Table 6 Results of the gravity model for all first-place applications to higher education institutions (2011–2017)

\(I_{j,t}\)

\(\beta _1\)

2.038

1.671

2.798

1.081

1.367

0.716

1.462

21.27%

\(I_{m,t}\)

\(\beta _2\)

2.938

2.719

2.882

2.974

2.442

2.828

2.814

39.82%

\(UR_{j,t}\)

\(\beta _3\)

0.099

0.677

0.509

1.126

0,750

1.141

0.808

10.15%

\(UR_{m,t}\)

\(\beta _4\)

\(-\)0.448

\(-\)0.192

\(-\)0.430

\(-\)0.580

\(-\)0.678

\(-\)1.814

\(-\)1.257

16.34%

\(d_{j,m}\)

\(\beta _5\)

\(-\)0.457

\(-\)0.596

\(-\)0.619

\(-\)0.688

\(-\)0.701

\(-\)0.724

\(-\)0.667

9.20%

\(RANK_{m,t}\)

\(\beta _6\)

\(-\)0.428

\(-\)0.386

\(-\)0.278

\(-\)0.138

\(-\)0.107

\(-\)0.095

\(-\).241

3.22%

\(R^2\)

0.872

0.847

0.729

0.682

0.539

0.730

0.663

100.00%

\({\overline{R}}^2\)

0.871

0.846

0.728

0.682

0.539

0.730

0.663

100.00%