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Table 2 Relationship between the independent variable \(\beta _{1} \in (0, 1]\) and the response variables using a simple linear regression model for SEPO-\(\ell _{0}\) with \(r=0.1\)

From: Proximal linearized method for sparse equity portfolio optimization with minimum transaction cost

Response variable

Estimate for intercept

Estimate for coefficient

Standard error for coefficient

p-value for coefficient

R-squared

Expected return, \(y_{1}\)

0.6514

−0.3396

0.0383

2.0737e–0.5

0.9076

Variance risk, \(y_{2}\)

3.1246

−2.2371

0.2992

7.0894e–0.5

0.8748

Sparsity ratio, \(y_{3}\)

0.6013

−0.2679

0.0796

9.8657e–0.5

0.5859