Annual Change per Capita GDP
The present study multiple regression analysis method is used to model Annual Change Per Capita GDP. The secondary data used here is collected from Koenker and Machado(1999). There are 13 covariates with dimnames corresponding to the original Barro and Lee source. See http://www.nber.org/pub/barro.lee/.
A data frame containing 161 observations on 14 variables:
Annual Change Per Capita GDP
Initial Per Capita GDP
Male Secondary Education
Female Secondary Education
Female Higher Education
Male Higher Education
Black Market Premium
Growth Rate Terms Trade
These data allows exploration of independent variables to try to explain the behavior of GDP per capita growth. In this exercise only observations from 1965 to 1975 were used. GDP is an important measure of the standard living of a country, and that is what makes it interesting to explore. As economists, identifying variables that may alter Annual Change Per Capita GDP positively or negatively is extremely important, since economical policies might be proposed according to these types of analyses. Although any of these variables could be used, the best explanatory variables for the multiple regression models are identified using correlation analysis.
Scatter Plot Analysis
The relationship between the dependent variable and the explanatory variables can be graphically illustrated using a scatter plot matrix (see Figures 1 and 2).
Figure 1 : Scatter diagram 1
Figure 2 : Scatter diagram2
The above two scatter diagrams suggest that Life Expectancy, Black Market Premium, and Initial per Capita GDP are significantly correlated with the dependent variable Annual Change Per Capita GDP. The following tables give the correlation among these variables along with P values.
y.net lgdp2 lexp2 lblakp2
y.net 1.00 0.03 0.24 -0.22
lgdp2 0.03 1.00 0.85 -0.56
lexp2 0.24 0.85 1.00 -0.43
lblakp2 -0.22 -0.56 -0.43 1.00
Probability values (Entries above the diagonal are adjusted for multiple tests.)
y.net lgdp2 lexp2 lblakp2
y.net 0.00 0.8 0.14 0.14
lgdp2 0.80 0.0 0.00 0.00
lexp2 0.05 0.0 0.00 0.00
lblakp2 0.07 0.0 0.00 0.00
Therefore, the purpose of this exercise will be to examine the behavior or Annual Change Per Capita GDP according to Life Expectancy, Initial Per Capita GDP and Black Market Premium. It is expected that the Annual Change in Per Capita GDP be influenced by these variables, since the initial value of the GDP at each year might hint if the Annual GPD change will be higher or lower. Additionally, the higher the Life Expectancy of the country, the longer and healthier its inhabitants live, and thus are more productive. Moreover, and in relation to Black Market Premium, the higher the gap between a country’s official currencies exchange rate and the one in the black market, the lower the GDP, because a higher gap in the official vs. black market rates means that there is a low availability or more complicated processes in order to obtain the necessary foreign currency to import raw materials or machinery for production. The summary table for these variables is presented in table 1.
T test is used to check the significance of the regression coefficients of the three explanatory variables . The following null and alternative hypotheses are considered for this purpose.
(Regression Coefficient = 0)
(Regression Coefficient 0)
Test Statistic used is
Significance level lpha = 0.05
Decision Rule: Reject the null hypothesis, if the observed significance value (p value) is less than the significance level.
The null hypothesis states that there are no changes on Annual GDP Change per Capita according to selected variables, so the predictors’ coefficients are statistically not different from zero. In contrast, the alternative hypothesis states that at least one of the coefficients will be different from zero. In this case:
H0: βIy2 = βlexp2 = βgcony2 = 0
H1: βIy2 or βlexp2 or βgcony2 ≠ 0
Where β is the coefficient for each variable.
Multiple Regression Analysis
The main objective of multiple regression analysis is to suggest an algebraic model that can be used to predict the value of Annual Change Per Capita GDP given values of the three explanatory variables.
The estimated values of the regression coefficients are given below.
The t test for the significance of the regression coefficients of the explanatory variables suggest that all the three independent variables are highly significant as the P values are less than the significance level.
The regression coefficients can be interpreted as
For a unit-increase in Black Market Premium, the Annual Change Per Capita GDP decreases by 0.038975 units.
For a unit-increase in Initial Per Capita GDP, the Annual Change Per Capita GDP decreases by 0.016557 units.
For a unit-increase in Life Expectancy, the Annual Change Per Capita GDP increases by 0.073114 units.
ANOVA (F-test) is used to check the global significance of the multiple regression models. Here F statistic is highly significant with F(3,63) =7.084, P value < 0.05 indicating that the model is able to explain the variability in the total bill. The adequacy of the regression model is measured using coefficient of determination (R2 statistic). Here R2 = 0.2522, indicating that the above multiple regression model is able to explain 25.22% variability in the total bill.
In the context of these data, the Annual Change per Capita GDP can be explained by variables such as Black Market Premium, Initial per Capita GDP and Life Expectancy, which produce a negative effect on Annual Change Per Capita GDP, except for Life Expectancy. All these effects are statistically significant at a 5% alpha level. This model explains about a quarter of the variability in Annual Change Per Capita GDP. However, the use of interaction terms and model selection techniques is advised, in order to find alternative models that better explain more variability in the dependent variable.
Neter, J., Wasserman, W., & Kutner, M. H. (1989). Applied linear regression models (2nd ed.). Homewood, IL: Irwin.
Koenker, R. and J.A.F. Machado (1999) Goodness of Fit and Related Inference Processes for Quantile Regression, JASA, 1296-1310.
Intro 5 good,for following assignments try something like To begin, the purpose of this write up is to examine the behavior of per capita GDP growth against independent variables life expectancy (lexp2), female secondary education (fse2) and male higher education (mhe2). Since per capita GDP is an important measure of the living standard in a country, we are interested in what may cause it. As economists, we are interested in determining whether or not these variables share a causal relationship with per capita GDP as we would then be able to suggest sound policy alternatives to developing countries, (assume).
theory 0 in the theory section you want to use economic reasons to explain why you are analyzing the data. ex: We think that lexp2, fse2 and mhe2 all positively affect y.net because we know that educated people are more likely employed in a skilled trade/profession. This would then imply that the country is developed and offers both goods and services. It is also highly possible that the life expectancy in a country strongly reflects how organized the health care system is
data 15 very good, for full marks include a summary table of the variables you are interested in analyzing
model 0 please state the regression equation before the results
hypothesis 0 please state the hypothesis before the results
resukts 0 please present in a nice table
interpretation 20 good
conclusion 0 please have a seperate section summarizing the work you have done that also includes suggestions on how to better the analysis the second time aroudn