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Essay代写范文-婴儿死亡率与人均GDP和人均公共支出的关系

发布于:2021-01-21 作者:留学写作网 阅读:763

统计学一直都是很多文科生最厌恶的课程之一,统计涉及建模和计算,又需要大家学习一些专业的统计分析软件,比如SPSS和Eviews。即便通过计算得到了一些关键数据,如何对这些数据进行分析也困扰着一部分的同学。但是,无论你是否在国内系统学习过统计课程,对于大部分留学生而言都需要掌握一些基本的统计知识,以便应付日常的作业以及最最重要的dissertation。

今天就来讲解一篇统计学essay,为了让基础不太扎实的同学能够更好的理解,本篇范文的难度不是太高,但却包含了一篇完整的统计学essay需要涉猎的全部内容。对于大多数非统计学专业的学生而言,这篇范文就已经足够应付大部分的assignment了。

首先,本篇范文研究的主题是婴儿死亡率,人均GDP和人均公共支出这几个变量之间的关系。很多的研究结果显示,一个国家的婴儿死亡率和该国的GDP总量,人均GDP以及政府在公共卫生和教育方面的支出有着直接的关系。

我们事先已经得到了印度从1960年至1990年相关变量的数据,通过一系列的统计计算和分析,我们可以验证多个假想(hypotheses):分别是婴儿死亡率是否如我们预想的一样和印度的人均GDP,人均教育支出和人均卫生支出负相关。

在本文中我们将给大家介绍一些统计学的基础概念,比如因变量 dependent variable和 independent variables(自变量),以及我们该如何通过这些变量来建立基础的统计模型以及构建各种学术上的hypothesis。

统计学的基础概念

第一部分大致介绍了全文的结构,然后提出本篇statistical essay中会用到的一个dependent variable和三个independent variables,以及根据这些变量所建立的回归模型。

1. Introduction

The paper chooses to analyze is “The Relationship between Infant Mortality, Income and Public Expenditures in India from 1960 to 1990”. In this project, we will conduct an empirical analysis to examine whether infant mortality is statistically related to multiple variables of per capita GPD, health expenditures per capita and educational expenditures per capita. 

The paper first describes depend and independent variables and the regression model that will be used to test hypotheses. Section 2 and 3 explain the descriptive statistics and the correlation coefficients of all parameters. Section 4 explains the statistic results of the basic regression model. 

Specifically, this part explains whether two independent variables, GDPPC and HEXPPC, are positively or negatively related to the dependent variable and assess whether these results are statistically significant. Section 4 provides an analysis of the degree of the basic regression model explains the variation in infant mortality rate. In section 5, another independent variable EDUCPC will be added to the basic model to examine whether this parameter is related to the dependent variable. 

One dependent variable, infant mortality (IMR), and three independent variables, per capita GPD (GDPPC), health expenditures per capita (HEXPPC) and educational expenditures per capita (EDUCPC), are used by this paper to conduct an empirical analysis. 

Many previous research outcomes suggest there is a strong negative correlation between infant mortality rate and gross national income percapita (Hanmer & White (2001); Kitsch & Linden, 2016). However, the results of whether health spending has a strong correlation with infant mortality rate remains inconclusive. 

Mendia & Ichihashi (2007) and Hanmer, Evens,& White (2008) indicate that there is no strong and direct relationship between health spending and infant mortality. Other research findings contend unless health spending budgets are spent efficiently, the increase of a country’s health spending doesn’t affect its infant mortality rate. 

The research evidence of Fang et al. (2013) suggests that the growth of government health expenditure leads to a significant decrease ininfant mortality rate. The relationship between educational expenditures and the infant mortality rate is more elusive. Thomason (2015) points out that the increase in educational expenditures doesn’t exhibit a strong correlation with infantmortality rate. 

