Comparative Multiple Regression Analysis of Household Electricity use in Latvia: Using Smart Meter Data to Examine the Effect of Different Household Characteristics Academic research paper on "Economics and business"

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Energy Procedia 72 (2015) 49 - 56

International Scientific Conference "Environmental and Climate Technologies - CONECT 2014"

Comparative multiple regression analysis of household electricity use in Latvia: using smart meter data to examine the effect of different household characteristics

Ilze Laicane*, Dagnija Blumberga, Andra Blumberga, Marika Rosa

Riga Technical University, Institute of Energy Systems and Environment, Azenes iela 12/1, Riga, LV1048, Latvia

Abstract

The development and implementation of effective policies for promoting energy efficiency in the household sector has been an emerging target of the EU. A recent analysis of Latvian households included in a smart metering pilot, shows this type of housing as the most statistically significant variable to impact electricity savings. This study deals with the statistical analysis of residential buildings to find simplified correlations for the assessment of factors affecting changes in electricity consumption, in particular, taking into account selected building characteristics, as well as the personal, socio-economic, socio-demographic characteristics of households. Multiple linear regression analysis is used to present and compare results between two groups - the target group with smart meters and control group without smart meters by differentiating among typical heating types as determined in a field study.

© 2015TheAuthors.Publishedby ElsevierLtd.This is an open access article under the CC BY-NC-ND license (http://creativecommons.Org/licenses/by-nc-nd/4.0/).

Peer-review under responsibility of Riga Technical University, Institute of Energy Systems and Environment

Keywords: Smart meters; household electricity consumption; user behavior; multiple regression; pilot project; space heating; building characteristics

1. Introduction

The EU countries have to deal with energy efficiency targets in order to reduce greenhouse gas (GHG) emissions by 20 % until 2020. According to the Energy Efficiency Status Report 2012, residential energy consumption

* Corresponding author. Tel.: +37126299018; fax: +37167089908 E-mail address: ilze.laicane@rtu.lv

1876-6102 © 2015 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).

Peer-review under responsibility of Riga Technical University, Institute of Energy Systems and Environment doi: 10.1016/j.egypro.2015.06.008

increased by 3.6 % between 2009 and 2010 accounting for 26.7 % of total final energy usage in 2010 in the EU [1]. Residential buildings in Latvia in 2012 consumed 28 % of total final electricity [2]. As already discussed previously [2-4] electricity demand in Latvian households has increased in recent years. At the same time, a number of energy efficiency policy instruments are introduced in Latvia and one of the main priorities is building insulation for promoting end-use efficiency in households [5].

Several building characteristics can be highlighted that cause significant impact on household energy consumption. Some studies have shown that electricity consumption is higher in single-home dwellings than in apartments [6-7], and larger houses [7-11]. In Kavousian et al. study it was found that household age does not show significant impact on electricity consumption [6], while the others found the opposite [12]. The use of a heating system has been found to be an important factor in determining electricity use in residential buildings. The parameters influencing energy demand for space heating are: the thermal quality of the building, building type, occupant behaviour and climate condition [13], as well as dwelling size, number of occupants, efficiency of heating equipment, and demand for useful energy per unit of area heated [14]. A significant variance in electricity consumption that is related to electrical floor heating as supplementary installation in households with a heat pump and combined electricity heating system has been found in [12, 15]. Ndiaye and Gabriel [16] concluded that electricity heated homes consume more electricity than natural gas heated homes. The US study results shows that the age of the household owner has a positive effect on heating energy consumption [17], whereas, Chen et al. [14] found the opposite.

The aim of this study is to examine the extent to which the abovementioned factors cause an effect on changes in consumption. Multiple regression analysis is used to present and compare results.

Nomenclature

E electricity consumption per household per month, kWh/ month

G the gender of the respondent

I households' total net monthly income in previous month after taxes, EUR

M the number of households' members

Ti time of staying home for all households' members, hours per day

Ag age of the main breadwinner in the household, years

Ed the education level of the main breadwinner in the household

Ty type of building (detached house, apartment etc.)

