Regression model is a powerful analytical tool for estimating the relationships between explanatory variables and the response variable. Traditionally, it is often assumed that the data are observed precisely and characterized by crisp values. However, in many cases, those data are collected in an imprecise way and characterized in terms of uncertain variables. In this paper, the residual analysis of uncertain regression models is provided. Furthermore, an approach to obtain the forecast value and the confidence interval of the response variable for the new explanatory variables is given. Finally, a numerical example of the uncertain regression model is documented.
CasalsM.R., GilM.A. and GilP., On the use of Zadeh’s probabilistic definition for testing statistical hypotheses from fuzzy information, Fuzzy Sets and Systems20 (1986), 175–190.
2.
CasalsM.R., GilM.A. and GilP., The fuzzy decision problem: An approach to the problem of testing statistical hypotheses with fuzzy information, European Journal of Operational Research27 (1986), 371–382.
3.
CorralN. and GilM.A., The minimum inaccuracy fuzzy estimation: An extension of the maximum likelihood principle, Stochastica8 (1984), 63–81.
4.
CorralN. and GilM.A., A note on interval estimation with fuzzy data, Fuzzy Sets and Systems28 (1988), 209–215.
5.
DiamondP., Fuzzy least squares, Information Sciences46 (1988), 141–157.
6.
EdgeworthF.Y., On observations relating to several quantities, Hermathena6 (1887), 279–285.
7.
EdgeworthF.Y., On a new method of reducing observations relating to several quantities, Philosophical Magazine25 (1888), 184–191.
8.
FisherR.A.Statistical Methods for Research Workers, Oliver and Boyd. Edinburgh. 1925.
9.
GaltonF., Regression towards mediocrity in hereditary stature, Journal of the Anthropological Institute15 (1885), 246–263.
10.
GaussC.F.Theory of the Motion of the Heavenly Bodies Moving about the Sun in Conic Sections, Sumtibus Frid Perthes. Hamburg, 1809.
11.
LegendreA.M., New Methods for the Determination of the Orbits of Comets, Firmin Didot, Paris, 1805.
12.
LioW. and LiuB., Uncertain data envelopment analysis with imprecisely observed inputs and outputs, Fuzzy Optimization and Decision Making (2017). DOI: 10.1007/sl 0700-017-9276-x
NejadZ.M. and Ghaffari-HadighehA., A novel DEA model based on uncertainty theory, Annals of Operations ResearchDOI: 10.1007/s10479-017-2652-7.
19.
NeymanJ. and PearsonE.S., On the problem of the most efficient tests of statistical hypotheses, Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences231 (1933), 289–337.
20.
NeymanJ., Outline of a theory of statistical estimation based on the classical theory of probability, Philosophical Transactions of the Royal Society A236 (1937), 333–380.
21.
SakawaM. and YanoH., Multiobjective fuzzy linear regression analysis for fuzzy input-output data, Fuzzy Sets and Systems63 (1992), 191–206.
22.
Student, The probable error of a mean, Biometrika6 (1908), 1–25.
23.
TanakaH., UejimaS. and AsaiK., Linear regression analysis with fuzzy model, IEEE Transactions on Systems, Man, and Cybernetics12 (1982), 903–907.
24.
WenM.L., ZhangQ.Y., KangR. and YangY., Some new ranking criteria in data envelopment analysis under uncertain environment, Computers and Industrial Engineering110 (2017), 498–504.
25.
WilksS.S., The large-sample distribution of the likelihood ratio for testing composite hypotheses, Annals of Mathematical Statistics9 (1938), 60–62.
26.
YangX.F. and LiuB., Technical Report, Uncertain time series analysis with imprecise observations2017.
27.
YaoK., Uncertain statistical inference models with imprecise observations, IEEE Transactions on Fuzzy SystemsDOI: 10.1109/TFUZZ.2017.2666846
28.
YaoK. and LiuB., Uncertain regression analysis: An approach for imprecise observations, Soft ComputingDOI: 10.1007/s00500-017-2521-y.
29.
YuleG.U., On the theory of correlation, Journal of the Royal Statistical Society60 (1897), 812–854.
