Multiple Linear Regression, its Statistical Analysis and Application in Energy Efficiency

In this project, we use a statistical multiple regression to study the impact of eight various predictors (relative compactness, surface area, wall area, roof area, overall height, orientation, glazing area, glazing area distribution) to estimate the cooling load energy efficiency of residential buildings. We try to analyze and visualize the effect of each predictor with each of the response variable using different classical statistical analysis tools used in describing linear models, in such a way so that we can find out the most strongly related predictor variables. Before starting all of this, we use the idea of model selection by stepwise regression technique and compare the AIC of these models and identified a better model between all of them. Then, we compare a classical linear regression approach by simulations on 768 diverse residential buildings show that we can predict CL with low mean absolute error. By using ANOVA we determine variation in the different residuals. Also, we use non constant variance test to verify it. Furthermore, we check leverage and influence points as well as outliers as well as determined cook distance for influential points. By taking box cox transformation and weights, we also introduce WLS technique to fit the model for better results and did all type of important analysis to understand the energy efficiency. Finally, we show 5-fold cross validation to verify our model.

A New Log-location Regression Model with Influence Diagnostics and Residual Analysis

A new four-parameter lifetime model called OddLog-Logistic Burr XII distribution, is defined and investigated. Some of itsmathematical properties are derived. Some useful characterization resultsbased on \ the ratio of two truncated moments, based on the hazard functionas well as on the conditional expectation of certain functions of the randomvariable are presented. The maximum likelihood method is used to estimatethe model parameters by means of a graphical Monte Carlo simulation study.Moreover, we introduce a new log-location regression model based on theproposed distribution. The Jackknife estimation method as an alternativemethod is used to estimate the unknown parameters of new regression model. Thegeneralized cook distance and likelihood distance measures are used todetect the possible influential observations. The martingale and modifieddeviance residuals are defined to detect outliers and evaluate the modelassumptions. The potentiality of the new regression model is illustrated bymeans of a real data set.