Y the mean year of household construction

Ar household total area, m2

Te the temperature maintained in household during winter time, °C

Ap the total number of electrical appliances in households

ao a constant (the intercept)

ai, a2 ...an are regression coefficients (the parameters of the regression model)

s the error term (disturbance term) of the regression equation

2. Methodology

2.1. Case study research. Households data and survey

The rationale of this study is based on the analysis of a large sample of buildings involved in a smart metering project in Latvia "Promoting energy efficiency of household using smart technologies" (further - pilot project) launched by JSC "Latvenergo" on 1 April 2013. In total, the project involves 1000 households - 500 households are directly included in the project installed with smart meters (i.e., target group) and another 500 households are not

directly involved in the project (i.e., control group, which serves as a "reference" group for the comparison of data before and after the project). The preliminary results in the first year of implementation of the pilot project show a decrease in electricity consumption by 23 % for the target group and by 6 % for the control group when compared with the year before pilot project implementation. The recent study on the analysis of factors that affected savings achieved by the pilot project households showed that type of housing has been found as the most statistically significant variable that impacts electricity savings (i.e., greater electricity savings were achieved in larger detached houses rather than in apartments [2]). Therefore the aim of this study is to enrich previous analysis [2-4] with additional statistical analysis. The basis of the statistical analysis is original data set of large household survey held in March and April, 2013. All households were surveyed through telephone interviews. During the survey important quantitative and qualitative data from households were obtained regarding their personal, socio-economic, socio-demographic issues, household characteristics, number and type of electrical appliances, as well as questions related to attitude, awareness, level of knowledge on energy efficiency, appliance usage habits, behaviour, etc. 61 of target group households refused to take the survey. Finally, survey data of 429 target group and 500 control group households were obtained.

Electricity consumption data for the observation period from 1 April 2013 till 31 March 2014 for target group households were obtained from smart metering data. The control group are not equipped with smart meters. A great proportion of control group households pay for electricity using a self-declaration method. This method is not really appropriate and suitable for the analysis of consumption data directly. Therefore additional electricity consumption data set of control group meter readings in the time period from 2012 till 2014 were obtained from the electricity supply company (JSC „Latvenergo"). The electricity consumption data were then normalized to be appropriate according to the observation period.

Our hypothesis is that significant differences in variance in electricity consumption can be observed in households using different types of heating. In other words, variance in electricity consumption can be explained by the existence of a particular heating type. We assume that greater variance in consumption are to be witnessed in households that use electricity for heating purposes. Most of the investigated households have natural gas heating and solid fuel boiler heating (i.e., 23 % and 22 % of all target group households, and 28 % and 28 % of all control group households). Only 13 % of target group and 10 % of control group households use direct electrical heating. 17 % of target group households use heat pumps (8 % of control group). Quite a small number of all households use alternative energy sources for heating (5 % of target group and 3 % of control group). Central heating is not a common type of heating used in the investigated households.

2.2. Development of regression model

Our preferred method for model selection is multiple linear regression. We used a multiple regression model to explain the variation in household electricity consumption. To summarize, our method enables working with large data sets of electricity consumption data and extensive household surveys, by a) using distribution of households by type of heating used in household that help to understand different aspects of consumption; b) selecting a subset of variables that contribute the most to each type of heating; c) properly considering the effect of selected variables that were identified in the empirical setting and d) ranking the contribution of different variables between two groups (target group with smart meters and control group without smart meters) through a regression model.

The proposed regression model is based on estimation of 11 selected independent variables reflecting household electricity consumption. The regression equation of our model is given by:

El = a0 + a^G + a2I + a3M + a^Ti + a5Ag + a6Ed + a7Ty + aaY + agAr + a10Te + a11Ap + £ (1)

Several variables derived from the questionnaire have numeral values (Ag, M, Ye, Te, Ti, Ar, Ap), some ordinal (G, Ty, Ed), or scale values (I). The parameters included in the regression model are chosen, because they are among the most frequently used factors for the regression analysis in other studies as discussed previously [6-17]. Some studies have proved that the age of the main breadwinner in the householdwas positively related to in-home

energy consumption levels (instead of average age and education of all household members) [6, 7, 11, 14, 17-18]. Also, other empirical studies examined age of the respondent as a predictor variable for energy conservation actions. Therefore, we chose the variable age of the main breadwinner in the household as the parameter for our model (similar as the education level of the main breadwinner in the household). Since household behaviour modelling is very complex, the assessment of user behaviour aspects will not be taken into account within this research. Also climatic conditions in relation to the geographical location of the building and the outdoor temperature are not included for regression analysis.

