A study of the percentage of the explained variance in the progressive multiple regression model In view of different sample sizes

Abstract
   The aim of the study is to identify the explained variance ratio at the multiple regression model of different sample sizes. To achieve this, the researcher used the descriptive approach. Random samples selected from the statistical observations generated using different sample sizes which are observations of one dependent variable (Y) and ten independent variables (X₁ , X₂ , X₃ , X₄ , X₅ , X₆ , X₇ , X₈ , X₉ , X₁₀) to study the efficiency of the multiple regression model and changes in the efficiency of this model  The samples of (25, 50, 75, 100, 125, 150, 200, 300, 400 ,500) were available for multiple regression assumptions.
    The results reached: Increasing the size of the sample accompanied by an increase in the value of (F) and the largest change in value (F) began when using the size of a sample (150) and increase at (R²) where it reached (17.80%) when the sample size (25), (85.10%) when the size of a sample (150) and (91.90%) when the sample size (500). Considering that increasing the sample size from (150) to (500) led to an increase of R² to (6.8%). As well, rapprochement of the values ​​of (R2) with the values ​​of Adj. R2 where the difference was (3.6, 4.0, 4.60, 3.70) when using samples of sizes (25, 50, 75, 100). The difference reached (0.10) when the sample size reached (500), considering that approach between the values ​​of (R²) and values ​​(Adj. R2) was when using the size of a sample of (150).