Indian Power Sector Demand and supply

Managerial Economics Final Project

AKSHAT VAID - 91004 CIJIL DICLAUSE - 91014

GOURAB KUNDU - 91020 HARSHDEEP GARG -91023 SAMARTH GULATI - 91047

FMG XVIII A FORE SCHOOL OF MANAGEMENT

Managerial Economics Final Project Report September 2009

FORE School of Management – FMG XVIII A – Trimester 1

2

Preface he Indian power sector is such a magnanimous entity in itself that deciphering the

intricate nuances of the sector becomes synonymous to fishing in the dark. Never

the less, this project is an earnest attempt made to unravel the dilemma of the

Indian Power Sector.

India is such a diverse country both in terms of geography and demography that

narrowing down to a few parameters that are responsible for the change/ alteration of

the demand of power is next to impossible. Hence, a better approach in determining

the power demand across India is to take into account the various seasonal variations

as well as the influences of the different regions in India.

Acknowledgement

The group members would sincerely like to thank Dr. Ravikesh Srivastava for his unending

support and motivation towards the execution of the project. Without his guidance, the

report would not have taken the shape that it has taken at this moment.

We’d also like to thank all the fellow students of FMG XVIII section A for their constant

pep-talk and encouragement.

Thanking one and all for all the help vented to the execution of the project.

Gourab Kundu

Samarth Gulati

Cijil Diclause

Akshat Vaid

Harshdeep Garg

T



3

Table of Contents

1. Introduction

2. Project Objective

3. Project Methodology

4. Data and parameters

5. Simple Regression

a. Per capita annual income in Rupees

b. Population

c. Price index with '93 as index of 100

d. Gross national Product

6. Multiple Regression Model

a. Degree of Correlation

b. Multiple Regression Model

c. Multiple Regression Model Obtained

d. Prediction according to multiple regression model of power in India

7. Moving Averages

a. 3 year moving average

b. 5 year moving average

8. Exponential Smoothing

a. Dumping Factor/ Weight: 0.3

b. Dumping Factor/ Weight: 0.5

9. Seasonal Trend Analysis

a. Region wise Analysis

b. Equation for Regression

c. Why Seasonal Variations?

d. Trend analysis in North India

e. Trend analysis in South India

f. Trend analysis in North India

g. Trend Analysis Regions/Seasons

h. Power Trading

10. Arima and Analysis

11. Annexure



4

1. Introduction Indian power sector has attained insurmountable importance because of the huge

boom in India’s economy. In fact, the visionary in Dr. Manmohan Singh has

acknowledged the fact that it is electricity that is a driving factor for India’s economy.

He was so forthright that he laid no stone unturned to have India sign the Indo-US

Nuclear Civil Agreement. Perhaps power has become the most important commodity

that needs to be taken into account for the estimation of India’s GDP.

But a lot needs to be done in the Indian Power Sector. As a matter of fact just 44% of the

rural households have access to electricity. This statement is both a danger and an

opportunity for India. A lot of uncaptured demand for power can be tapped into

hence, an industry as large as the Power sector awaits expansion of magnanimous

proportions.

Some facts and figures about the Indian Power Sector:

Due to India's economic upturn, the demand for energy in India has grown at an

average of 3.6% per annum in the past 30 years.

The theft of electricity, a common phenomenon in most parts of urban India

amounts to about 1.5% of India's total GDP.

India is world's 6th largest energy consumer, accounting for 3.4% of global energy

consumption.

Electricity losses in India during transmission and distribution are extremely high

and vary between 30 to 45%.

Electricity demand outstripping supply by 7-11%, is a trend in the past few years.

The government policy to date:

100% FDI is permitted in generation, transmission and distribution of power. The

Government is inclined to draw private investment in the sector.

The various kinds of projects that are/will be undertaken in the coming months/years in

India:

Hydro Projects

Ultra Mega Power Projects

Nuclear Power

Rural Electrification

Renewable Sources of Energy



5

2. Project Objective

The project objectives have been classified as follows:

Forecasting the demand of power in the coming years 2009-10, 2010-11, 2011-12.

Understanding the intricacies of the Indian Power Sector by looking into the

various geographical regions.

Collating data that establishes the influence of seasons on the demand of power

in India.