The purpose of the research is to assess the factors that affect electricity consumption in two main study groups (target group and control group). 7 regression models were applied to target group and control group households for each heating type separately. It is done with the aim to assess whether there are significant differences between households with and without smart meters. Table 1 presents a description of each selected regression model and number of cases included for each model.

Table 1. Explanation of investigational regression models and number of cases for target group and control group

Model No. Explanation (Type of heating used in households) Number of target group households Number of control group households

1 Central heating 67 86

2 Natural gas heating 117 154

3 Boiler with solid fuel (wood, coal, briquettes, wood chips, pellets) 100 151

4 Electrical heating (convection, calorifers, infrared, oil electric heaters, electric under floor heating system, ion boiler) 68 52

5 Heat pump (Geothermal, air, water) 89 43

6 Heating systems using alternative energy sources (wind generator, solar collectors, solar photovoltaic system) 24 15

7 Other types of heating - boiler with liquid fuel (diesel, fuel oil, biofuels), fireplace (kamin) heating water floor heating, portable oil-fired generator 29 33

The development of these regression models is based on similar approaches used in other studies. Several studies have focused on consumption analysis depending on the type of heating. Bartusch et al. [12] and Theodoridou et al.

[15] discovered significant variance in electricity consumption in households with heat pump and combined electricity heating system. Romero-Jordán [19] and Baker and Rylatt [20] evaluated the effect of electrical heating. The impact of central (district) heating was assessed by Brounen et al. [21] and Bedir et al. [22]. Ndiaye and Gabriel

[16] found that type of heating (for example, different fuels used in the heating system, net electricity used for heating homes and natural gas heated homes) has a significant impact on consumption. On the basis of recent studies, we use similar distribution of households according to heating types. For the case of individual boilers we allocated several types of solid fuel: wood, coal, briquettes, wood chips, pellets. As suggested by Theodoridou et al. [15], households with heat pumps are separated from the group of households that use electric power from network (convection, calorifers, infrared, oil electric heaters, electric under floor heating system, ion boiler). Taking into account that around 7 % of households use other types of heating, it was interesting to investigate factors that affect electricity use for these households. The creation of the 6th model where alternative energy sources are used for heating was particularly interesting.

3. Results and analysis

We applied our model to a data set of monthly interval consumption data. We analysed consumption data on a monthly basis to ensure that the fluctuations in electricity consumption are considered, but not obscured by sudden spikes in consumption.

A multivariate regression analysis software package, STATGRAPHICS Centurion XVI (version 2.16.04.) were used. Regression analysis showed that results vary considerably among different models tested. First, we tested all 7 models for both groups based on all variables which were originally included in the model, as described in equation (1). In many cases there were no statistically significant relationships between the variables at the 95.0 % or higher confidence level, since p-values in the ANOVA table were greater than 0.05. To increase the accuracy of the models, we simplified all 7 models by including only statistically significant variables. Therefore, our analysis was divided into two parts - 1st testing of all models when all variables were included in the analysis (i.e., 1st testing) and 2nd testing of all models when only statistically significant variables were included in the model (i.e., 2nd testing). A comparison of the results for the 1st testing and 2nd testing and overall statistics (empirical relationship among variables, R2, adjusted R2, ANOVA, p-values, and F-ratios) are summarized in Appendix A.

In the 1st testing, the results of the 6th model for control group showed the highest R2 value and adjusted R2 = 73.24 %. These values are very close, anticipating minimal shrinkage based on this indicator. It means that the variables included in the 6th model explain 95.55 % variance in electricity consumption for the households that use alternative energy sources for heating. In case of target group this model showed lower results (R2 = 50.73 and adjusted R2 = 12.83). It indicates that the model as fitted explains 50.73 % of the variability in consumption. Moreover, the p-value of the 6th model (target group) is 0.30 which means that there is no statistically significant relationship between the variables at the 95.0 % or higher confidence level. The next higher R2 and adjusted R2 values showed 2nd model (target group; R2= 62.97; adjusted R2= 59.05), the 5th model (control group, R2= 57.12; adjusted R2= 41.91) and the 1st model (target group; R2= 55.4642; adjusted R2= 46.56). However, all other models showed much lower R2 and adjusted R2 values. The lowest R2 and adjusted R2 values were discovered in the 1st model (control group, R2 = 15.63; adjusted R2= 3.09), the 3rd model (control group, R2= 17.41; adjusted R2= 10.87) and the 7th model (target group, R2 = 37.89; adjusted R2 = 0 and control group, R2 = 32.52; adjusted R2 = 0). If adjusted R2 is 0 % it indicates that the model explains none of the variability of the response data around its' mean.