Meanwhile, Genowska et al.(2017) contend that mothers’ educational level can be an influential determinant of infant mortality. To shed more lights on this issue, this paper will try to apply an empirical study to evaluate the relationship of different variables. Therefore, the major research question of this paper is to examine the possible links between infant mortality rate and public expenditures. To investigate this proposition, the regression model can be defined as follow:

IMRt =α + β1GDPPCt+ β2HEXPPCt +β3EDUCPCt +ut

第二部分是针对四个主要变量的描述性统计分析

2. Descriptive Statistics

Table 1: Descriptive Statistic Results

Table 1: Descriptive Statistic Results

Table 1 demonstrates descriptive statistics for both dependent and independent variables in the regression model assessing the relationship among various infant mortality determinants. During the period from 1960 to 1990, India’s infant mortality rate has gradually declined with a mean value of 53.629 while the median figure of IMR is also hovering around 54. 

The standard deviation of IMR is 12.425, indicating IMR fluctuates rather substantially during the period. The mode value of IMR suggests 53 is the most frequently appeared IMR figure from 1960 to 1990. India’s per capita GDP has progressively improved during the three decades with a mean value of 751.132. 

GDPPC has a standard deviation of 122.362 which suggests India’s per capita GDP significantly varied. The sample figures of GDPPC during the observation years are largely dispersed. As for the variable of health expenditures per capita, statistics show a relatively stable picture.

Mean, mode and median values of HEXPPC indicate that compare to the noticeable improvement of GDPPC, the public health budgets didn’t proportionally increase from 1960 to 1990.  The standard deviation of HEXPPC is 1.976 indicating samples are closely spread out from the mean. 

Another public expenditure item, educational expenditures, displaces a moderately different situation. There was an indication that India increased its educational expenditures more significantly than its health expenditures. The standard deviation of EDUCPC reflects this phenomenon. However, the raise of EDUCPC still largely lags behind the enhancement of GDPPC. Both GDPPC and EDUCPC have no mode value suggesting no figure frequently appeared in the period.

第三部分是对各个变量进行的相关性系数分析

3. Correlations

Figure 1: Scatter plot of IMR and GDPPC

Figure 1: Scatter plot of IMR and GDPPC

Figure 2: Scatter plot of IMR and HEXPPC

Figure 2: Scatter plot of IMR and HEXPPC

Figure 3: Scatter plot of IMR and EDUCPC

Figure 3: Scatter plot of IMR and EDUCPC

Figure 1 illustrates the tendency that with the increase of per capita GDP the infant mortality rate decreases accordingly. The scatter plot between IMR and GDPPC shows a negative relationship between these two variables. 

Nevertheless, figure 2 and figure 3 which demonstrated two pairs of variables of IMR and HEXPPC and IMR and EDUCPC does not display a definitive positive or negative correlation. Even though, we still can identify a relatively negative tendency between the infant mortality rate and two public expenditure items.

Table 2: Correlation coefficients between IMR and GDPPC, HEXPPC and EDUCPC

Table 2: Correlation coefficients between IMR and GDPPC, HEXPPC and EDUCPC

Table 2 presents the correlation coefficients of all the dependent and independent variables. This table also displays the results of the calculated significance of each pair of correlation coefficients. The statistical results of three pairs of correlation between dependent variable IMR and independent variables GDPPC, HEXPPC and EDUCPC are -0.866, -0.781 and -0.770 respectively. 

The outcomes suggest a strong negative correlation between infant mortality rate and each chosen independent variable. After testing the statistical significance of each correlation coefficient, the statistics are 4.29948E-10, 2.1553E-07 and 4.08928E-07 respectively, meaning three pairs of correlation coefficients are extremely close to zero and thereby all statistically significant.

回归模型

在第四部分中,我们先使用两个independent variables(自变量):GDPPC(人均GDP)和 HEXPPC(人均健康支出)来建立第一个基础版的回归模型,并且根据这两个变量提出两个hypotheses,然后把通过回归分析所得到的数据进行分析已检验我们所提出的两个假想是否成立。

4. Regression Model and Empirical Results

The basic model contains one dependent variable IMRt and two independent variables GDPPCt and HEXPPCt, then the regression model can be defined as:

IMRt =α + β1GDPPCt+ β2HEXPPCt +ut

Where IMR represents infant mortality rate, GDPPC represents gross domestic product per capita, HEXPPC indicates health expenditures per capita. Based on the definition of variables and the simple literature review presented in section 1, this paper formulates two hypotheses for this model. 

