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The method of least squared suffers a setback when there is multicollinearity and outliers in the linear regression model. In this article, we developed a new estimator to jointly handle multicollinearity and outliers by pooling the following estimators together: the M-estimator, the principal component and the ridge estimator. The new estimator is called the robust r-k estimator and is employed. We established theoretically that the new estimator is better than some of the existing ones. The simulation studies and real-life application supports the efficiency of the new method. K E Y W O R D SM-estimator, multicollinearity, outliers, principal component, ridge estimator 1 the impact of an outlier on the following: fitted values, the regression coefficient, estimated variance of or the goodness of fit statistics. Outliers are observations that posed a noticeable change on the model estimates. 16 The presence of an outlier in a model affects the efficiency of LSE. 17,18 Robust regression estimator produced more reliable and stable estimates than LSE for linear regression models with outliers. [19][20][21][22][23][24] Examples include the M-estimator that is resistant to an outlier in the y-direction. 19

New born baby is a gift from God and what a newborn baby looks like is not a baby model, rather a newborn baby looks varies from baby to baby in terms of weight, height and head circumferences. In this research, a sample of 200 male and female babies was used for the analysis. The aim is to identify if there is a significant difference between the means of the variables considered. In this research, three variables were considered for both male and female babies at birth. The result showed that the mean birth weight is 3.55kg and 3.39kg for male and female babies respectively. The mean height and head circumference of female babies recorded higher than their male counterpart. The Hoteling's T 2-test showed that there is a significant difference between the mean vectors of the variables considered; hence a discriminant analysis was conducted. The discriminant function obtained fairly classifies the group at 42% error rate. From the results gotten, there is significant difference between the height, weight and head circumference of male and female babies and conclude that male babies are heavier in terms of weight while female babies have bigger head circumference than the male babies.

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