Two major reasons can be highlighted for low R2 values in the 1st testing. In some cases it is entirely expected that R2 values will be low due to predicted human behaviour, such as psychology. Humans are simply harder to predict than physical processes, for instance. Second, if R2 values are low, but the models have statistically significant predictors, it can still draw important conclusions about how changes in the predictor values are associated with changes in the response value and regardless of low R2. User behavioural aspects were not included in the analysis, hence this may explain why there are such low R2 values in many cases.

When looking to the variables included in the regression analysis for the 1st testing, in most cases the models do not precisely explain variance in electricity consumption. Therefore, addition analysis is needed. In case of multiple regression analysis F-ratio is of even greater importance than the t-statistics test. The F-test is used to decide whether the model as a whole has a statistically significant predictive capability, that is, whether the regression is large enough, considering the number of variables needed to achieve it. The null hypothesis is rejected if the F ratio is far larger than 1, it provides compelling evidence against the null hypothesis. However, the F ratio depends on the values of n (sample size) and p. When n is large, an F-statistic that is just a little larger than 1 might still provide evidence against the null hypothesis. In contrast, a larger F-statistic is needed to reject the null hypothesis if n is small.

One of the difficulties for our modelling, of course, is the quite small number of cases for particular model testing. For example, the smallest number of observations is for the 6th model. Also the 7th model has a small number of observations. This indicates that the F-test should be conducted and analysed.

The aim of the 2nd testing was to improve the accuracy of all models by eliminating predictors with low significance. By doing this, it is important to look whether the F-ratio increased. The results of the 2nd testing showed that the p-values and F-ratios' in the ANOVA table were improved. In many cases the F-ratio of the particular model in the 2nd testing is 2-3 times higher than in the 1st modelling. R2 values of the models in the 2nd testing have decreased slightly in comparison to the corresponding R2 values of the models in the 1st testing. This, of course, can be explained with a smaller number of variables. However, adjusted R2 values in the 2nd testing are much higher indicating a better fit of model with the variables included for modelling. It means that if adjusted R2 is greater, better fit quality for that model is compared to the previous model. Nevertheless, if only 2 to 3 significant

predictors are included in the 2nd testing, R2 value does not decrease so dramatically. For example, the 2nd testing of the 3rd model target group include only 3 predictors (Age, Area and Temp), still R2= 35.41 remains similar to the R2 value of the 1st testing (39.36). While F-ratio increased 3 times, thereby increasing that the accuracy of the model has been increased in the 2nd testing. It can be concluded that reducing the number of variables in the 1st testing and including only important ones for the 2nd testing, the model as fitted can explain nearly percentage of the variability. Looking to other models, similar conclusions can be drawn. When comparing the results of all models in the 2nd testing it can be concluded that most statistically significant factors affecting household electricity use are: Apl and Area, followed by Income, Year, Temp. While in many cases Type, Time, No of memb., Age, Edu, and Gen did not show significant influence on electricity use.

4. Conclusions and discussion

We used data derived from the smart metering pilot project households in order to carry out more detailed analysis of the factors affecting household electricity use. We classified households into 7 groups according to types of heating used in households. Multiple regression analysis shows considerably different results between the target and control groups. The results of the 1st testing (when all variables were included in the analysis) did not show a statistically significant relationship between the variables in almost any of the cases. When eliminating predictors with low significance (i.,e., 2nd testing) we focused more on F-ratio importance. For some models F-ratio in the 2nd modeling increased 2-3 times, indicating that the accuracy of the model has increased. Thus, an important finding can be drawn that, by reducing the number of variables it is possible to explain part of the variability of electricity use. The 2nd testing shows that most statistically significant factors affecting household electricity use are: Ap and Ar, followed by I, Y, Te. While in many cases Ty, Ti, M, Ag, Ed, and G did not showed significant influence on electricity use.

Further research has to be based more on in-depth analysis of user behavioural factors that influence changes in consumption. User psychology, habits, routines, attitude and expectations need to be investigated more specifically. This model can be applied when analyzing factors affecting household electricity use.

