## 3 Results
### Panel Data Analysis of Dynamic Pricing Schemes
We verify whether these effects are significantly tariff dependent by regressing on the willingness to use energy, and set the dependent variable in (1) to price sensitivity \(\vartheta_{i,t}\). We test for multicollinearity by observing correlations between household variables, but find that the predictor variables correlate enough to bias results. We perform a Hausman test, to select random effects or fixed effects for the  
Figure 3: Average relative daily load profile and tariff price for Real-Time Pricing (RTP) (with Min and Max) and Time-Of-Use (TOU) pricing. panel data regression [38]. This approach ensures the sufficient measurement of the interrelatedness of the variables of this study, while accounting for individual differences across households and time. Controlling for fixed effects obliges us to explore the relationship between the proposed individual and outcome variables within a household. A random effect model assumes that entity error terms are not correlated with the household level attributes. As the Hausman test was insignificant for all 24 data sets, we make use of random effects. Results can be found in Tables A3 and A4 in Appendix B and C.  
When examining the 24 different panel data regression coefficients between the RTP and TOU treatment groups, it becomes evident that the household attributes have a very different influence on both groups. The observed differences are either time-differentiated or show an opposite relationship with the willingness to use electrical energy. We find that some variables, such as the building size, have a distinct time gap in which the influence of the variable is not relevant. Moreover, the variables of building type and roof insulation are shown to be insignificant in the overall panel data regression, but have specific times during the day in which they indeed are significant. Lastly, we test for significant differences between treatment coefficients. We introduce RTP as a dummy variable \(g_{i}\) for the Real-Time Price treatment, and connect it with all the coefficients of interest. As the above regression indicated error terms \(\varepsilon_{i}\) to be independent for both treatments, we form the combined model. With \(\gamma\) representing the difference in slope between both coefficients, allowing for testing the difference in slopes between regression coefficients. Results are given in Table 4.  
\[\theta_{i,t}=\alpha_{i}+\beta X^{\prime}_{i,t}+\gamma(X^{\prime}_{i,t}g_{i})+ \varepsilon_{i,t} \tag{2}\]  
We find that the willingness to use electricity is negatively correlated with building age, building size and building type. The analysis indicates that households in the RTP group have a significantly lower willingness to use electricity according to the mentioned household attributes. However, we find a significant positive correlation for the number of household occupants. We argue that this may be the case for larger families, where the utility of shifting demand is lower due to a more inelastic demand curve. The panel regression analysis shows a clear influence of household attributes on the effect of energy demand by home energy systems operating under dynamic pricing contracts. Home energy management systems with different tariff structures lead to different types of behavior from the customer, depending on their household attributes. Home energy management systems should learn