Influence of Educational and Financial Status of Parents on the Academic Performance of Secondary School Students: A Case Study in Hyderabad Division-Sindh

This research is conducted, in order to analyze the students’ academic performance at secondary school level in Pakistan. This is a case study conducted in Hyderabad Division of Sindh Province in Pakistan. The study was focused to the students who have passed matriculation class (Class-X), equivalent to secondary level in Pakistan(10 years of education). Sample size of 1097 higher Secondary level students were randomly selected from various colleges and schools in a way that around 150 students should take part in the survey from each institute. The sample selection was further divided on gender (Male = 448, Female = 648) and locale (Urban=455, Rural=641) basis. A data collection questionnaire was developed by the researchers and implemented for data collection. After collection of the data from desired population, the statistical analysis based on Pearson’s Chi-square and Correlation models were carried out in SPSS. The conclusion inferred from the data analysis of the study, strongly revealed that the students’ academic achievement at high school secondary level was highly associated to their parent’s educational level and socio-economic background. Therefore, it is strongly recommended financial condition of the population must be enhanced by taking appropriate measures. In order to coup tough financial conditions at their homes, deprived students should be provided adequate scholarships. Free stationary and books should also be provided at schools.

New Diagnostic Methods for Influential Observations in Linear Regression With Some Biased Estimation Methods

This thesis is concerned with the expansion of diagnostic methods in parametric regression models with some biased estimators. Of which, the Liu estimator, modified ridge estimator, improved Liu estimator and ridge estimator have been developed as an alternative to the ordinary least squares estimator in the presence of multicollinearity in linear regression models. Firstly, we introduce a type of Pena’s statistic for each point in Liu regression. Using the forecast change property, we simplify the Pena’s statistic in a numerical sense. It is found that the simplified Pena’s statistic behaves quite well as far as detection of influential observations is concerned. We express Pena’s statistic in terms of the Liu leverages and residuals. For numerical evaluation, simulated studies are given and a real data set has been analyzed for illustration. Secondly, we formulated Pena’s statistic for each point while considering the modified ridge regression estimator. Using this statistic, we showed that when modified ridge regression was used to mitigate the effects of multicollinearity, the influence of some observations could be significantly changed. The normality of this statistic was also discussed and it was proved that it could detect a subset of high modified ridge leverage outliers. The Monte Carlo simulations were used for empirical results and an example of real data was presented for illustration. Next, we introduce a type of Pena’s statistic for each point in the improved Liu estimator. Using this statistic, we showed that when the improved Liu estimator was used to mitigate the effects of multicollinearity, the influence of some observations could be significantly changed. The Monte Carlo simulations were used for empirical results and an example of real data was presented for illustration. The ridge estimator having growing and wider applications in statistical data analysis as an alternative technique to the ordinary least squares estimator to combat multicollinearity in linear regression models. In regression diagnostics, a large number of influence diagnostic methods based on numerous statistical tools have been discussed. Finally, we focus on ridge version of Nurunnabi et al. (2011) method for identification of multiple influential observation in linear regression. The efficiency of the proposed method is presented through several well-known data sets, an artificial large data with high-dimension and heterogeneous sample and a Monte Carlo simulation study.