Acknowledgements

The work has been supported by the National Research Program "Energy efficient and low-carbon solutions for a secure, sustainable and climate variability reducing energy supply (LATENERGI)".

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Appendix A. Multivariate regression analysis results and models' evaluation for both groups (target and control group)

The results of 1st testing (by including all 11 variables in the models) for the target group

E = 274.09 - 54.40-G + 37.63-I - 51.28-M - 4.89-Ti+ 5.63- Ag + 114.86- Ed- 80.53-Ty - 31.82-Y + 2.61- Area - 13.0915- Te -1.45-Ap

F-Ratio = 6.23; P-Value = 0.000; R2 = 55.46; R2 (adjusted) = 46.56

E = - 1800.4 - 44.96-G + 0.52-I + 30.53-M - 42.49-Ti + 10.57-Ag + 375.25-Ed - 5.04-Ty + 25.38-Y + 2.60-Ar + 43.75-Te + 25.41-Ap

F-Ratio = 16.08; P-Value = 0.000; R2 = 62.9671; R2 (adjusted) = 59.05 3rd E = - 1314.51 - 74.24-G + 16.83-I+ 57.59-M - 36.68-Ti + 19.16-Ag - 10.83- Ed- 9-Ty - 6.61-Y + 2.3-Ar + 64.95-Te - 3.67-Ap model F-Ratio = 5.19; P-Value = 0.000; R2= 39.37; R2 (adjusted) = 31.79

E = - 1713.44 - 142.79-G + 28.11- I + 5.19-M+ 70.31- Ti + 3.62- Ag+ 94.73-Ed+ 30.02-Ty + 56.52-Y + 0.75-Ar + 41.73-Te + 3.42-Ap

F-Ratio = 1.36; P-Value = 0.218; R2 = 21.07; R2 (adjusted) = 5.57

E = 1390.02 + 102.75-G - 11.64- I - 41.26-M + 8.02-Ti + 5.59- Ag - 144.02-Ed - 214.26-Ty+ 44.79-Y + 3.04- Ar - 48.09-Te + 9.41-Ap

F-Ratio = 2.77; P-Value = 0.0044; R2 = 28.36; R2 (adjusted) = 18.13

6th E = 8591.01 - 865.77-G - 186.51I + 113.60-M + 61.15-Ti - 8.88- Ag - 196.51-Ed - 441.67-Y + 2.77- Ar - 89.49-Te - 54.23-Ap

model F-Ratio = 1.34; P-Value = 0.3057; R2 = 50.73; R2 (adjusted) = 12.83

E = -2849.26 + 96.68-G + 40-I + 132.76-M - 10.63-Ti + 13.7-Ag + 574.82-Ed+ 660.07-Ty + 141.03-Y + 2.66-Ar - 21.58-Te + 9.84-Ap

F-Ratio = 0.94; P-Value = 0.53; R2 = 37.89; R2 (adjusted) = 0_

The results of 1st testing (by including all 11 variables in the models) for the control group

t E = -1592.99 - 76.69-G + 10.24-I + 70.95-M+ 16.07-Ti + 9.82-Ag + 129.83-Ed + 193.68-Ty + 77.98-Y + 0.99-Ar + 36.59-Te -

d . 21.69-Ap

mo e F-Ratio = 1.25; P-Value = 0.27; R2 = 15.63; R2adjusted) = 3.09

d E = -3405.68 + 144.26-G + 34.64-I - 10.94-M + 12.58-Ti + 0.91-Ag + 255.05-Ed - 132.2-Ty - 170.78-Y + 3.36-Ar + 143.91-Te +

model 8 47 Ap

E = -1029.22 + 35.41-G + 38.76-I + 19.37-M - 11.13-Ti + 6.18-Ag - 38.55-Ed + 127.92-Ty - 29.17-Y + 0.69-Ar + 32.61-Te +

13.47-Ap

F-Ratio = 2.66; P-Value = 0.004; R2 = 17.41; R2 (adjusted) = 10.87

E = -7049.55 + 741.26-G + 172.77-I + 66.96-M - 57.1-Ti + 13.96-Ag + 47.28-Ed - 351.14-Ty - 322.47-Y + 0.85-Ar + 306-Te + 17.89-Ap

