The responsibility of heart organ is to supply blood to every part of the human body. The method of diagnose heart disease in medical hospital is extremely costly and also consume doctors time of operations. This research work applied forward, backward, and enter method for selection of variables in the logistic regression model, sensitivity, specificity, accuracy, and area under characteristic curve (AUC). The logistic regression model, at 5% level of significance with the enter method is used which denotes that the risk variables associated with heart disease gives accuracy of 87.9%. The preferred model of variable selection method used was the model from forward which has 88.6%. Also using the forward method of variables selection, the process produces 10 models with the best accuracy of 88.6%. The specificity and sensitivity of the analysis model was 91.4% and 85.6%. Also, the misclassification rate was also 11.4%, Positive predicted value is 87% and negative predicted value is 90.5%. Finally, the suitable model to predict the heart disease is from the forward method of variables selection and the positive likelihood ratio is 6 i.e the patients are 6 times likely to have the heart disease and the model has AUC value of 1.

The ordinary least square (OLS) estimator is the Best Linear Unbiased Estimator (BLUE) when all linear regression model assumptions are valid. The OLS estimator, however, becomes inefficient in the presence of multicollinearity. To circumvent the problem of multicollinearity, various one and two-parameter estimators have been proposed. This paper a new two-parameter estimator called Liu-Kibria Lukman Estimator (LKL) estimator. The theoretical and simulation results show that the proposed estimator performs better than some existing estimators considered in this study under some conditions, using the mean square error criterion. A real-life application to Portland cement and Longley datasets supported the theoretical and simulation results.

The most popularly used estimator to estimate the regression parameters in the linear regression model is the ordinary least-squares (OLS). The existence of multicollinearity in the model renders OLS inefficient. To overcome the multicollinearity problem, a new two-parameter estimator, a biased two-parameter (BTP), is proposed as an alternative to the OLS. Theoretical comparisons and simulation studies were carried out. The theoretical comparison and simulation studies show that the proposed estimator dominated some existing estimators using the mean square error (MSE) criterion. Furthermore, the real-life data bolster both the hypothetical and simulation results. The proposed estimator is preferred to OLS and other existing estimators when multicollinearity is present in the model.

Economy of a country can absorb shock and as well boost confidence through external reserves. Hence, external reserves play an important role to the extent that it helps in stabilizing the country’s economy. This study focuses on modeling the Nigeria external reserves using time series technique. 30-year data were extracted from the Central Bank of Nigeria (CBN) bulletin from 1990 – 2019. Some economic tools used to diagonize the data are Augmented Dickey Fuller (ADF) test, unit root tests Kwaitkowshi – philips – Schmiot – Shin test in order to ascertain the stationary of the data. Meanwhile, Auto Regression Integrated Moving Average (ARIMA) model was used as model for prediction whereby Akaike Information Criterion (AIC) and Hannan-Quinn Information Criterion (HQIC) were used as model diagnostic checking. At original level, the data showed an upward trend and found out to be non-stationary. When further examined using the diagnostic economic tools, at first difference the data were found to maintain a state of equilibrium. Also, model diagnostic checking revealed that ARIMA (2,1,7) was found to be the appropriate optimal model and thereby used for forecast for the next five years. Hence, the forecasted values revealed that the Nigeria external reserves will continue to increase steadily. Consequently, government should put in place legal policies that will enhance, increase accumulation and proper management of external reserves.