This paper reports the use of a numerical solution of nanofluid flow. The boundary layer flow over a stretching sheet in combination of two nanofluids models is studied. The partial differential equation that governs this model was transformed into a nonlinear ordinary differential equation by using similarity variables, and the numerical results were obtained by applying the shooting technique. Copper (Cu) nanoparticles (water-based fluid) were used in this study. This paper presents and discusses all numerical results, including those for the local Sherwood number and the local Nusselt number. Additionally, the effects of the nanoparticle volume fraction, Brownian motion Nb, and thermophoresis Nt on the performance of heat transfer are discussed. The results show that the stretching sheet has a unique solution: as the nanoparticle volume fraction φ (φ = 0), Nt (Nt = 0.1), and Nb decrease, the rate of heat transfer increases. Furthermore, as φ (φ = 0) and Nb decrease, the rate of mass transfer increases. The data of the Nusselt and Sherwood numbers were tested using different statistical distributions, and it is found that both datasets fit the Weibull distribution for different values of Nt and rotating φ.

In a linear regression model, the ordinary least squares (OLS) method is considered the best method to estimate the regression parameters if the assumptions are met. However, if the data does not satisfy the underlying assumptions, the results will be misleading. The violation for the assumption of constant variance in the least squares regression is caused by the presence of outliers and heteroscedasticity in the data. This assumption of constant variance (homoscedasticity) is very important in linear regression in which the least squares estimators enjoy the property of minimum variance. Therefor e robust regression method is required to handle the problem of outlier in the data. However, this research will use the weighted least square techniques to estimate the parameter of regression coefficients when the assumption of error variance is violated in the data. Estimation of WLS is the same as carrying out the OLS in a transformed variables procedure. The WLS can easily be affected by outliers. To remedy this, We have suggested a strong technique for the estimation of regression parameters in the existence of heteroscedasticity and outliers. Here we apply the robust regression of M-estimation using iterative reweighted least squares (IRWLS) of Huber and Tukey Bisquare function and resistance regression estimator of least trimmed squares to estimating the model parameters of state-wide crime of united states in 1993. The outcomes from the study indicate the estimators obtained from the M-estimation techniques and the least trimmed method are more effective compared with those obtained from the OLS.

In this study, the Tiwari and Das model is numerically studied, in case of a moving plate containing both single-walled and multiwalled carbon nanotubes (SWCNTs and MWCNTs, respectively), in the presence of thermal radiation and the slip effect. Employing the similarity transformation, a set of 2nd-order partial differential equations (which are used to model the flow and heat transfer) are solved numerically using the boundary value problem with 4th-order accuracy (BVP4C) method. The effects of related parameters, such as the volume fraction of nanoparticles, moving, slip, and radiation parameter on the heat transfer performance are analysed and discussed. Results indicate that a unique solution was placed when the plate travels in assisting flow conditions. Additionally, as the nanoparticle volume fraction (φ) rises at φ = 0.2, the skin friction and heat transfer rate decrease. It is also observed that when the slip parameter (β) increases at β = 0.4, the skin friction decreases, whereas the heat transfer rate increases. Meanwhile, the heat transfer rate decreases when the thermal radiation (NR) increases to 0.7. Moreover, it is found that the SWCNTs are more efficient when the skin friction coefficient and the Nusselt number are considered. It is found that the Weibull distribution is more suitable in fitting the skin friction data.

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In the multiple linear regression analysis, the ridge regression estimator is often used to address the problem of multicollinearity. Besides multicollinearity, outliers also constitute a problem in the multiple linear regression analysis. We propose a new biased estimators of the robust ridge regression called the Ridge Least Median Squares (RLMS) estimator in the presence of multicollinearity and outliers. For this purpose, a simulation study is conducted in order to see the difference between the proposed method and the existing methods in terms of their effectiveness measured by the mean square error. In our simulation studies the performance of the proposed method RLMS is examined for different number of observations and the different percentage of outliers. The results of different illustrative cases are presented. This paper also provides the results of the RLMS on a real-life data set. The results show that RLMS is better than the existing methods of Ordinary Least Squares (OLS), Ridge Least Absolute Value (RLAV) and Ridge Regression (RR) in the presence of multicollinearity and outliers.