Austin White Niko Kritsonis Ivan Aguilar Stephen Rogers Multiple Regression – 35 points (5 pages plus output) Modeling Higher grades on the final project are given to those teams who take the time to analyze the data and relate it to the topic studied. Just evaluating the numbers without referencing the bigger context of why you are doing this analysis will not get you an A grade. Make sure you show how much you love your data in this final team project. Introduction In the world today, the health of a nation’s economy is gaged by GDP per Capita. GDP per Capita has become the standard measure for determining economic prosperity of a country. A country with a high GDP per Capita typically contains a strong industrial sector, a strong centralized government, and a large presence in international trade, while a country with a low GDP per Capita typically contains a weak industrial sector, a weak centralized government, and/or a weak international trade presence. What we wanted to analyse is whether social/economic factors such as Poverty Rate, Fertility Rate, Inflation Rate, and unemployment rate had a strong correlation with the GDP per Capita of a country. For Example, does the 5% U.S Unemployment rate have anything to do with the U.S’s $54,000 GDP per Capita? Or, Does the GDP per Capita of Argentina have any correlation with its 23.7% inflation rate in 2014? These are questions that are central to modern economic and social science. Data from individual reports (Revised from the individual sections. Select the best of the individual reports.) Limitations: The data does not take into account economic conditions of the countries outside of GDP per Capita. The data does not take into account different laws and regulations affecting each country. The data does not take into account the social stability or instability of each country. Adequacy: The data in our analysis was gathered from Published Sources. We gathered a large portion of our Data from the World Bank because of their reliability and their broad range of data on countries all across the world.
Transcript
Austin White
Niko Kritsonis
Ivan Aguilar
Stephen RogersMultiple Regression – 35 points
(5 pages plus output)
ModelingHigher grades on the final project are given to those teams who take the time to analyze the data and relate it to the topic studied. Just evaluating the numbers without referencing the bigger context of why you are doing this analysis will not get you an A grade. Make sure you show how much you love your data in this final team project.
Introduction
In the world today, the health of a nation’s economy is gaged by GDP per Capita. GDP per Capita has become the standard measure for determining economic prosperity of a country. A country with a high GDP per Capita typically contains a strong industrial sector, a strong centralized government, and a large presence in international trade, while a country with a low GDP per Capita typically contains a weak industrial sector, a weak centralized government, and/or a weak international trade presence.
What we wanted to analyse is whether social/economic factors such as Poverty Rate, Fertility Rate, Inflation Rate, and unemployment rate had a strong correlation with the GDP per Capita of a country. For Example, does the 5% U.S Unemployment rate have anything to do with the U.S’s $54,000 GDP per Capita? Or, Does the GDP per Capita of Argentina have any correlation with its 23.7% inflation rate in 2014? These are questions that are central to modern economic and social science.
Data from individual reports (Revised from the individual sections. Select the best of the individual reports.)
Limitations: The data does not take into account economic conditions of the countries outside of GDP per Capita. The data does not take into account different laws and regulations affecting each country. The data does not take into account the social stability or instability of each country.
Adequacy: The data in our analysis was gathered from Published Sources. We gathered a large portion of our Data from the World Bank because of their reliability and their broad range of data on countries all across the world.
Independent Variables:Poverty Rate is defined as minimum line of income that is deemed adequate for a particular country.
Fertility Rate is defined as the ratio of living births in an area to the population in an area. Typically, show as 1000 population per area.Inflation is defined as the general increase in prices and the depreciation and appreciation of the value of money. Unemployment Rate is defined as the percentage of people who are in the labor force who are looking for a job.
Dependent Variable:GDP per Capita is defined as the average income per person in a country. Since this is a major economic representation of a country its should have a strong relationship with the rest of the economic measurements.
Hypothesis: We hypothesize that the independent variables will all be negatively correlated with our dependent variable since they all seem to reflect economic factors that would seem to diminish with higher levels of GDP per Capita. this means that economic policies that decrease our x-values (poverty rate, fertility rate, unemployment rate, inflation) will increase our y-value (GDP per Capita).
