Introduction: One of the basic principles of development in any country is education sector. Nowadays access to education is an important factor in creating many of inequalities. Also, the mutual and cyclic relationship between education and economy caused the focus of this research to be on these dimensions. Therefore, the purpose of this study is to estimate the indexes of education, economy and two dimensional developments of each province by the method of principal component analysi.
Method: In the first step, by using 11 related indices (general, higher, technical and vocational education) of which its correlation was approved by Bartlett's test, the education index was acquired and educational inequalities of their 30 provinces of the country has been studied. In the second step by applying 11 economic indices that indicate the economic status of the country regions, the economic index was estimated and economic inequality has been analyzed. The data set of this research, which have been collected from the available data method is related to the year 2018.
Findings: The findings of this research indicate that the two provinces Alborz and Tehran have the highest two dimensional index of development in the country and Sistan and Baluchestan province with the lowest index suffers from the inequalities of development in the country.
Conclusion: Based on the correlation matrix between education and economics dimension, there is 75% correlation, so it can be generally concluded that provinces that have better educational index enjoy higher rank in economy and vice versa.
Study of Education Index and Two Dimensional Index of Development Based on the Principal Component Analysis Method in Iran Provinces
 Introduction: The education sector is one of the fundamental pillars of national development. Today's inequalities are largely a result of how easily people can access education. A region's educational shortcomings will result in high interregional migration flows, which will lead to differences in the human capital of the regions (Faggian and McCann 2009). Among the other factors that influence population migration in Iran are economic measures like the gross domestic product and the unemployment rate. Education and the economy are therefore among the factors that can have an impact on regional inequality and population transfer because of their close relationship. As a result, one of the questions and concerns raised in the country is the degree of educational and economic inequality in Iran's provinces. Based on this, one of the aims of this research is to estimate the economic and educational indicators in the various regions of the nation. Additionally, using a novel technique, the two dimensional index of development has been extracted for the 2018 data. The use of variables that clearly depict educational and economic inequalities in the country, as well as the increase of indicators for each dimension to 11 indicators, distinguishes this study from other research (Bin 2015) in another way.
Materials and methods: The dataset method used in the current study is an applied research type. The most recent data from the Iranian Statistics Center, including the statistical yearbooks and information on the economic, social, and cultural standing of the provinces, as well as data from the Central Bank for 2018, were used in this study. In addition, the information gathered concerns 30 provinces of the country, with the exception of North Khorasan province (due to the unavailability of 2018 data). The principal component analysis method has been applied to determine each province's index of education, economy, and development. The PCA calculated by Chen and Woo (2010) and Bin (2015), which was used to calculate the development index in the regions of China, was the basis for the method employed in this research. This methodology begins by estimating the economy index and the education index separately before combining the two to produce the composite index of development. As a result, the current study will be conducted in two different ways. In the first case, each province's economic and educational indices are estimated separately. In the second case, two-stage PCA was used to create a two dimensional index of development.
Findings and discussion: Eleven indicators have been used in the education sector, including teacher-student ratio, actual coverage of elementary school, actual coverage of first secondary school, actual coverage of second secondary school, rate of promotion of the first course of secondary school, rate of promotion of the second course of secondary school, ratio of professors and associate professors to all teachers, the ratio of professors to total teachers, the ratio of professional doctoral students to total students, the ratio of specialized doctoral students to total students, and the ratio of instructors to technical and professional centers. In the second part, eleven indicators have been used to estimate the economic index of each province, including: GDP per capita, average annual income of an urban household, average annual income of a rural household, the inverse of the unemployment rate, the inverse of the urban Gini coefficient, the inverse of the rural Gini coefficient, the inverse of changes in the urban consumer price index, the inverse of the changes in the rural consumer price index, the business environment index, the penetration coefficient of production insurance and per capita bank deposits based on economic theories and studies. After calculating the index of education and economy, the two dimensional index of development has been estimated with the PCA method.
Based on the results obtained from this study with the PCA method, the provinces of the country can be divided into four levels based on the two dimensional index of development. The first level includes the provinces of Alborz, Tehran, Mazandaran, Yazd, Isfahan and Fars. The second level includes the provinces of Gilan, Bushehr, Semnan, Qom, East Azerbaijan, Zanjan and Qazvin. Kohgiluyeh and Boyer Ahmad, Kerman, Chaharmahal and Bakhtiari, Markazi, Ardabil, Hormozgan, Ilam, Khuzestan, and Razavi Khorasan are situated on the third level, while the provinces of  Kermanshah, South Khorasan, Hamedan, Golestan, Kurdistan, West Azerbaijan, Lorestan, and Sistan and Baluchistan are situated on the fourth level and are atthe lowest level of development.This stratification can help the decision makers of the country to use a balanced development policy sensitive to the location, to help both the rich provinces and the less developed provinces and cause development, social cohesion and political stability in the country.
Conclusion: Many inequalities have human capital as their root cause. So, if education improves, maybe some other fields like health and culture will also see improvements. The research's results suggest that the provinces close to the nation's center have better indicators than other regions, especially the border regions, in both the education and economy sectors. As a result, it can be said that the research's findings are in line with the reality of the country. The provinces of the country's state of development in terms of education are not properly coordinated with social justice.