影响我国GDP增长的主要因素（数据分析方法与R软件）

一、问题的提出

经济增长是我国宏观经济政策的目标之一，研究影响经济增长的因素对促进我国经济快速发展有着十分重要的意义。本次实验运用R软件编写代码拟合多元线性回归模型、选择最优模型，最终进行区间预测，定性的研究影响我国经济增长的主要因素。

二、试验的设计与数据收集过程

三、数据的描述性分析

计算方差分析表：

由以上实验结果表明选择影响GDP增长的因素主要有进出口总额、 会消费品零售总额以及全 会固定资产投资。重新拟合最优模型：

五、结论与讨论

通过本次实验得到了影响GDP增长的各种因素构成的多元线性回归方程：y=-1887+0.5565×1+2.263×2-2.283×3。该回归方程的截距项是-1887，EM每增加一个单位会引起GDP增加0.557个单位，Consumption每增加一个单位引起GDP增长2.263个单位，Investment每增加一个单位会引起GDP减少0.228个单位。也就是说，为了促进我国经济的快速发展，可以扩大对外开放程度来增加进出口总额，可以采取刺激消费、适当的减少投资从而促进经济增长。同时此次试验也可以在一定程度上对2019年的GDP进行预测，更好的掌握经济动向。

六、参考文献

[1]范金城, 梅长林. 2002. 数据分析. 北京: 科学出版 .
[2]薛毅, 陈立萍. 2007. 统计建模与R软件. 北京: 科学出版 .
[3]王斌会. 2010. 多元统计分析与R语言建模. 广州: 暨南大学出版 .
[4]李素兰.2017. 数据分析与R软件（第二版）.北京: 科学出版 .

附件1：数据

附件2：代码

GDP<-c(4587.6,4935.8,5373.4,6020.9,7278.5,9098.9,10376.2,12174.6,15180.4,17179.7,18872.9,22005.6,27194.5,35673.2,48637.5,61339.9,71813.6,79715.0,85195.5,90564.4,100280.1,110863.1,121717.4,137422.0,161840.2,187318.9,219438.5,270092.3,319244.6,348517.7,412119.3,487940.2,538580.0,592963.2,641280.6,685992.9,740060.8,820754.3,900309.5)
EM<-c(570.00,735.34,771.37,860.15,1201.03,2066.71,2580.37,3084.16,3821.79,4155.92,5560.12,7225.75,9119.62,11271.02,20381.90,23499.94,24133.86,26967.24,26849.68,29896.23,39273.25,42183.62,51378.15,70483.45,95539.09,116921.77,140974.74,166924.07,179921.47,150648.06,201722.34,236401.95,244160.21,258168.89,264241.77,245502.93,243386.46,278099.24,305100.00)
MO<-c(346.20,396.34,439.12,529.78,792.11,987.83,1218.36,1454.48,2134.03,2344.02,2644.87,3177.80,4336.00,5864.70,7288.60,7885.34,8802.01,10177.61,11204.15,13455.50,14652.65,15688.80,17278.03,19745.99,21468.30,24031.67,27072.62,30334.32,30218.96,38245.97,44628.17,50748.46,54659.77,58574.44,60259.53,63216.58,68303.87,70645.60,73208.00)
Consumption<-c(2140.0,2350.0,2570.0,2849.4,3376.4,4305.0,4950.0,5820.0,7440.0,8101.4,8300.1,9415.6,10993.7,14270.4,18622.9,23613.8,28360.2,31252.9,33378.1,35647.9,39105.7,43055.4,48135.9,52516.3,59501.0,68352.6,79145.2,93571.6,114830.1,133048.2,158008.0,187205.8,214432.7,242842.8,271896.1,300930.8,332316.3,366261.6,380987.0)
Investment<-c(910.90,961.00,1230.40,1430.10,1832.90,2543.20,3120.60,3791.70,4753.80,4410.40,4517.00,5594.50,8080.10,13072.30,17042.10,20019.30,22913.50,24941.10,28406.20,29854.70,32917.73,37213.49,43499.91,55566.61,70477.40,88773.62,109998.20,137323.94,172828.40,224598.77,251683.77,311485.13,374694.74,446294.09,512020.65,561999.83,606465.66,641238.40,635636.00)

summarize <- function(x){
n <- length(x)
m <- mean(x)
v <- var(x)
s <- sd(x)
me <- median(x)
cv <- 100s/m
css <- sum((x-m)^2)
uss <- sum(x^2)
R <- max(x)-min(x)
R1 <- quantile(x,3/4)-quantile(x,1/4)
M3=quantile(x,1/4)(1/4)+me*(1/2)+ quantile(x,3/4)(1/4)
g1 <- n/((n-1)(n-2))sum((x-m)^3)/s3
g2 <- ((n(n+1))/((n-1)(n-2)(n-3))sum((x-m)^4)/s4- (3(n-1)^2)/((n-2)*(n-3)))
data.frame(N=n, Mean=m, Var=v, std_dev=s,Median=me, CV=cv, CSS=css, USS=uss,M3=M3,R=R, R1=R1, Skewness=g1, Kurtosis=g2, row.names=1)
}

data=data.frame(GDP=GDP,EM=EM,MO=MO,Consumption=Consumption,Investment=Investment)
data

cor(data)

scatterplotMatrix(data,spread=FALSE,main=“Scatter Plot Matrix via car package”)

fit<-lm(GDP~EM+MO+Consumption+Investment)
fit

summary(fit)

anova(fit)

par(mfrow=c(2,2))
plot(fit)
fit1<-lm(GDP~EM+MO+Consumption+Investment,data=data)
fit2<-lm(GDP~EM+Consumption+Investment,data=data)
fit3<-lm(GDP~Consumption+Investment,data=data)
fit4<-lm(GDP~Consumption,data=data)
AIC(fit1,fit2,fit3,fit4)

fitter<-lm(GDP~EM+Consumption+Investment,data=data)
summary(fitter)

coefficients(fitter)

ARsqured<-summary(fitter)$adj.r.squared
ARsqured

plot(GDP~EM)
abline(lm(GDP~EM))
plot(GDP~Consumption)
abline(lm(GDP~Consumption))
plot(GDP~Investment)
abline(lm(GDP~Investment))

resid<-residuals(fitter)
stdresid<-rstandard(fitter)
GDP.pre<-predict(fitter)
plot(GDP.pre,resid)
plot(GDP.pre,stdresid)
plot(fitter,2)

new<-data.frame(EM=(335000.00),Consumption=c(400000.0),Investment=c(655000.00))
lm.pred<-predict(fitter,new,interval=“prediction”,level=0.95)
lm.pred