Y-Value (GDP per Capita):Mean: the average GDP per Capita among our 50 countries is $30712.648.Median: the GDP per Capita that is at the 50% point of our sorted data is $24406.5.Mode: there is no two countries with the same GDPStandard Deviation: the amount of variation between the GDP per Capita of our countries as a whole is $24406.5.Min: the lowest GDP per Capita of our countries is $1086.8. (Bangladesh)25 percentile: the GDP per capita at the lower 25% of our data is $9707.45.75 percentile: the GDP per capita at the upper 25% of our data is $49944.825.Max: the highest GDP per capita of our countries is $97429.7. (Norway)Empirical rule?: It does satisfy the empirical rule meaning 68% of the countries fall within the first standard deviation, 95% of the countries fall within the second standard deviation, 99% of the countries fall within the third standard deviation.
Austin White:Mean: the average poverty rate among our 50 countries is 17.284%.Median: the poverty rate that is between 50% of our 50 countries is 15.15%. Mode: the poverty rate that appeared the most often was 6.2% (Australia and Austria).Standard Deviation: the amount of variation in the poverty rate of our countries as a whole is 12.259%.Min: the lowest poverty rate of the countries is 1.5% (Taiwan).25 percentile: the poverty rate at the lowest 25% is 8.875%.75 percentile: the poverty rate at the upper 25% is 21.175%. Max: the highest poverty rate of the countries is 70% (Nigeria).Empirical Rule?: It does not satisfy the empirical rule which means one of the 3 criterias are not met: 68% of the countries fall within the first standard deviation, 95% of the countries fall within the second standard deviation, 99% of the countries fall within the third standard deviation.
Niko Kritsonis:Mean: the average unemployment rate is 7.32%.Median: the unemployment rate that is at the 50% point in the data is 6.2%.Mode: the most common unemployment rate is 6.2% (U.K., Indonesia, and Czech Republic)Standard Deviation: the amount of variation in the unemployment rate of our countries as a whole is 5.461%.Min: the lowest unemployment rate in the data is .03%. (Qatar)25 percentile: the unemployment rate at the lowest 25% is 4.1%.
75 percentile: the unemployment rate at the upper 25% is 8.5%.Max: the highest unemployment rate is 26.3%. (Greece) Empirical Rule?: It does satisfy the empirical rule meaning 68% of the countries fall within the first standard deviation, 95% of the countries fall within the second standard deviation, 99% of the countries fall within the third standard deviation.
Stephen Rogers:Mean: the average inflation rate is .974%.Median: the inflation rate that is at the 50% point in our sorted data is 1%.Mode: there are 3 common inflation rates, they are .4%, -0.6%, and 1%. (Netherlands, Poland, Finland) (Canada, Greece, Australia) (US, India, Denmark)Standard Deviation: the amount of variance in inflation rates of our countries is 6.18%Min: the lowest inflation rate is -23.3%. (Qatar)25 percentile: the inflation rate at the lowest 25% is -0.4%.75 percentile: the inflation rate at the upper 25% is 2.7%.Max: the highest inflation rate is 23.7%. (Argentina)Empirical Rule?: It does not satisfy the empirical rule which means one of the 3 criterias are not met: 68% of the countries fall within the first standard deviation, 95% of the countries fall within the second standard deviation, 99% of the countries fall within the third standard deviation.
Ivan Aguilar:Mean: the average fertility rate of our countries is 1.937%Median: the fertility rate that is at the 50% of our data is 1.8%Mode: the most common fertility rate is 1.8% (U.K., Brazil, Belgium, Norway, Chile, Finland)Standard Deviation: the amount of variation in the fertility rate of our countries is .752%Min: the lowest fertility rate of our countries is 1.18% (Taiwan)25 percentile: the fertility rate of the lowest 25% is 12.5%75 percentile: the fertility rate of the upper 25% is 37.5%Max: the highest fertility rate of our countries is 5.7% (NIgeria) Empirical Rule?: It does not satisfy the empirical rule which means one of the 3 criterias are not met: 68% of the countries fall within the first standard deviation, 95% of the countries fall within the second standard deviation, 99% of the countries fall within the third standard deviation.
