Regresyon Ağaçları ve Çoklu Doğrusal Regresyon Analizlerinin PISA 2022 Matematik Okuryazarlığı Becerisini Yordama Performanslarının İncelenmesi

Öz

Araştırmada çoklu doğrusal regresyon analizinin ve regresyon ağacı algoritmasının PISA 2022 matematik okuryazarlığı becerisini yordama performanslarına ilişkin kestirimler yapılmıştır. Buna ek olarak yordamada önemli olan değişkenlerin tespiti gerçekleştirilmiştir. Buna göre 6645 kişinin verileri kullanılmıştır. Bağımsız değişkenler olarak dijital kaynakların kullanımı ile ilgili iki anket maddesi, haftalık ders saati sayısı, matematik öz yeterliğine ilişkin iki farklı indeks, matematiksel kavramlara aşinalık, Bilgi ve İletişim Teknolojisi kaynakları, ev olanakları, ekonomik, sosyal ve kültürel statü indeksi, okuduğunu anlama becerisine ilişkin birinci olası değer kullanılmıştır. Tahmin performansları ortalama mutlak hata, ortalama mutlak hata yüzdesi, hata kareler ortalaması, hata kareler ortalamasının kökü, yanlılık, beklenen ve gözlenen değerler arasındaki korelasyon ve açıklanan varyans metriklerine göre karşılaştırılmıştır. Elde edilen sonuçlara göre (1) her iki yöntemin tahmin performansı iyi düzeyde olmakla birlikte, çoklu doğrusal regresyon analizi daha iyi performans göstermiştir. (2) Her iki yöntemde değişkenlerin önem sıralaması büyük ölçüde benzer olmakla birlikte, en önemli iki değişken okuduğunu anlama puanı ve formal ve uygulamalı matematiğe yönelik öz yeterlik düzeyi olmuştur. Elde edilen sonuçlar veri setinin özellikleri bağlamında tartışılmıştır.

Anahtar Kelimeler

• Regresyon ağacı
• Çoklu doğrusal regresyon
• PISA 2022
• Matematik okuryazarlığı

Examining the Performance of Regression Trees and Multiple Linear Regression Analyses in Predicting PISA 2022 Mathematical Literacy Skills

Öz

In the study, predictions were made regarding the performance of multiple linear regression analysis and regression tree algorithm in predicting PISA 2022 mathematical literacy skills. In addition, the variables that are important in prediction were identified. Accordingly, data of 6645 individuals were used. As independent variables, two questionnaire items related to the use of digital resources, the number of weekly class hours, two different indices of mathematics self-efficacy, familiarity with mathematical concepts, ICT resources, home possessions, economic, social and cultural status index, and the first plausible value for reading literacy skills were used. Prediction performances were compared according to the metrics of mean absolute error, mean absolute error percentage, mean squared error, root mean squared error, bias, correlation between expected and observed values and explained variance. According to the results obtained, (1) although the prediction performance of both methods was good, multiple linear regression analysis showed better performance. (2) Although the importance ranking of the variables was largely similar in both methods, the two most important variables were reading literacy score and self-efficacy level towards formal and applied mathematics. The results obtained are discussed in the context of the characteristics of the data set.

Anahtar Kelimeler

• Regression tree
• Multiple linear regression
• PISA 2022
• Mathematics literacy

Kaynakça

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