3. Project Methodology

The following tools have been used to determine the demand of power in India:

Simple Regression

Multiple Regression Model

Moving Averages

Exponential Smoothing

Seasonal Trend Analysis (by Region)

Auto Regression Integrated Moving Averages (ARIMA)

4. Data and parameters

Data used for tenure

1981 to 2008

Parameters considered:

Per Capita Income in India in Rupees

Population of India

Price Index of electricity with 1993 as Index = 100

(GNP) Gross National Product in Rupees



6

5. Simple Regression In statistics, linear regression refers to any approach to modeling the relationship

between one or more variables denoted y and one or more variables denoted X, such

that the model depends linearly on the unknownparameters to be estimated from

the data. Such a model is called a "linear model." Most commonly, linear regression

refers to a model in which the conditional mean of y given the value of X is an affine

function of X. Less commonly, linear regression could refer to a model in which

the median, or some other quantile of the conditional distribution of y given X is

expressed as a linear function of X. Like all forms of regression analysis,linear

regression focuses on the conditional probability distribution of y given X, rather than on

the joint probability distribution of y and X, which is the domain of multivariate analysis.

Linear regression was the first type of regression analysis to be studied rigorously, and to

be used extensively in practical applications. The reason for this is that models that

depend linearly on their unknown parameters are easier to fit than models that are

related non-linearly to their parameters and the statistical properties of the resulting

estimators are easier to determine.

Linear regression has many practical uses. Most applications of linear regression fall into

one of the following two broad categories:

If the goal is prediction, or forecasting, linear regression can be used to fit a

predictive model to an observed data set of y and X values. After developing such a

model, if an additional value of X is then given without its accompanying value of y,

the fitted model can be used to make a prediction of the value of y.

If we have a variable y and a number of variables X1, ..., Xp that may be related to y,

we can use linear regression analysis to quantify the strength of the relationship

between y and theXj, to assess which Xj may have no relationship with y at all, and to

identify which subsets of the Xj contain redundant information about y, so that once

one of them is known, the others are no longer informative.

Linear regression models are often fit using the least squares approach, but may also be

fit in other ways, such as by minimizing the "lack of fit" in some other norm, or by

minimizing a penalized version of the least squares loss function as in ridge regression.

Conversely, the least squares approach can be used to fit models that are not linear

models. Thus, while the terms "least squares" and linear model are closely linked, they

are not synonymous.

http://en.wikipedia.org/wiki/Statistics

http://en.wikipedia.org/wiki/Parameters

http://en.wikipedia.org/wiki/Estimation_theory

http://en.wikipedia.org/wiki/Data

http://en.wikipedia.org/wiki/Conditional_expectation

http://en.wikipedia.org/wiki/Affine_transformation



http://en.wikipedia.org/wiki/Median

http://en.wikipedia.org/wiki/Quantile

http://en.wikipedia.org/wiki/Regression_analysis

http://en.wikipedia.org/wiki/Conditional_probability_distribution

http://en.wikipedia.org/wiki/Joint_probability_distribution

http://en.wikipedia.org/wiki/Multivariate_analysis

http://en.wikipedia.org/wiki/Regression_analysis

http://en.wikipedia.org/wiki/Prediction

http://en.wikipedia.org/wiki/Forecasting

http://en.wikipedia.org/wiki/Least_squares

http://en.wikipedia.org/wiki/Norm_(mathematics)

http://en.wikipedia.org/wiki/Loss_function

http://en.wikipedia.org/wiki/Ridge_regression



7

a. Per capita annual income in Rupees

Coefficients

Intercept (a) -2299699.673

Year (b) 1159.777846

Y* = a + b X*

Projected Values

for 2009 (Y*) 30294.01984

for 2010 31453.79769

for 2011 32613.57553

b. Population

Intercept (a) -35404582017

Year (b) 18211019.86

Y* = a+ b X*

Projected Values

for 2009 (X*) 1181356876

for 2010 1199567896

for 2011 1217778916

c. Price index with '93 as index of 100

Intercept (a) - 20920.70602

Year (b) 10.55749863

Y* = a + b X*

Projected Values

for 2009 (X*) 289.3087302

for 2010 299.8662288

for 2011 310.4237274

d. Gross national Product

Intercept (a) -298672038

Year (b) 150468.8985

Y* = a + b X*

Projected Values

for 2009 (X*) 3619978.992

for 2010 3770447.891

for 2011 3920916.789



8

6. Multiple Regression Model

Data used for tenure 1981 to 2008 (28 observations)

Parameters considered (4): Degree of freedom = 24

Per Capita Income in India in Rupees

Population of India

Price Index of power with 1993 as 100

Gross National Product (GNP) in Rupees

a. Degree of Correlation

Coefficients of correlation (r) Calculated by doing a regression using the power

demand (Y) and individual parameters(X). The value of R2 (coefficient of determination

is thus determined)