First, we assume that IMR and GPD per capita should be negatively related. Next, we hypothesize that IMR and health expenditures per capita are negatively related as well.

H1:There is a negative association between infant mortality rate and per capita GPD.

H2: Thereis a negative association between infant mortality rate and health expenditures per capita.

By contrast, the null hypotheses can be defined as:

H0: There is not a relationship between IMR and GDPPC and there is not a correlation between IMR and HEXPPC.

Table 3: Statistic results between dependent and independent variables

Table 3: Statistic results between dependent and independent variables

According totable 3, there is a strong correlation between parameters examined by this model. Intercept is 146.008 which implies when other variables are zero, the infant mortality rate can be predicted to be 146.008. Coefficients of GDPPC and HEXPPC are negative which confirm our hypotheses that the variable of percapita GDP and variable HEXPPC have a negative relationship with India’s infant mortality rate during the period from 1960 to 1990. 

The coefficient from the regression of IMR on GDPPC is -0.068. This figure indicates that there has been a downward tendency in the observations over time. As for the t-statistic, we can find out that for GDPPC, the absolute value of t =10.799 and highly significant. 

Additionally, for HEXPPC, the absolute value of t = 8.261 and is statistically significant as well. And the critical value of T28 =1.701, and then we can reject the null hypotheses of H0 since both absolute values of the t statistic are greater than the critical value of T28.

This paper’s statistical results are in line with most of the previous research findingsthat advocate the negative relationship between the income level and IMR. Statisticsare in accordance with literatures that contend the negative correlation between government health expenditures and infant mortality rate.

第五部分,我们在原有模型的基础上再加上第三个自变量EDUCPC(人均教育支出)并且提出了第三个hypothesis。

5. Re-estimating the Model with an Additional Variable EDUCPC

Based on the basic regression model, another variable EDUCPC is added to test hypothesis 3.

IMRt =α + β1GDPPCt + β2HEXPPCt+ β3EDUCPCt +ut

H3: Infant mortality rate and educational expenditures per capita are negatively related. The additional null hypothesis of this model can be established as:

H0: There is not a relationship between IMR and EDUCPC.

Table 4: Statistic results with an additional independent variable EDUCPC

Table 4: Statistic results with an additional independent variable EDUCPC

The regression evidence seems to tally with hypothesis 3. The coefficient sign of three independent variables are all negative with the figure of EDUCPC is -0.426 which both negative and significant. In this updated model, the statistics of R-squared and Adjusted R-squared are 0.927 and 0.946 which are larger than the results of the basic model. 

The absolute value of the t statistic of EDUCPC is 2.084 which is greater than the critical value of T28 = 1.701. Then the null hypothesis that states there is no causal relationship between IMR and EDUCPC can be rejected at the 5% significance level. 

One thing needs to be identified, if we test the model at the 1% significance level, the criticalvalue of T28 = 2.467. Therefore, we cannot reject the third null hypothesis since the absolute value of EDUCPC is less than 2.467. 

Furthermore, adding additional variables to a regression model can always enhance the model because a new term can inherently force a better fit. This rule is particularly practical for a model that has the limited number of variables. In this case, by adding another variable EDUCPC, the overall explanatory power of the regression model is improved.

6. Conclusion

This research paper analyzes the relationship between infant mortality rate and per capita GDP and two public expenditures in India. By introducing one dependent variable IMR and three independent variables GDPPC, HEXPPC and EDUCPC and building two regression models, this paper is able to test hypotheses and find out the correlation between different parameters. 

The statistical evidence suggests IMR has a negative relationship with all three independent variables which is in line with the propositions of our hypotheses. Given tests of all the coefficients are statistically significant and larger than the critical valueof t, then we can reject the null hypotheses and conclude that all three independent variables are key determinants of infant mortality rate.

统计学essay都是有一个基本套路的,无论你研究哪一种topic,其实每一篇statistic essay的格式都跟今天的范文差不太多。

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