An economist at T&TEC is analysing the determinants of electricity demand in his
ID: 3220167 • Letter: A
Question
An economist at T&TEC is analysing the determinants of electricity demand in his country. The independent variables he uses in the model are:
1. nocust - average number of customers in thousands
2. price - the average price in cents per kwh for families
3. incm – Total personal income in $ millions population in thousands
The dependent variable, rekwh, represents the electricity demand, which is the kilowatt-hour sale to residential customers (million).
The results of the regression model along with the correlation matrix and residual plots are shown below:
Model 2: OLS, using observations N=75
Dependent variable: reskwh
Coefficient Std. Error t-ratio p-value
Const -322.52 208.941 -1.5436 0.12713
Nocust 2.28999 0.483557 4.7357 0.00001
Price -12.2772 4.99846 -2.4562 0.01649
Incm -0.0355949 0.0204259 -1.7426 0.08573
Mean dependent var 1027.491 S.D dependent var 238.2678
Sum squared resid 482388.5 S.E of regression 82.42696
R-squared 0.885176 Adjusted R-squared 0.880324
F(3,71) 182.4450 P-value(F) 2.74e-33
Log-liklihood -435.2585 Akaike criterion 878.5170
Schwartz criterion 887.7870 Hannan-Quinn 882.2184
Correlation matrix of variables used in the model
Reskwh
Nocust
Price
Incm
Reskwh
1.0000
0.9366
0.7196
0.9245
Nocust
1.0000
0.8211
0.9930
Price
1.0000
0.8056
Incm
1.0000
a. Write down the OLS regression model estimate.
b. Is the model statistically significant?
c. Which variables in the model are statistically significant? Use a=5%?
d. What is the term multicollinearity?
e. Would you use this model to analyze the determinants of demand for electricity? Provide reasons to support your answer.
Reskwh
Nocust
Price
Incm
Reskwh
1.0000
0.9366
0.7196
0.9245
Nocust
1.0000
0.8211
0.9930
Price
1.0000
0.8056
Incm
1.0000
Explanation / Answer
Answer:
An economist at T&TEC is analysing the determinants of electricity demand in his country. The independent variables he uses in the model are:
1. nocust - average number of customers in thousands
2. price - the average price in cents per kwh for families
3. incm – Total personal income in $ millions population in thousands
The dependent variable, rekwh, represents the electricity demand, which is the kilowatt-hour sale to residential customers (million).
The results of the regression model along with the correlation matrix and residual plots are shown below:
Model 2: OLS, using observations N=75
Dependent variable: reskwh
Coefficient Std. Error t-ratio p-value
Const -322.52 208.941 -1.5436 0.12713
Nocust 2.28999 0.483557 4.7357 0.00001
Price -12.2772 4.99846 -2.4562 0.01649
Incm -0.0355949 0.0204259 -1.7426 0.08573
Mean dependent var 1027.491 S.D dependent var 238.2678
Sum squared resid 482388.5 S.E of regression 82.42696
R-squared 0.885176 Adjusted R-squared 0.880324
F(3,71) 182.4450 P-value(F) 2.74e-33
Log-liklihood -435.2585 Akaike criterion 878.5170
Schwartz criterion 887.7870 Hannan-Quinn 882.2184
electricity demand = -322.52+2.28999*Nocust-12.2772*price-0.0355949*incm
Calculated F=182.445, P=0.000 which is < 0.05 level.
The model is significant.
c. Which variables in the model are statistically significant? Use a=5%?
The variable nocust is significant, t=4.7357, P=0.00001 which is < 0.05 level.
The variable price is significant, t=-2.4562, P=0.01649 which is < 0.05 level.
The variable incm is not significant, t=-1.7426, P=0.08573 which is > 0.05 level.
d. What is the term multicollinearity?
Multicollinearity is a state of very high intercorrelations or inter-associations among the independent variables.
Correlation matrix of variables used in the model is used to check for this.
e. Would you use this model to analyze the determinants of demand for electricity? Provide reasons to support your answer.
The model is significant and 88% variation in electricity demand is explained by the model.
We can use this model to analyze the determinants of demand for electricity.
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