_k = \sum\nolimits^{n}_{i=1} X_{ki}/n$$ has a finite probability limit which is different from zero.