Square root of R2

Per Capita Income = 0.9544

Population of India = 0.9955

Price Index of power = 0.9719

Gross National Product = 0.9706

b. Multiple Regression Model

Y* = a + b1 X1 + b2 X2 + b3 X3 + b4 X4

Where,

Y* = Estimated demand a = coefficient of Regression b1 = coefficient of X1

b2 = coefficient of X2 b3 = coefficient of X3 b4 = coefficient of X4

X1 = Per Capita Income X2 = Population X3 = Price Index X4 = GNP

c. Multiple Regression Model Obtained

Y* = -221590.9 + (-4.32) X1 + 0.0005X2 + (-280.11)X3 + 0.092X4

(-3.20210696) (-1.85033966) (5.1014939) (-1.2485916) ( 6.4988346)

Figures given in braces are that of the t-statistic value

d. Prediction according to multiple regression model of power in India

2009: 4,78,432.1569 GWH

2010: 4,93,186.5125 GWH

2011: 5,07,940.8682 GWH



9

7. Moving Averages In statistics, a moving average, also called rolling average, rolling mean or running

average, is a type of finite impulse response filter used to analyze a set of data points by

creating a series of averages of different subsets of the full data set. A moving average

is not a single number, but it is a set of numbers, each of which is the average of the

corresponding subset of a larger set of data points. A moving average may also use

unequal weights for each data value in the subset to emphasize particular values in the

subset.

A moving average is commonly used with time series data to smooth out short-term

fluctuations and highlight longer-term trends or cycles. The threshold between short-

term and long-term depends on the application, and the parameters of the moving

average will be set accordingly. For example, it is often used in technical analysis of

financial data, like stock prices, returns or trading volumes. It is also used in economics to

examine gross domestic product, employment or other macroeconomic time series.

Mathematically, a moving average is a type of convolution and so it is also similar to

the low-pass filter used in signal processing. When used with non-time series data, a

moving average simply acts as a generic smoothing operation without any specific

connection to time, although typically some kind of ordering is implied.

A simple moving average (SMA) is the unweighted mean of the previous n data points.

For example, a 10-day simple moving average of closing price is the mean of the

previous 10 days' closing prices. If those prices are then the

formula is

When calculating successive values, a new value comes into the sum and an old

value drops out, meaning a full summation each time is unnecessary,

Results and Analysis

a. 3 year moving average:

2009: 4,60,756.7 GWH Root Mean Square Error = 33380

b. 5 year moving average:




10

8. Exponential Smoothing In statistics, exponential smoothing is a technique that can be applied to time

series data, either to produce smoothed data for presentation, or to make forecasts.

The time series data themselves are a sequence of observations. The observed

phenomenon may be an essentially random process, or it may be an orderly, but noisy,

process. Whereas in the simple moving average the past observations are weighted

equally, exponential smoothing assigns exponentially decreasing weights as the

observation get older.

Exponential smoothing is commonly applied to financial market and economic data,

but it can be used with any discrete set of repeated measurements. The raw data

sequence is often represented by {xt}, and the output of the exponential smoothing

algorithm is commonly written as {st} which may be regarded as our best estimate of

what the next value of x will be. When the sequence of observations begins at

time t = 0, the simplest form of exponential smoothing is given by the formulas

where α is the smoothing factor, and 0 < α < 1.

The simplest form of exponential smoothing is given by the formulae

where α is the smoothing factor, and 0 < α < 1. In other words, the smoothed statistic st is

a simple weighted average of the latest observation xt and the previous smoothed

statistic st−1. Simple exponential smoothing is easily applied, and it produces a smoothed

statistic as soon as two observations are available.

Values of α close to one have less of a smoothing effect and give greater weight to

recent changes in the data, while values of α closer to zero have a greater smoothing

effect and are less responsive to recent changes. There is no formally correct procedure

for choosing α. Sometimes the statistician's judgment is used to choose an appropriate

factor.

RESULTS AND ANALYSIS

a. Dumping Factor/ Weight: 0.3


b. Dumping Factor/ Weight: 0.5


http://en.wikipedia.org/wiki/Statistics

http://en.wikipedia.org/wiki/Time_series



http://en.wikipedia.org/wiki/Stochastic_process

http://en.wikipedia.org/wiki/Statistical_noise

http://en.wikipedia.org/wiki/Simple_moving_average



11

9. Seasonal Trend Analysis

a. Region wise Analysis

Estimation of Power for a particular month

(Here a month has been taken as a benchmark for a season) the months taken into

account are:

January

April

July

October

b. Equation for Regression:

Y* = a + b X*

Where,

Y* = Estimated value of Demand of power in Regional India

X* = Year in which the estimation is being done

a = constant of regression

b = coefficient of X

c. Why Seasonal Variations?

