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Table 1 Result for the estimates of a missing value by Lagrange interpolation, linear interpolation and linear regression estimation: in case of one missing value

From: Missing data management and statistical measurement of socio-economic status: application of big data

Year 2000 2001 2002 2003 2004 2005 2006
Y(t)_Actual 41.18 36.69 35.50 38.25 40.05 47.21 48.81
Lagrange interpolation 41.18 85.34 30.58 39.45 42.07 46.31 46.92
Linear interpolation 41.18 38.34 37.47 37.78 42.73 44.43 47.14
Linear spline interpolation 41.18 42.75 42.42 41.51 40.99 40.12 39.84
Lagrange error 0.00 − 48.65 4.92 − 1.20 − 2.02 0.90 1.89
Linear interpolation error 0.00 − 1.65 − 1.96 0.47 − 2.67 2.77 1.67
Linear regression error 0.00 − 6.06 − 6.91 − 3.27 − 0.94 7.09 8.97
Year 2007 2008 2009 2010 2011 2012 2013
Y(t)_Actual 47.07 47.97 35.37 38.44 38.79 36.89 33.22
Lagrange interpolation 49.51 41.77 44.78 30.86 52.39 − 31.64 33.22
Linear interpolation 48.39 41.22 43.21 37.08 37.67 36.00 33.22
Linear spline interpolation 39.76 39.38 40.37 39.85 39.60 39.87 33.22
Lagrange error − 2.45 6.20 − 9.40 7.59 − 13.61 5.25 0.00
Linear interpolation error − 1.32 6.75 − 7.84 1.36 1.12 0.89 0.00
Linear regression error 7.31 8.59 − 5.00 − 1.40 − 0.81 − 2.98 0.00