# Electricity Usage Efficiency and Electricity Demand Modeling in the Case of Germany and the UK
## 3 The Methodology of Electricity Demand Model Creation  
The hypothesis analyzed in this article is that electricity usage efficiency is an important factor affecting electricity demand in Germany and it is responsible for decoupling between industrial output and electricity consumption variables. To further confirm this, the hypothesis linear regression model was built, where electricity efficiency usage was one of the inputs. Variables analyzed in the previous section constitute the main part of the regression model created. Multiple variable regression models were confirmed to provide excellent results in forecasting a long-term demand for electricity by many different publications analyzing various regions and periods [20; 21; 22]. A comparison of different forecasting electricity demand techniques was also presented by [PERSON] et al. [23]. Linear regression is characterized by the following formula:  
\[Y=a+b_{1}\times X_{1}+b_{2}\times X_{2}+\ldots+b_{p}\times X_{p} \tag{1}\]  
where \(Y\) is the dependent variable and \(X_{1}\) to \(X_{p}\) are independent variables. In this case, six variables were used to explain the monthly consumption dataset. Figure 3: Industry Output, average yearly % change over the following periods: 1995–2005, 2005–2008, 2008–2010, and 2010–2012 (data source: Eurostat). Figure 2: GDP (REAL), average yearly % change over the following period: 1995–2005, 2005–2008, 2008–2010, and 2010–2012 (data source: worldbank.org). For the regression model described in this article, monthly data regarding the German market from 2005 until April 2013 were used. The output of the model was the monthly electricity consumption forecast until the year 2020. The dependent dataset in the model is German electricity consumption. Independent input into the model consists of six different datasets:  
* The monthly average temperature in Germany (measured as an average of 10 different places in Germany) in Celsius degrees (variable \(X_{1}\));
* Dataset measuring subtraction between average temperature in Germany and 17 degrees Celsius. In the case of a negative value, the dataset value returns to zero. This dataset is designed to account for increased electricity usage due to air conditioning in summer (variable \(X_{2}\));
* The monthly industrial production in Germany based on Eurostat data (variable \(X_{3}\));
* The number of days in a month (variable \(X_{4}\));
* Yearly GDP data for Germany (variable \(X_{5}\));
* Electricity efficiency usage coefficient with a gradually decreasing value for every month. We assume that electricity efficiency improves gradually and regularly, which is certainly not the case, but such an approach still leads to much better results than neglecting this factor completely (variable \(X_{6}\)). The variables were chosen based on the fundamentals of the electricity market [24; 25]. Household demand especially depends on temperature. Heating demand is strong during the winter months while cooling demand increases during the summer months. This is reflected by the temperature variables chosen. Business electricity demand depends on GDP and industrial output. Logically, the number of days in a month also affects electricity demand. The innovative variable in the model is gradually increasing the efficiency of the electricity usage variable. It is confirmed by the R square of the model and the \(p\)-value of the efficiency variable that this input is indeed crucial for the modeling of electricity demand on the present markets. We have not seen this variable to be used by other researchers, and thus, the research presented in this article is innovative in this respect. While from a modeling perspective, there might be better ways to incorporate this variable into the model, it is our strong belief confirmed by the data that it should not be neglected by the researchers and analysts dealing with the subject. The model developed explains electricity demand movements reasonably well, with an R square coefficient on the level of 0.788 (Figure 4).