Seasonal variation has been done by using data of the last five years with respect to 4

regions in India.

For incorporating this seasonal variations we can either use

Ratio to trend method

Dummy variable method

We did by ratio to trend method and is based on the assumptions that past trends and

seasonal patterns in data will persist.



12

d. Trend analysis in North India

Month

Seasonal

Adjustment

Factor

Estimated Demand for Power in MWH

2009 2010 2011

Estimated

Value

Adjusted

Value

Estimated

Value

Adjusted

Value

Estimated

Value

Adjusted

Value

January 0.99994 35585.5 35584.4 37695.2 37694.0 39804.9 39803.7

April 0.99995 33490.5 33484.7 35666 35659.8 37841.5 37834.9

July 1.00002 37834.3 37835.1 40126.4 40127.2 42418.5 42419.4

October 0.99998 34627.1 34621.6 36549 36543.2 38470.9 39803.7

e. Trend analysis in South India

Month

Seasonal

Adjustment

Factor


2009 2010 2011

Estimated

Value

Adjusted

Value

Estimated

Value

Adjusted

Value

Estimated

Value

Adjusted

Value

January 00..9999999988 2299442211 2299441133 3311008811 3311007766..88 3322774411 3322773366..66

April 00..9999999988 2299331177..55 2299331144..11 3300992244 3300992200..44 3322553300..55 3322552266..77

July 11..0000000099 2277333377 2277333366..66 2288991166..44 2288991166 3300449955..88 3300449955..33

October 00..9999999977 2299112200..55 2299111144..33 3300996644 3300995577..44 3322880077..55 3322880000..55



13

f. Trend analysis in North India

Month

Seasonal

Adjustment

Factor


2009 2010 2011

Estimated

Value

Adjusted

Value

Estimated

Value

Adjusted

Value

Estimated

Value

Adjusted

Value

January 11..00000055 11669944..99 11669955..7777 11881188..3344 11881199..2299 11994411..7788 11994422..7777

April 11..00000066 11772200..88 11772211..8899 11883355..5522 11883366..6644 11990088..5544 11990088..9999

July 11..00000022 11778899..2299 11998877..6699 11990088..5544 11990088..9999 22002277..8811 22002288..2288

October 11..00000055 11991111..4477 11991122..5599 22006622..6622 22006633..8811 22221133..7755 22221155..0044

g. Trend Analysis Regions/Seasons

Geographical factors have a huge say in the demand of power in India.

Temperature and rainfall have a direct correlation with the rise/fall of demand.

Uniformity of demand in power is absent in India.

The Concept of Power Trading can be employed: regions of surplus can trade

power with states running in deficit.

h. Power Trading

Power trading inherently means a transaction where the price of power is

negotiable and options exist about whom to trade with and for what quantum.

In India, power trading is in an evolving stage and the volumes of exchange are

not huge.

The Electricity Act, 2003, mandated development of power markets by

appropriate commissions through enabling regulations

In India, while there is a huge section of consumers, who are power deprived,

there are a lot of Power Plants that are under utilized

The emerging trends will help in proper flow of power from surplus regions to

deficit regions and thus try to bring about a balance in the power sector

PTC India Ltd. (PTC), is the leading provider of power trading solutions in India.



14

10. Arima and Analysis

In statistics and signal processing, autoregressive moving average (ARMA) models, sometimes

called Box-Jenkins models after the iterative Box-Jenkins methodology usually used to estimate

them, are typically applied to time series data.

Given a time series of data Xt, the ARMA model is a tool for understanding and, perhaps,

predicting future values in this series. The model consists of two parts, an autoregressive (AR) part

and a moving average (MA) part. The model is usually then referred to as the ARMA(p,q) model

where p is the order of the autoregressive part and q is the order of the moving average part.

As for our case, we had chosen data for the past 57 years to apply ARMA. For applying ARMA,

we used an add inn in the the software MS EXCEL. There we tried various combinations of the

values of p and q but p=2 and q=5 was the best fit one as it showed the least values of mean

absolute percentage errors(MAPE).The model then obtained was as follows:-

timeseries: y

Method: Nonlinear Least Squares (Levenberg-Marquardt)

date: 09-07-09 time: 19:40

Included observations: 55

p = 2 - q = 5 - no constant - autoselection (AIC)

Coefficient Std. Error t-Statistic Prob.

