Analysis of School Education in India

Introduction

School education is not just a fundamental necessity but also an inherent right for every citizen in india. the country has embraced the principle that primary and upper primary education, catering to children ageI 6 to 14, is not only free but also mandatory. this foundational stage places significant emphasis on core subjects like mathematics, science, social studies, and languages, reflecting a commitment to fostering a well-rounded and educated citizenry.

The importance of school education in india is pivotal for the nation's overall development. beyond imparting knowledge, it empowers the youth, laying the groundwork for a knowledge-based economy. the potential for progress stemming from investing in the education of the younger generation is immeasurable. india's journey through school education is poised to shape the future of millions, contributing profoundly to the nation's socio-economic fabric.

Amidst this backdrop, an ambitious project is underway, with the primary goal of uncovering the correlation between the number of students enrolled and government spending. this correlation is critical for understanding the effectiveness and impact of public investment in education. by exploring the intricate relationship between enrollment figures and government expenditures, the project aims to shed light on resource allocation efficiency and identify areas for improvement in the education system.

As the nation advances on its trajectory of educational reform, this project serves as a crucial tool for policymakers and stakeholders. it seeks to provide evidence-based insights into the dynamics of educational funding and enrollment trends. the holistic understanding derived from this research endeavor is expected to inform future policies and interventions, ensuring that the transformative potential of school education in india is maximized for the benefit of its citizens and broader society. the journey of school education in india is one to be observed closely, holding the promise of shaping a brighter and more enlightened future for the nation.

Abstract

This research looks closely at how schools work in india, paying attention to the connection between the number of students, how much the government spends on education, and how many schools are set up. at first, we used a test to see if these things were too connected (multicollinearity test), and it turned out the results were not in the right range. so, we changed our way of studying and used something called a linear regression model instead.

We're looking specifically at the number of students as the main thing we want to understand. we're also looking at how much money the government spends on education and how many schools are built as separate things. the linear regression model helps us figure out how these factors affect the number of students, giving us numbers to show how well money and policies are working.

This study is important for both academics and people who make policies. by using statistics, we get a better understanding of the complicated connections in education. this information helps policymakers make better decisions based on evidence, ultimately improving the education system in india.

In summary, our study, using the linear regression approach, gives us insights into important aspects of school education. this helps decision-makers understand the relationships between different factors, contributing to the ongoing discussions about making education better in india.

Methodolgy

The following is a general methodology for predicting the students enrolled in school in india with one variable which is government spending on education in this case by using the linear regression model (lmtest).

Data collection:

The first step is to collect a dataset of annual students enrolled and annual government spending for our sample size (31). we also used different websites such as mospi and data.gov for the integration of data.

Data pre-processing:

The next step is to pre-process the collected data by removing any irrelevant information and cleaning the data. we used r's [is.na(student_enroll)] for this step.

Exploratory data analysis (eda):

We checked the summary and structure of the dataset to understand its characteristics. confirmed that there are no missing values in the dataset. this can help us identify the which including coefficients, p-values, and other relevant statistics from the data.

Linear regression model:

Created a linear regression model using the lm function with students enrolled as the dependent variable and government spending as the independent variable.

Residual analysis:

Plotted the residuals against the fitted values to check for any patterns or outliers. checked the density plot and quantile-quantile (qq) plot for normality of residuals.

Train-test split:

Split the data into training and testing sets, with 80% of the data used for training the model and 20% for testing.

Model evaluation:

Applied the trained model to the test data to make predictions. calculated root mean

square error (rmse) and mean absolute error (mae) to evaluate the performance of the model on the test data.

Visualization:

Plotted the residuals against fitted values and checked for normality using qq plot.

Interpretation and Result

Tool used

? R language

Coefficients:

Statistical significance:

The p-value for government spending is 5.383e-06, which is less than the typical significance level of 0.05. this suggests that there is evidence to reject the null hypothesis that the coefficient for government spending is zero. in other words, government spending appears to be a statistically significant predictor of students enrolled.

Model fit:

r-squared (0.5284): this is the proportion of the variance in the dependent variable (students enrolled) that is predictable from the independent variable (government spending). an r-squared of 0. 5284 indicates that in the model 52.84% of variations are caused by independent variable .

Density plot of residuals:

This provides a visual check for the normality of residuals. our model assumptions are generally valid if the residuals are approximately normally distributed.

Train-test evaluation:

Root mean square error (rmse): the rmse is a measure of the average magnitude of the errors between predicted and actual values. in our case, an rmse of 431.6 suggests that, on average, your model's predictions are off by approximately 431.66 units of students enrolled.

Mean absolute error (mae):

The mae is another measure of prediction accuracy. an mae of 331.23 indicates the average absolute difference between predicted and actual students enrolled values.

Prediction:

For each observation in the test set, we have compared the actual students enrolled values with the predicted values from your model.

Recommendations:

while the model shows statistical significance, the low r-squared indicates that a large portion of the variability in students enrolled is not explained by government spending alone. we should consider exploring additional variables that may improve the model's performance.

Interpretation from graph (r)

In the q-q plot, the points do not fall exactly on a straight line, but they are close. this suggests that the data is approximately normally distributed, but there are some slight deviations. the deviations are most noticeable in the tails of the distribution, where the points fall slightly below the line. this suggests that the data may have slightly heavier tails than a normal distribution.

Overall, the normal qq plot suggests that the data is approximately normally distributed. however, it is important to keep in mind that this is just a visual assessment. there are other tests such as shapiro-wilk test that can be used to assess normality more formally.

Multicollinearity

We did a multicollinearity test and found a correlation of 84% within independent variables.

So, we took only one independent variable.

Conclusion

In this analysis, a linear regression model was developed to explore the relationship between government spending and students enrolled. the model revealed a statistically significant, association between the variables. the positive coefficient for government spending suggests a small, inverse relationship with students enrolled, indicating that as government spending increases, students enrolled tends to increase. however, the model's limited explanatory power, as reflected in the low r-squared value (52.84%), highlights the influence of unaccounted factors on students enrolled variability.

It is crucial to note that government spending alone may not suffice for comprehensive students enrolled prediction, and further exploration of additional variables is recommended.

In conclusion, while the model contributes valuable insights into the government spending enrolled relationship, its limitations underscore the complexity of student enrolled variation. continued refinement of the model and incorporation of additional variables will be essential for enhancing predictive accuracy and understanding the broader dynamics influencing student-enrolled patterns.

Sources

1.https://www.education.gov.in/sites/upload_files/mhrd/files/statistics-new/public-expenditure.pdf

2. https://ncert.nic.in/pdf/esd_ptse.pdf

3.https://www.education.gov.in/sites/upload_files/mhrd/files/statistics/sse1112.pd