Fill in the following correlation table from your individual projects and draw conclusions from your analysis of the correlations:
y (GDP per Capita
Poverty Rate (Austin)
Fertility Rate (name)
Unemployment Rate [Name]
Inflation [Name]
y (GDP per Capita) -0.381 -0.306 -0.159 -0.376Poverty Rate (Austin) -0.111 0.156 -0.083fertility rate[name] -0.068 0.023unemployment rate[Name]
0.156
inflation [Name]
As a team, we have decided that the x variables that should be used for final analysis are the Poverty Rate, The Fertility Rate, and the Inflation. These variables were chosen because they have the strongest correlation with our y-value (GDP per Capita) and therefore have the strongest chance of having a relationship with our Y-value (GDP per Capita).
We chose combination #2 as our best model (poverty rate and inflation). We took into account three different factors when deciding our best model. we first took a look at the model significance and noticed that all combinations were valid (F significant is less than .05). We then took a look at parameter significance and noticed that combination #2 and #4 both had valid parameters (parameter significance is less than .05). Lastly, we looked at Adjusted R-Squared and noticed that Combination #2 had the largest adjusted R-Squared (largest percent of variation explained by the graph) while meeting our first two significance checks. After these three checks, we came to the conclusion that Combination #2 (poverty rate and inflation) was our best model.
Best Model Improvement:
Final modeling:
Best Model(combination
#2)
Best Model with first outliers removal
Best Model with second outliers removal
Intercept 43109.34 42723.18 40315.71
Slope 1 -646.213 -641.691 -576.627
Slope 2 -1260.32 -1261.65 -1186.08
Slope 3 N/A N/A N/A
Model Significance .001812 0.002033 0.002697
Adjusted R-Square .203059 0.203015 0.19703
Parameter significance(Poverty Rate)
.020286 0.021979 0.028298
Parameter significance (Fertility Rate)
N/A N/A N/A
Parameter significance(Inflation)
.022386 0.023093 0.022837
Assumption Checks XXXXXXXX XXXXXXXXXX XXXXXXXXXX
Mean of 0 PR: yesI: no
PR: yesI: no
PR: yesI: no
Variance constancy PR: noI: yes
PR: noI: yes
PR: noI: yes
Independence PR: IndependentI: Dependent
PR: IndependentI: Dependent
PR: IndependentI: Dependent
Normality no no no
Compared to the original model, the new model has a higher model significance meaning that it is closer to accepting the null. The parameter significance for both x’s are different but not enough to really affect how we see or read the data and because it's still a small number we can accept the value. The slope and the intercepts are getting closer to 0 which means the data is becoming more and more reliable. For the final best model there is one normal outlier of 2.3 on the 19th data point but besides that there are no extreme outliers.
y=-1762.707x+40315.71. The equation for the multiple regression here explains a best fit line for our data points since no line actually fits though every single point. We are given an intercept and slopes from the regression summary and that line is the best explanation of how the data is acting.
Prediction Interval:
X variable t value (alpha/2,df)
Point Prediction
Prediction Interval Confidence Interval Actual y value
The prediction interval is an estimate interval of where an observation should be, given a probability. In our case alpha = .01. For the poverty Rate, given that the U.S’s Poverty Rate was 15.1% in 2014, the prediction interval predicted that the U.S’s GDP per capita was between $23244.68-$41604.67. The actual U.S GDP per Capita in 2014 was $54398.5, which is inside the prediction interval. This meant that the prediction interval accurately predicted where the U.S’s GDP per Capita would land (in an interval) given the only the U.S’s Poverty Rate. This same trend occurred for Inflation with Germany and Fertility Rate with Australia.
The prediction interval is fairly similar to the confidence interval in both what it’s trying to capture and in formula. However, the prediction interval is a much larger interval than the confidence interval and therefore doesn’t give us as much accuracy as possibly desired. The Prediction Interval is a useful tool in statistics because of it’s strong predictive characteristics but does have the drawback that its interval is so large that it can be more advantageous to use a confidence interval given certain circumstances.
Discussion for Final Model (I will look to this section to see if you really understood what you did.)