AR(1) 0.397428032 0.18841621 2.109309127 0.040159332

AR(2) 0.716593943 0.200329027 3.577084936 0.000805756

MA(1) 1.095130154 0.158698018 6.90071729 1.044E-08

MA(2) 0.533752611 0.108851108 4.903511072 1.11893E-05

MA(3) 0.882860313 0.035104024 25.14983223 -2.22045E-16

MA(4) 1.080898221 0.153486824 7.042286719 6.33377E-09

MA(5) 0.585551794 0.116176175 5.040205458 7.02898E-06

R-squared 0.999081

Mean

dependent var 133354.323273

Adjusted R-

squared 0.998966

S.D.

dependent var 128580.853224

S.E. of regression 4134.981337

Akaike info

criterion 19.258835

Sum squared

resid 820707391.547770

Schwarz

criterion 19.514314

Log likelihood -522.617969

Durbin-Watson

stat 1.845670



15

But even in this graph we had one portion where the model did not fit very well instead the

spike over their showed huge deviation from the actual value. This caused deviation not just in

the portion where it was present, but the deviation it caused deviation in the whole of the

model. This is shown below.

To remove this error we followed outlier deletion as per which the value which had caused an

unacceptable deviation is removed from the data and the same process is again applied

upon. The results were encouraging as shown below.

-20000

-15000

-10000

-5000

0

5000

10000

15000

0 10 20 30 40 50 60

Residualplot

Residual

-20000

-15000

-10000

-5000

0

5000

10000

15000

20000

0 10 20 30 40 50 60

Residualplot

Residual



16

We just removed one entry from the 57 that we had taken initially [1.75% sampling] and in the

process the MAPE reduced from 0.077 to 0.05 and at the same time the Median of Absolute

residuals {MAR} reduced from 2224 to 1308.

On the basis of the new model we obtained the following forecasts for the next 10 years.

Table

Period IR Forecast

1 1.000000 504900.515272

2 1.656811 560753.674775

3 2.202814 621694.158683

4 2.536284 685205.377056

5 2.592833 750279.007608

6 2.411722 814653.053112

7 1.972840 877917.986331

8 1.367065 939074.264170

9 0.632118 998877.677111

10 -0.116531 1057891.283728

These values don’t fit very well if seen in light of the day as too steep an increase is predicted as

per the model. The reason for this lies in the fact that ARIMA as a tool takes only the past values

of a function into consideration. Any other external factor which may have a bearing on the

actual results are not considered in the forecasts.



17

11. Annexure

year

power

demand in

India GWH

per capita

income annual population

price with '93

as Index = 100

Gross

National

product

1981 90245 3456 683329097 31.4 61099

1982 95589 3598 698362337 35 68959

1983 102344 3740 713726308 37.9 79875

1984 144068 4024 729428287 39.2 86543

1985 123099 4308 745475709 43.9 99876

1986 135952 4592 761876175 48.2 117812

1987 145613 4876 778637451 52.4 196814

1988 160196 5160 795767475 55.5 328004

1989 175419 5444 813274359 59 459194

1990 190357 5728 831166395 63.1 590384

1991 207645 6012 846421039 70 721574

1992 220674 6440.25 864534449 78.2 852764

1993 238569 7698 883035486 100 983954

1994 259629 8955.75 901932445 113.6 1115144

1995 277029 10213.5 921233800 127.8 1246334

1996 280143 11471.25 940948203 133.5 1377524

1997 296749 12729 961084495 151.8 1508714

1998 309734 14682 981651703 157.2 1639904

1999 312841 16635 1002659050 168.9 1771094

2000 316600 18588 1024115953 200 1902284

2001 322459 20541 1028737436 224.8 2077658

2002 339598 22494 1048797816 238 2244725

2003 360937 24447 1069249373 248.8 2519921

2004 386134 26400 1090099736 253 2855331

2005 411887 28353 1111356681 263.4 3249554

2006 425748 30306 1133028136 271.7 3643777

2007 440774 32259 1155122185 273 4038000

2008 453800 34212 1169266890 275 4432223



18

Multiple regression data:

SUMMARY OUTPUT

Regression Statistics

Multiple R 0.997742312

R Square 0.995489721

Adjusted R Square 0.994705325

Standard Error 9025.442084

Observations 28

ANOVA

df SS MS F

Significanc

e F

Regressio

n 4

4.13522E+

11

1.0338E+1

1

1269.11

6 1.31E-26

Residual 23

187354791

1

81458604.

