Modelling and Forecasting of Residential Electricity Consumption in Nigeria Using Multiple and Quadratic Regression Models

In this paper statistical analysis of the residential electricity demand in Nigeria is presented Particularly, multiple regression model with one period lagged and quadratic regression model without interactions were used to estimate residential electricity consumption and to forecast longterm residential demand for electricity based on annual data over the period 2006– 2014. For the regression models’ explanatory variable, population which is a socio economic variable is used along with temperature which is a climatic variable are used. The results showed that the quadratic regression model without interactions was more accurate due to the fact that it has the highest coefficient of determinant of 93.87 and the least value of Root Mean Square Error (RMSE) of 52.77as compared to the multiple regression model with one period lagged of the dependent variable with coefficient of determinant of 93.50 and RMSE of 53.16. The quadratic regression model was then selected and used to forecast the residential electricity demand in Nigeria for the years 2015 to 2029.


Introduction
Electricity is one of the most important commodities for the development of any nation [1][2][3]. Yet, electricity shortage still remains one of the main challenges facing the Nigeria nation [4][5][6][7][8]. This problem has been attributed to the inability of the electricity supply to meet the consumer demand [9][10][11]. The phenomenal increase in the population, economic activities as well as lack of maintenance of the existing power stations has also contributed to this problem [12][13][14][15][16][17]. More especially, with privatization at the power generation sector, more independent power generation stations are being installed. It is required that adequate plan for meeting the energy demand for different sectors and in this case, the residential sector should be considered. Available studies have focused on the integrated power demand for Nigeria. However, such model is not suitable for planning in many cases since there are different tariff for different power consumer sector.
Moreover, available studies have worked on power demand models data up to 2005. Models and analysis based on more recent data is essential, especially the one that identifies and focuses on the diverse consumer categories. In the research, the problem is on residential, electricity demand, modelling and forecasting for Nigeria.

Model 1: Multiple Regression with One Period Lagged Dependent Variable
The multiple regression model with one period lagged dependent variable expresses electricity consumption (E t ) as a linear function of Population (P) and Temperature (T t ) as follows: Where 0 α is the intercept, 1 α , 2 α and 3 α are the contributions of Population (P) and Temperature (T) respectively. Econometric Views (EViews) statistical package is used to perform the regression from which the values of the intercept 0 α and the regression coefficients 1 α , 2 α and 3 α are obtained for the multiple regression model.

Model 2: Quadratic Regression Model Without Interaction
Making t ε the subject gives; Sum of the square of the error, S is given as; ( ) Again, Econometric Views (EViews) statistical package is used to perform the regression from which the values of the intercept 0 α and the regression coefficients 1 α , 2 α 3 α and 4 α are obtained for the quadratic regression model with interaction.

F-Test
To check the goodness of fit of the models, F test is use and it is given as: 1 SSR MSR P = − (8) Where P is the number of parameters Where n is the number of observation The sum of square Total , SST is given as; Sum of square regression, SSR, can be calculated for each model as follows: Where, J is the matrix, Sum of square Error (SSE) = SST-SSR (13)

Coefficient of Determination
The coefficient of determination shows the percentage of the variation in the dependent variable explained by the independent variables. It is given as

Root Mean Square Error (RMSE)
The square of the sum of square of differences between the predicted and observed value divided by the number of observation: It can be expressed mathematically as:

Result and Discussion
The coefficient of determination r 2 of 0.935 shows that 93.5% of the variation in residential electricity consumption was accounted for by the multiple regression with one period lagged of the dependent variable. The contribution of population (α =16.02) is positive meaning that as population increases, residential electricity consumption also increases. Table 2 and figure 1 show the actual and the predicted residential electricity consumption in Nigeria for the years 2007 to 2014.   Table 3 shows the model parameters and performance measures for the quadratic regression with interaction. From the results in Table 3, the quadratic regression with interaction is given as; 2 The r-square value of 0.9389 indicates that 93.89% of the variation in residential electricity consumption was explained by the quadratic regression with interaction. The model also reveals that the linear term of population ( =386.57) and the quadratic term for temperature ( = 177.38) have positive contribution to residential electricity consumption. This result indicates that as these variables increases in value, residential electricity consumption also increases. Summary results of the actual and predicted residential electricity consumption in Nigeria for the years 2007 to 2014 are as shown in Table 4 and figure 2.     Table 5 shows performance evaluation of the two competing models. The result shows that the two models were highly competitive as the r-square obtained for each model were very high. The quadratic regression with interaction gave the highest value of coefficient of determination (r 2 ) and the least Root Mean Square Error (RMSE) compared with multiple regression with one period lagged of the dependent variable. Hence, quadratic regression with interaction is recommended for forecasting residential electricity consumption in Nigeria.
The population for 2015 and 2019 were projected using the formula; Where n = number of years, 1 t P − = previous year population, t P = the population of the year to be estimated and r is the population growth rate of Nigeria which is given to 3.2% according to 2006 population census. Also, the temperature was predicted using simple linear regression where a simple regression model of temperature versus time was fitted as follows; The model parameters 0 a and 1 a were estimated using Microsoft excel programme. 0 34.602 a = , 1 0.0613 a = 34.602 0.0613 t = time, 10, , 24 t = ⋯ Table 6 and figure 3 show the forecasted residential electricity consumption in Nigeria from 2015-2029 using the quadratic regression with interaction. From the results in Table  5, the Residential Electricity Consumption in Nigeria will reach 6521.09 MW/h in the year 2029.

Conclusion
The paper statistical analysis of the residential electricity demand in Nigeria is presented, employing annual data over the period 2006-2014. Particularly, multiple regression model with one period lagged and quadratic regression model without interactions were used to estimate residential electricity consumption and to forecast long-term residential demand for electricity. The results showed that the quadratic regression model without interactions was more accurate due to the fact that it has the highest coefficient of determinant and the least value of Root Mean Square Error as compared to the multiple regression model with one period lagged of the dependent variable. The quadratic regression model was then selected and used to forecast the residential electricity demand in Nigeria for the years 2015 to 2029.