F-Ratio = 2.44; P-Value = 0.0195; R2 = 40.15; R2 (adjusted) = 23.69

E = -922.3 - 69.77-G + 77.97-I - 12.8-M + 37.95-Ti - 15.49-Ag + 109.23-Ed + 710.89-Ty - 77.61-Y + 0.11-Ar + 2.82-Te + 34.9-Ap F-Ratio = 3.75; P-Value = 0.0018; R2 = 57.12; R2 (adjusted) = 41.91

E = 7094.75 + 1571-G + 26-I - 1810.79-M + 588.69-Ti + 79.89-Age - 8011.18-Ed + 940.83-Y + 8.34-Ar - 876.03-Te + 155.55-Ap F-Ratio = 4.83; P-Value = 0.071; R2 = 92.35; R2 (adjusted) = 73.24

E = -324.42 + 94.62-G + 16.88 I - 31.85-M + 38.13-Ti + 6.45-Ag - 122.19-Ed + 738.06-Ty - 3.84-Y + 1.15-Ar - 79.76-Te +

32.48-Ap

_F-Ratio = 0.92; P-Value = 0.54; R2 = 32.52 R2 (adjusted) = 0_

The results of 2nd testing (regression models where simplified by including only statistically significant variables) for the target group

1st E = -321 + 28.21-I - 43-M + 7.57-Ag + 2.43-Ar

model F-Ratio = 16.63; P-Value = 0.000; R2 = 51.76; R2 (adjusted) = 48.65 2nd E = -905.89 - 35.18-Ti + 9.55-Ag + 387-Ed + 2.74-Ar + 27.36-Ap model F-Ratio = 35.78; P-Value = 0.000; R2 = 61.92; R2 (adjusted) = 60.19 3rd E = -1615.48 + 15.11-Ag + 2.78-Ar + 61.29-Te model F-Ratio = 17.54; P-Value = 0.000; R2 = 35.41; R2 (adjusted) = 33.39 4th E = -803.96 + 36.58 I + 77.57-Ti + 79.3-Y

model F-Ratio = 4.66; P-Value = 0.0053; R2 = 17.91; R2 (adjusted) = 14.07 5th E = 871.58 - 206.21-Ty + 3.29-Ar

model F-Ratio = 14.05; P-Value = 0.000; R2 = 24.63; R2 (adjusted) = 22.87 6th E = 6296.74 - 673.74-G - 128.98-I- 287.49-Y - 39.19-Ap

model F-Ratio = 2.56; P-Value = 0.072; R2= 34.98; R2 (adjusted) = 21.29 7th E = -540.06 + 745.53-Ty+ 3.5-Ar

model F-Ratio = 3.64; P-Value = 0.041; R2 = 21.86; R2 (adjusted) = 15.85_

The results of 2nd testing (regression models where simplified by including only statistically significant variables) for the control group

1st El= 89.91 + 67.94-M + 9.45-Ag + 71.47-Y - 22.11-Ap

model F-Ratio = 2.47; P-Value = 0.051; R2 = 10.88; R2 (adjusted) = 6.48

2nd E = - 2357.61 - 181.15-Y + 3.97-Ar + 148.61-Te model F-Ratio = 14.18; P-Value = 0.000; R2 = 22.1; R2 (adjusted) = 20.54

3rd E = -120.45 + 37.67- Ie + 17.11-Ap

model F-Ratio = 12.33; P-Value = 0.000; R2 = 14.28; R2 (adjusted) = 13.12

4th E = -7834.41 + 657.13- G + 182.49-I - 299.58-Y + 311.51-Te + 28.05-Ap

model F-Ratio = 5.38; P-Value = 0.0006; R2 = 36.9; R2 (adjusted) = 30.04

5th E = -1242.92 + 74.92-I + 753.12-Ty + 33.59-Ap

model F-Ratio = 14.34; P-Value = 0.000; R2 = 52.45; R2 (adjusted) = 48.79

6th E = 7366.63 + 642.87-G - 759.97-M + 296.34-Ti - 3362.57-Ed + 6.19-Ar - 414.61-Te+ 53.37-Ap

model F-Ratio = 7; P-Value = 0.01; R2 = 87.5; R2 (adjusted) = 75

7th E = 1767.88 - 84.86-Te + 32.34-Ap

model F-Ratio = 3.32; P-Value = 0.0498; R2 = 18.12; R2 (adjusted) = 12.66_

model 5th

model 7th