8

Total 27

4.15395E+

11

Coefficien

ts

Standard

Error t Stat P-value Lower 95%

Upper

95%

Lower

95.0%

Upper

95.0%

Intercept -221590.9001 69201.59223 -3.202107 0.003959 -364745

-

78436.5 -364745

-

78436.5

per

capita

income

annual -4.320341501 2.334891044 -1.8503397 0.077153 -9.15043

0.50974

9

-

9.15043

0.50974

9

populatio

n 0.000491486 9.63415E-05 5.10149393 3.63E-05 0.000292

0.00069

1

0.00029

2

0.00069

1

price with

'93 as

Index =

100 -280.1083272 224.3394251 -1.2485916 0.224375 -744.19

183.973

1 -744.19

183.973

1

Gross

National

product 0.091525749 0.014083409 6.49883463 1.24E-06 0.062392 0.12066

0.06239

2 0.12066

ppGpppG



19

RESIDUAL OUTPUT MULTIPLE REGRESSION MODEL

Observation

Predicted power demanded in

India GWH Residuals

Standard

Residuals

1 96121.23991 -5876.23991 -0.705422

2 102607.3771 -7018.37705 -0.8425316

3 109731.8424 -7387.84242 -0.8868846

4 116468.317 27599.68297 3.31324517

5 123032.223 66.77697032 0.00801634

6 130302.9811 5649.018877 0.67814491

7 143368.1945 2244.80547 0.26948103

8 161699.3073 -1503.30731 -0.1804668

9 180103.5983 -4684.59833 -0.5623696

10 198529.1208 -8172.1208 -0.9810344

11 214874.0992 -7229.09923 -0.867828

12 231636.7706 -10962.7706 -1.3160422

13 241196.7586 -2627.75864 -0.3154532

14 253248.225 6380.774955 0.76598966

15 265330.3808 11698.6192 1.40437822

16 279996.465 146.5349797 0.01759101

17 291340.5364 5408.463629 0.6492671

18 303506.0771 6227.922901 0.74764031

19 314123.257 -1282.25704 -0.1539305

20 319527.2864 -2927.2864 -0.3514105

21 322465.6025 -6.60246845 -0.0007926

22 335480.8687 4117.13129 0.49424718

23 359257.2408 1679.759227 0.20164921

24 390589.4664 -4455.4664 -0.5348631

25 425767.7536 -13880.7536 -1.6663358

26 461737.9942 -5989.99419 -0.7190778

27 499876.6917 897.3082766 0.10771871

28 533912.3243 11887.67566 1.42707378



20

Forecasting Per Capita Income Annually In India


Multiple R 0.948678

R Square 0.899991

Adjusted R

Square 0.896144

Standard

Error 3240.844

Observatio

ns 28

ANOVA

df SS MS F

Significanc

e F

Regression 1

2.46E+0

9 2.46E+09

233.976

3 1.63E-14

Residual 26

2.73E+0

8 10503071

Total 27

2.73E+0

9

Coefficients

Standard

Error t Stat P-value Lower 95%

Uppe

r 95%

Lower

95.0%

Uppe

r

95.0%

Intercept -2299700 151226 -15.207 1.87E-14 -2610549

-

1988

8

-

261054

9

-

198885

0

year 1159.778 75.82089 15.29628 1.63E-14 1003.926

1315.

2

1003.9

6

1315.6

3



21

RESIDUAL OUTPUT

Observation

Predicted per

capita income

annual Residuals

Standard

Residuals

1 -2179.76 5635.76 1.772105

2 -1019.98 4617.982 1.452076

3 139.7958 3600.204 1.132046

4 1299.574 2724.426 0.856667

5 2459.352 1848.648 0.581288

6 3619.129 972.8706 0.305909

7 4778.907 97.09278 0.03053

8 5938.685 -778.685 -0.24485

9 7098.463 -1654.46 -0.52023

10 8258.241 -2530.24 -0.79561

11 9418.019 -3406.02 -1.07099

12 10577.8 -4137.55 -1.30101

13 11737.57 -4039.57 -1.2702

14 12897.35 -3941.6 -1.2394

15 14057.13 -3843.63 -1.20859

16 15216.91 -3745.66 -1.17778

17 16376.69 -3647.69 -1.14698

18 17536.46 -2854.46 -0.89756

19 18696.24 -2061.24 -0.64814

20 19856.02 -1268.02 -0.39872

21 21015.8 -474.797 -0.14929

22 22175.57 318.4251 0.100125

23 23335.35 1111.647 0.349546

24 24495.13 1904.869 0.598966

25 25654.91 2698.092 0.848386

26 26814.69 3491.314 1.097807

27 27974.46 4284.536 1.347227

28 29134.24 5077.758 1.596648



22

population

SUMMARY

OUTPUT


Multiple R 0.999281057

R Square 0.998562631

Adjusted R

Square 0.998507347

Standard

Error 5791797.75

Observatio

ns 28

ANOVA

df SS MS F

Significan

ce F

Regressio

n 1

6.06E+1

7 6.06E+17

18062.

