Version 1
: Received: 4 October 2020 / Approved: 5 October 2020 / Online: 5 October 2020 (12:16:38 CEST)
How to cite:
Mostafa, F. Multiple Linear Regression, its Statistical Analysis and Application in Energy Efficiency. Preprints2020, 2020100082. https://doi.org/10.20944/preprints202010.0082.v1
Mostafa, F. Multiple Linear Regression, its Statistical Analysis and Application in Energy Efficiency. Preprints 2020, 2020100082. https://doi.org/10.20944/preprints202010.0082.v1
Mostafa, F. Multiple Linear Regression, its Statistical Analysis and Application in Energy Efficiency. Preprints2020, 2020100082. https://doi.org/10.20944/preprints202010.0082.v1
APA Style
Mostafa, F. (2020). Multiple Linear Regression, its Statistical Analysis and Application in Energy Efficiency. Preprints. https://doi.org/10.20944/preprints202010.0082.v1
Chicago/Turabian Style
Mostafa, F. 2020 "Multiple Linear Regression, its Statistical Analysis and Application in Energy Efficiency" Preprints. https://doi.org/10.20944/preprints202010.0082.v1
Abstract
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.
Keywords
exploratory analysis; model selection; MLR; K fold cross validation
Subject
Engineering, Automotive Engineering
Copyright:
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
