The issues concerning global rainfall distribution and warming/climate change cannot be over emphasized since it affects virtually every part of live. The study used rainfall pattern in two states of Nigeria. Data on the monthly rainfall distribution in Imo and Rivers state, for a period of 37 years was examined. The result showed a continuous increase in the pattern of rainfall for a period of thirty seven years within the period under study. However the pattern was inconsistence for the remaining years with some kind of fluctuations. The monthly mean series plots showed a clear presence of trend with the peak period being September annually in both series with coefficient of determination- R square value of 83% and 86% for Imo and Rivers series respectively. The yearly mean series plots showed a clear irregular variation over the years in both series. The irregularity in the pattern of rainfall calls for serious commitment in joining the force for climate change abatement process. Pearson correlation coefficient between the two series is 0.80 (substantial correlation), which is the same result with cross correlation between the two rainfall series (0.79988 approx. 0.80). The series reveal the following characteristics: high correlations appear seasonality of order 12 in the monthly mean plots (every September), irregular variation and trend curve which is quadratic trend. ARIMAX model with independent variable was employed to identify the best bivariate time series model for prediction purpose. The result reveal an increase in Rivers series (Yt ) would tend to a linear combination of some increase of the preceding Imo series (It ) values which is vise visa. SARIMAX (1, 2) and SARIMAX (2, 1) models are identified as the best model with respect to Rivers on Imo series rainfall; via Imo on Rivers series rainfall.

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The paper examined students' performance in six subjects from WAEC examination from 2018 to 2020 using multivariate analysis through Hotelling T2 distribution and paired t-test statistics. Four objectives where formulated and used for this study. Based on the factors in the objectives, relevant related literatures were reviewed. A secondary data extracted from the WAEC results from the public senior secondary schools under study were used for this study and the analyses of the data were done using Hotelling T2 distribution, Quadratic form, and paired t-test statistics. All computations were done via Microsoft Excel 2010, SPSS (version 23.0) and MINITAB (version 16.0). The Hotelling T2 statistics results between the students' academic performance for (2018 & 2019), (2019 & 2020) and (2018 & 2020) were all significant. Paired t-test statistics results showed a decrease in the Students' average performance for four subjects (Mathematics, English Language, Marketing and Biology), while an increase in the Students' average performance for Economics and Civic Education subjects. It was discovered that students' average performances in Economics and Civic Education subjects were better than other subjects. This research recommend the effective implementation of the Nigeria education policies that emphasizes on teachers qualification, years of teaching experience and the UNESCO policy on Teacher-Students ratio (this policy stipulates that the maximum number of students that should be in a secondary class is 25), since there is significant difference between students' average performance for four subjects.

The paper examined univariate time series forecast of consumer price index on the consumption of food and nonalcoholic beverages in Nigeria. It filled the knowledge gap by explicitly modeling and forecasting consumer price index in Nigeria using the univariate ARIMA model. The work was restricted to Nigerian Consumer Price Index. It was also restricted to food consumption (FC) data and food & nonalcoholic beverages consumption (FNBC) data from 1995-2021. This paper analyses were carried out using gretl 2019c, Minitab 16 and Micro software Excel (2010). The monthly and yearly means plots were done, so as to have a better understanding of the series behaviours. The series plots points to the fact that there is possibility that the time series are integrated of order 1 for food consumption series with no seasonality, while integrated of order 1 for food & nonalcoholic beverages consumption series with seasonality of order 12. Stationarity after second difference of the first differencing was obtained for both series. A suitable ARIMA Model was obtained for both series and was used for models forecast computation. Hence, the computed result suggested that ARIMA(0,1,1) and ARIMA(0,1,1)(0,0,0)12 model were the best model for estimating and forecasting the two time series, using model selection criteria and accuracy measures. The plots of the forecasts generated for the FC and FNBC shows that the two variables are dependent and also shows that any gradual increase in the food consumption tends to pave way for increase in the food & nonalcoholic beverages consumption or a drastic drop in the food consumption will also drop the food & nonalcoholic beverages consumption in the same manner. It seems reasonable to conclude that there is significant relationship between the food consumption and food & nonalcoholic beverages consumption series. It was recommended that more detailed work should be carried out in the area of co-integration analysis of the two variables to enhance a better understanding and prediction distribution in Nigeria.