6 1.73E-38

Residual 26

8.72E+1

4 3.35E+13

Total 27

6.07E+1

7

Coefficient

s

Standar

d Error t Stat

P-

value Lower 95%

Upper

95%

Lower

95.0%

Upper

95.0%

Intercept

-

354045820

17 2.7E+08 -131.002

3.37E-

38 -3.6E+10

-

3.5E+10

-

3.6E+10

-

3.5E+10

year

18211019.8

6

135501.

5 134.3972

1.73E-

38 17932493

184895

47

179324

93

184895

47

y



23

RESIDUAL OUTPUT OF

PREDICTED

POPULATION IN INDIA

Observation

Predicted

population Residuals

Standard

Residuals

1 671448320.3 11880777 2.090387

2 689659340.2 8702997 1.531266

3 707870360.1 5855948 1.030336

4 726081379.9 3346907 0.588878

5 744292399.8 1183310 0.2082

6 762503419.6 -627244 -0.11036

7 780714439.5 -2076988 -0.36544

8 798925459.3 -3157984 -0.55564

9 817136479.2 -3862120 -0.67953

10 835347499.1 -4181104 -0.73565

11 853558518.9 -7137480 -1.25582

12 871769538.8 -7235090 -1.27299

13 889980558.6 -6945072 -1.22196

14 908191578.5 -6259133 -1.10128

15 926402598.3 -5168798 -0.90943

16 944613618.2 -3665415 -0.64492

17 962824638.1 -1740143 -0.30617

18 981035657.9 616045.4 0.108391

19 999246677.8 3412372 0.600397

20 1017457698 6658256 1.1715

21 1035668717 -6931281 -1.21954

22 1053879737 -5081921 -0.89415

23 1072090757 -2841384 -0.49993

24 1090301777 -202041 -0.03555

25 1108512797 2843884 0.500373

26 1126723817 6304320 1.109226

27 1144934837 1018748 1.792433

28 1163145856 6121034 1.076977



24

Predicted Price


Multiple R 0.97567

R Square 0.951932

Adjusted R

Square 0.950083

Standard Error 19.88692

Observations 28

ANOVA

df SS MS F Significance F

Regression 1 203638.8 203638.8

514.90

3 1.16E-18

Residual 26 10282.73 395.4897

Total 27 213921.6

Coefficien

ts

Standar

d Error t Stat

P-

value

Lower

95%

Upper

95%

Lower

95.0%

Upper

95.0%

Intercept -20920.7 927.9742 -22.5445

1.36E-

18 -22828.2

-

19013.2

-

22828.2

-

19013.2

year 10.5575 0.465263 22.69147

1.16E-

18 9.601137

11.5138

6

9.60113

7

11.5138

6

y



25

RESIDUAL OUTPUT

Observatio

n

Predicted

price with '93

as Index = 100

Residual

s

Standar

d

Residual

s

1 -6.30123 37.70123 1.931893

2 4.256267 30.74373 1.575376

3 14.81377 23.08623 1.182989

4 25.37126 13.82874 0.708615

5 35.92876 7.971237 0.408464

6 46.48626 1.713738 0.087816

7 57.04376 -4.64376 -0.23796

8 67.60126 -12.1013 -0.62009

9 78.15876 -19.1588 -0.98174

10 88.71626 -25.6163 -1.31263

11 99.27375 -29.2738 -1.50005

12 109.8313 -31.6313 -1.62085

13 120.3888 -20.3888 -1.04476

14 130.9463 -17.3463 -0.88886

15 141.5037 -13.7037 -0.70221

16 152.0612 -18.5612 -0.95112

17 162.6187 -10.8187 -0.55438

18 173.1762 -15.9762 -0.81866

19 183.7337 -14.8337 -0.76011

20 194.2912 5.708758 0.292529

21 204.8487 19.95126 1.022346

22 215.4062 22.59376 1.157754

23 225.9637 22.83626 1.17018

24 236.5212 16.47876 0.844408

25 247.0787 16.32126 0.836337

26 257.6362 14.06377 0.720658

27 268.1937 4.806267 0.246284

28 278.7512 -3.75123 -0.19222



26

Gross National Product

SUMMAR

Y

OUTPUT


Multiple R 0.957543

R Square 0.916889

Adjusted R

Square 0.913692

Standard

Error 379752.6

Observations 28

ANOVA

df SS MS F

Significan

ce F

Regression 1 4.14E+13 4.14E+13

286.833

9 1.46E-15

Residual 26 3.75E+12 1.44E+11

Total 27 4.51E+13

