Yishuo School District (31) | SPSS Statistical Analysis (41) Curve Regression Analysis
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上一期，我们一起来学习了如何进行多元回归分析，在实际问题中，如果变量间的关系是非线性的，那么问题就要复杂得多。变量之间的非线性关系可以划分为本质线性关系和本质非线性关系。
所谓的本质线性关系是指，变量关系形式上虽然呈非线性关系（如二次曲线），但可以通过变量变换化为线性关系，并可最终通过线性回归分析建立线性模型。本质非线性关系是指，变量关系不仅形式上呈非线性关系，而且也无法通过变量变换化为线性关系，最终无法通过线性回归分析建立线性模型。
In the last issue，we learned how to conduct multiple regression analysis. In practical problems，spss曲线回归分析结果解释，if the relationship between variables is nonlinear，the problem is much more complex. The nonlinear relationship between variables can be divided into essential linear relationship and essential nonlinear relationship.
The so-called essential linear relationship means that although the variable relationship is nonlinear in form (such as a quadratic curve)，it can be transformed into a linear relationship through variable transformation，and finally a linear model can be established through linear regression analysis. The essence of nonlinear relationship refers to that the variable relationship is not only nonlinear in form，but also cannot be transformed into linear relationship through variable transformation，and ultimately cannot establish a linear model through linear regression analysis.
在实际问题中，用户往往不能确定究竟何种函数模型更接近样本数据，在SPSS中进行曲线估计的一般步骤如下：
第二个表Anova表示方差分析结果，主要看F和sig值两个，F值为方差分析的结果，是一个对整个回归方程的总体检验，指的是整个回归方程有没有使用价值（与随机瞎猜相比），其F值对应的Sig值小于0.05就可以认为回归方程是有用的。
首先，根据实际问题的特点，在多种可选择的模型中选择几种；其次，SPSS自动完成模型参数的估计，并输出回归方程显著性检验的F值和概率P值、决定系数R方等统计量；最后，以决定系数为主要依据选择其中的最优模型（R方最大），并进行预测操作。
In practical problems，users often cannot determine which function model is closer to the sample data. The general steps for curve estimation in SPSS are as follows:
First of all，according to the characteristics of the actual problem，select several models from a variety of choices; Secondly，SPSS automatically completes the estimation of model parameters，and outputs statistics such as F value，probability P value and determination coefficient R square of regression equation significance test; Finally，the optimal model (R maximum) is selected based on the determination coefficient，and the prediction operation is carried out.
实例训练
分析X的显著性（P值），如果呈现出显著性，则说明X对Y有影响关系。如果不显著，则应剔除该变量。第三步：判断X对Y的影响关系方向及影响程度 结合回归系数B值，对比分析X对Y的影响程度。B值为正数则说明X对Y有正向影响。
接下来，我们进入一个实际案例，下图是1989年~2001年国家保费收入与国内生产总值的数据，试研究保费收入与国内生产总值的关系。
Next，let's enter into an actual case. The figure below shows the data of national premium income and GDP from 1989 to 2001. Try to study the relationship between premium income and GDP.
分析
The first step is analysis. First，analyze in the form of scatter chart to see whether there is a linear relationship of one variable. If there is a linear relationship of one variable，use a linear regression analysis of one variable，otherwise use curve estimation to solve.
组织数据
Step 2: organize data，define three variables，namely &34;，&34; (premium income) and &34; (gross domestic product)，enter data and save them.
作出散点图，初步判定变量的分布趋势
从下图可以看出，保费收入y随国内生产总值x的提高而逐渐提高，而且当国内生产总值达到一定的水平过后，保费收入的增幅则更加明显。因此用线性回归模型表示x，y的关系是不恰当的。应该去找拟合效果更好的模型。
The third step is to make a scatter chart to preliminarily determine the distribution trend of variables. It can be seen from the figure below that the premium income y gradually increases with the increase of GDP x，and when the GDP reaches a certain level，the increase of premium income is more obvious. Therefore，it is inappropriate to express the relationship between x and y with linear regression model. We should find a better fitting model.
T值就是对回归系数的t检验的结果，绝对值越大，sig就越小，sig代表t检验的显著性，在统计学上，sig<0.05一般被认为是系数检验显著，显著的意思就是你的回归系数的绝对值显著大于0，表明自变量可以有效预测因变量的变异，。
进行曲线回归
选择菜单“分析->回归->曲线估算”，将所有模型都选上，按下图进行设置，看运行结果中哪些模型的拟合效果更好。
The fourth step is curve regression. Select the menu &34;，select all models，and set them according to the following figure to see which models have better fitting effect in the running results.
From the determination coefficient (R square)，the cubic curve is the best，and the significance probability value of ANOVA is 0，so repeat the above process，and only select the &34; model.
主要结果及其分析
下图是对三次曲线模型的摘要及参数估算值表，决定系数R方=0.990，且显著性概率值为0.000，故可判断保费收入与国内生产总值之间有较显著的三次曲线关系。
下期预告：本期，我们学习了
曲线回归分析的实践操作。
下一期，我们将会学习
关于非线性回归分析的问题。
Preview of the next issue: In this issue，we learned the practical operation of curve regression analysis. In the next issue，we will learn about nonlinear regression analysis.
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让我们相约明天
看回归系数对应的sig值，若小于0.05，说明该自变量对因变量具有显著营销，反之没有影响。在统计学中，回归分析（regression analysis)指的是确定两种或两种以上变量间相互依赖的定量关系的一种统计分析方法。回归分析按照涉及的。
祝您今天过得开心快乐！
翻译：百度翻译
