Zane's Notes

Investigation 1 - Bivariate Data Analysis

Zane Fitzgerald, Oct 01, 2023

Note

(Almost) every ‘link’ on here goes to another page, they don’t work since other notes aren’t downloaded.

Also any of these boxes with an arrow next to the title can be collapsed / expanded, by clicking the title, most are collapsed by default

Introduction

In this investigation I will be investigating whether or not there is a significant association between the numerical variables; Tertiary School Enrollment, and GDP.

Relevancy

This association is relevant because it allows us to see how changes in Tertiary Education affect Gross Domestic Product.

Allowing us to Gain insight into whether Tertiary Education growth was the Explanation or even affected GDP growth. That same growth who’s Knock-on effects brought the average person’s Living Standards above that of royalty centuries prior.

We can use the information on the Association to make a prediction on how different GDP would be if every single person today had undergone Tertiary Schooling.

Data Collection Plan

To ensure that I collect accurate data I will utilise official international resources like the World Bank to collect my data, this will ensure that my data is reliable and correct since they are a international organisation, and keep reliable records. I will use Data regarding the European Union as they have the most reliable datasets for both Indicators required within that time frame.

procrastinated got sidetracked, made my own data tracking websiteusing the World Bank API and a chart library

Data Time Scale

I will take the datapoints at yearly frequencies, collecting datapoints going from 2020 to 1972, the data used will be about the European Union since they have the most reliable datasets on Tertiary Enrollment. (Australia’s is extremely sporadic, non-consistent recording, and not recorded for as long).

Data Collection:

GDP

Investigation 1 - Chart.js Graphs < This likely won’t link, in submission, more for personal reference

Calculations

Legend

Using the ClassPad, I have determined that Given is the response variable, the Least-Squares Regression Line formula for this assosciation is: This equation tells us that every time the explanatory variable s increases by 1, the GDP is expected to increase by 0.2638 Trillion.

And the equations proposes that at y-intercept, where Tertiary School Enrollment () is 0, GDP will be at -3.225 Trillion.

Correlation Coefficient = 0.9693 Coefficient of Determination = 0.9395

The data, Plotted - Regression Line:

Analysis

This association is positive, as indicated by the Correlation Coefficient’s positive sign. GDP and Tertiary Education have a strong correlation as the Correlation Coefficient is 0.96, which is above 0.75.

The assosciation of this data is also likely linear as can be infered by a high Coefficient of Determination of , meaning that 94% of the variation in Gross Domestic Product () can be explained by variation in Tertiary Education Enrollment.

The Residual plot below does not depict a easily recognisible pattern indicating that the linear model is likely a good fit for this relationship.

However it is not completely random, indicating that the linear model is not a good fit for the relationship, it has large spikes of positive residual at the end, and negative residuals at around ~7.5.

These can be explained by the expansive growth of GDP & Tertiary Enrollment near the end, causing a increase in positive residuals. and the plateau of growth at ~7.5, causes a increases in negative residuals as the actual values do not keep up with those predicted by the Linear model, which expects constant and unchanging growth at 0.2638 Trillion GDP per 1% increases Tertiary School Enrollment throughout the data. The parts of the data that do not conform to the linear model can be seen in the Graphs under the Collapsed Callout called: Graphical Representation of the Data (pre-analysis), these can be found right above the Calculations section.

This discrepancy shows us that in this association, according to the linear model Tertiary School Enrollment can explain 94% of the varience in GDP, however the oddities in the Residual Plot show us that the model is not entirely accurate, and that it is not consistantly linear, but does follow a linear pattern overal.

Dangers of Prediction

We can make predictions based on the Least-Squares Regression Line, we can use this to predict the GDP at a specific value aka. Tertiary Enrollment, however predictions using a value outside the range <-> are a #ff5582a6;">Extrapolation as we do not have any datapoints beyond 75.1% for . This means that that prediction is unreliable.

Evidence of Extrapolation Unreliabality in this context

The unreliability of Extrapolation is evident by a value of , or 0% Tertiary School Enrollment predicting, based on the Least-Squares Regression Line, a value of which is obviously incorect, as represents GDP, which is a measure of the Total value of final goods produced, you can not produce negative value.

However even #bbfabba6;">Interpolation, predictions made between the range of the data could potentially be unreliable as, Correlation does not equal Causation. Due to this, there could be a non-causal explanation, like it being a coincidence, or a Confounding Variable, could be the causal link between both variables in this association, for example, Increases in Global Trade often correlates to increases in GDP, which in-turn often correlates to increases in wages (see Knock-On effects of Economic Growth) and an increase in Wages could be what’s causing more and more people to consider Tertiary Education.

Or it could have become more accessible as Highly educated jobs became higher in demand as Europe transitioned from a Industrial, manufacture based economy to a Highly Developed Economy, thus being more reliant on educated labour, causing them to create more universities to satiate this increase in demand, which just so happened to correlate with GDP increases as Highly developed economies traditionally have a higher GDP than more than Industrial, based economies.

Prediction given s = 100

Conclusion / Interpretation

While there appears to be a strong association between GDP and Tertiary Education, complications with the Residual Plot show us that it does not conform perfectly to the Linear Model, and due to the diversity of causes for changes in GDP it is likely a Confounding Variable is involved, and thus while the two data sets are strongly associated, we can not be sure of the weight of the impact Tertiary Education has upon GDP. Due to not conforming well to a Linear Model, predictions, even Interpolations are less reliable.

Graph View

Search

SearchSearch

Backlinks