Summary:
Although the correlations weren’t strong, there is some evidence to show that economic factors such as inflation and poverty rate are interconnected with a country’s GDP per Capita. Our final model (which contained Poverty Rate and Inflation as the x variables) proved that with all valid parameters from the x values and intercepts we received a adjusted R-Squared of 0.197. While our adjusted R-Squared is fairly small, almost 20% of our regression plots can be explained by our multiple regression model. This means that there is sufficient evidence to prove that the size of a country’s GDP per Capita has an effect on the poverty rate and inflation of that country.
In our final model, our data contained no extreme outliers (z score greater than or equal to 3 or less than or equal to -3). However, our data did contain one outlier which was Turkey with a z score of 2.32.
Our model appears to be valid based on Parameter significance and Model Significance. The Parameter significance for all three values (two x values and one intercept) had a significance level less than .05 meaning the parameters are valid. The Model Significance level was also below .05 meaning the model is valid. However, it must be noted that our assumption check for our two x variables gave mixed results as to whether a linear regression model was valid for our final values. in our mean of 0 test and independence test we found that the poverty rate passed both tests while inflation did not pass either. For the variance constancy test, inflation passed while the poverty rate did not. Neither values had a Normal distribution meaning a linear regression model may not be acceptable for these values.
Our model would not be a reliable predictor of GDP per Capita of a country. Although we believe that there is sufficient evidence to prove that there is a correlation between the poverty rate and inflation of a country and its GDP per Capita, that correlation according to our data is small. based on our adjusted R-Squared, our regression can only explain about 19.7% of the whole model distribution. We do not believe our model to be a reliable predictor because of its low ability to explain the variation of data points on our model.
In statistical terms, this model is recommended because of its parameter validity and its model validity. Having validity to these pieces of data is highly important to the success of a model. If our model did not have valid parameters or a valid F significance than the model could not be used to determine the GDP per Capita of a country and our model would then be useless. That being said, in the real world our model allows us to see how poverty rates and inflation correlate with the size of a country’s GDP per Capita, which is something that economists and social scientists study frequently in today’s world.
The drawbacks of our model is that the Adjusted R-Squared is vary low (0.197) indicating that our model is not a very good indicator of the correlation between GDP per Capita and the poverty rate and inflation of a country.
Conclusion (I will look to this section to see if you love your data.)There are a myriad of ways to make improvements to our study in the future. In this study we used GDP per Capita of a country as our y-value to find out whether there was a correlation between this and our x-values poverty rate, fertility rate, unemployment rate, and inflation. In the future I would not use the GDP per Capita of a country but rather the increase or decrease of a country’s GDP per Capita from a specific year to another. This would probably give us a better correlation with our x-values because it would reflect the current prosperity of a country rather than comparing to a country's prosperity that may have been accumulated in the past and then became stagnant economically. I would also change x-values such as poverty rate and Fertility Rate to something more economically focused such as interest rates and international trade. Using poverty rate and fertility rate as an x-value was not bad, however, these measures are more socially driven statistics rather than economically driven like GDP per Capita. If we were to use interest rates and international trade of a country instead, we would probably see better regression models being made from the data that can be attained.
From our final model, we can see that the two slopes of our x-values (poverty rate and inflation) were negative. meaning as x increased, y decreased. This matches our hypothesis to a point. Any policies that decrease poverty such as work programs, training programs, educational programs, etc that are used to decrease poverty would increase a nation's GDP per Capita. Also, policies that are aimed at decrease inflation would increase GDP per Capita according to our model. Our model must be taken with a grain of salt though because of the low adjusted R-Squared that has already been noted which questions the reliability of our model.
Going back to our original hypothesis, we found that none of our variables had a strong correlation with GDP per Capita. When we correlated each x-value with our y-value (GDP per Capita) we found the poverty rate, fertility rate, and unemployment rate to have moderate negative correlations with our y (GDP per Capita. However, our R-Squared was very low (.157 for poverty rate, .0937 for fertility rate, and .1417 for inflation). When we combined these x-values in our multiple regression, our Adjusted R-Squared wasn’t reading much better than our individual x R-Squared values.
Works Cited
Unemployment, total (% of total labor force) (modeled ILO estimate). (n.d.). Retrieved
November 20, 2016, from http://data.worldbank.org/indicator/SL.UEM.TOTL.ZS
Inflation, GDP deflator (annual %). (n.d.). Retrieved November 20, 2016, from
