The ridge-type regression estimators are frequently being used to address multicollinearity in the linear regression model due to the inefficiency of the famous ordinary least squares estimator. The ridge-type regression estimator can be in one or two-parameter form. This paper proposes another ridge-type estimator, a two-parameter ridge-type estimator, and establishes its statistical properties theoretically and through Monte Carlo simulation studies. Two different biasing parameters (k 1 d 1 and k 2 d 2 ) were considered for the proposed and compared with six other existing estimators. Results of Monte Carlo simulation studies show the dominance of the proposed method over some existing ones using the mean squared criterion. In addition, the proposed dominated the existing estimators when applied to real-life datasets using mean squared error and cross-validation as the criterion.

Background: Cataract surgery is the most common operation performed in ophthalmology. It is the commonest cause of reversible blindness globally, in Sub-Saharan Africa and Nigeria. The study examined some factors affecting the outcome of cataracts surgery measured by Visual acuity after 6 weeks. Methods: Data was collected from the records of ophthalmic patients who had cataract surgery at LAUTECH Teaching Hospital Ogbomoso, from the period of January 2013 to December 2018. Two hundred and twenty-seven patients’ records were retrieved for the study. Logistic Regression was used to investigate factors associated with the outcome of Cataracts Surgery. The goodness of fit test was used to determine the fit of the model to the data. Results: Two variables; intraoperative complication, and unaided visual acuity on the fir st postoperative day were statistically significant (p-value < 0.05). The outcome of surgery using unaided visual acuity after six weeks of surgery showed that 47.1% of the patients had a good visual outcome (6/18) or better and 52.9% had a poor outcome (worse than 6/60). Factors such as complications within six weeks, presence of ocular and systemic comorbidity, and presence of intraoperative complications were found to increase the likelihood of poor outcomes in cataract surgery. Conclusion: This study has shown that Intraoperative complications and unaided visual acuity on the first postoperative day are important to the outcome of cataract surgery. Therefore, the two factors should be given attention during cataract surgery

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.

Background: COVID-19, a global pandemic ravaging many countries, shares some semblances with influenza, whose transmission can be affected by many factors. Atmospheric temperature and population density have been identified as two key factors influencing the spread of viruses. Nigerian states with different weather patterns and varying populations across her states have recorded about 173,908 COVID-19 cumulative confirmed cases between March 2020 and July 2021. Methods: Data sets of confirmed Covid-19 cases, average monthly temperature and population of each State, and Nigeria’s Federal Capital Territory were obtained. A test of assumptions of linear regression was carried out and there is the presence of outliers in the dataset. M-estimator as an alternative to Ordinary Least Square (O.L.S.) estimator for regression analysis was used to investigate the impacts of each State’s population size and atmospheric temperature on the rate of COVID-19 cases confirmed. The spearman rank correlation coefficient was also used to investigate the strength of the relationship be-tween the confirmed cases, the population and temperature. Results: Results show no multicollinearity (VIF=1.041) between the independent variables, and there is no autocorrelation as the Durbin-Watson test value gives 2.113 (approximately 2). There is a weak positive correlation between cumulative confirmed cases and population (r = 0.281), but a weak negative correlation exists between COVID-19 cumulative confirmed cases and atmospheric temperature (r = -0.341). For OLS estimation method, only population is significant (β1= 0.002, p < 0.002) but the population (β1= 0.0006, p < 0.05) and the atmospheric temperature ( β2= -683, p < 0.05) are both significant when M-estimation method was applied. Conclusion: The findings in this study show that population size and temperature are important factors in the spread of Covid-19. The spread of the pandemic may be partially suppressed with higher temperatures but increases with an increased population.

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.