Coefficien

ts

Standar

d Error t Stat

P-

value Lower 95%

Upper

95%

Lower

95.0%

Upper

95.0%

Intercept -3E+08

1772022

1 -16.8549

1.63E-

15 -3.4E+08

-

2.6E+08

-

3.4E+08

-

2.6E+08

year 150468.9 8884.47 16.93617

1.46E-

15 132206.6

168731.

2

132206.

6

168731.

2

y



27

RESIDUAL OUTPUT

Observati

on

Predicted Gross

National product Residuals

Standard

Residuals

1 -593150 654249.2 1.755649

2 -442681 511640.3 1.372964

3 -292212 372087.4 0.99848

4 -141743 228286.5 0.612597

5 8725.429 91150.57 0.244599

6 159194.3 -41382.3 -0.11105

7 309663.2 -112849 -0.30283

8 460132.1 -132128 -0.35456

9 610601 -151407 -0.40629

10 761069.9 -170686 -0.45803

11 911538.8 -189965 -0.50976

12 1062008 -209244 -0.5615

13 1212477 -228523 -0.61323

14 1362946 -247802 -0.66496

15 1513414 -267080 -0.7167

16 1663883 -286359 -0.76843

17 1814352 -305638 -0.82017

18 1964821 -324917 -0.8719

19 2115290 -344196 -0.92363

20 2265759 -363475 -0.97537

21 2416228 -338570 -0.90854

22 2566697 -321972 -0.864

23 2717166 -197245 -0.5293

24 2867634 -12303.5 -0.03302

25 3018103 231450.6 0.621087

26 3168572 475204.7 1.275191

27 3319041 718958.8 1.929294

28 3469510 962712.9 2.583397



28

Trend Analysis: data

year

demand of electricity in north india in APRIL in

MW

2004 22097

2005 25063

2006 27512

2007 29284

2008 30864

Intercept -4337089

X Variable 1 2175.5

demand of electricity in north

india in APRIL in MW

forecasted value using

regression value actual/forecasted

22097 22613 0.977181267

25063 24788.5 1.011073683

27512 26964 1.020323394

29284 29139.5 1.004958905

30864 31315 0.985597956

AVAERAGE OF

ACTUAL/FORECASTED 0.999827041

DEMAND IN 2009 33490.5

DEMAND IN 2009 AFTER SEASONAL

ADJUST 33484.71

DEMAND IN 2010 35666


ADJUST 35659.83

DEMAND IN 2011 37841.5


ADJUST 37834.95



29

year

demand of electricity in north india in JULY in

MW

2004 26808

2005 27661

2006 31516

2007 33412

2008 35393

demand of electricity in north

india in JULY in MW



26808 26373.8 1.016463308

27661 28665.9 0.964944411

31516 30958 1.01802442

33412 33250.1 1.004869158

35393 35542.2 0.995802173

AVAERAGE OF


Intercept -4566994.6

X Variable 1 2292.1

DEMAND IN 2009 37834.3


ADJUST 37835.08

DEMAND IN 2010 40126.4


ADJUST 40127.23

DEMAND IN 2011 42418.5


ADJUST 42419.38



30

year

demand of electricity in north india in

OCTOBERin MW

2004 24049

2005 27608

2006 30290

2007 29795

2008 32565

demand of electricity in

north india in OCTOBERin

MW



24049 25017.6 0.961283257

27608 26939.5 1.024814863

30290 28861.4 1.049498638

29795 30783.3 0.96789493

32565 32705.2 0.99571322

AVAERAGE OF


Intercept -3826470

X Variable 1 1921.9

DEMAND IN 2009 34627.1


ADJUST 34621.59

DEMAND IN 2010 36549


ADJUST 36543.19

DEMAND IN 2011 38470.9


ADJUST 38464.78



31

year

demand of electricity in north india in

JANUARY in MW

2004 24997

2005 27095

2006 29173

2007 31848

2008 33169

demand of electricity in

north india in JANUARY in

MW

forecasted value using regression

value actual/forecasted

24997 25037 0.998402365

27095 27146.7 0.998095533

29173 29256.4 0.997149342

31848 31366.1 1.015363721

33169 33475.8 0.99083517

AVAERAGE OF


Intercept -4202801.8

X Variable 1 2109.7

DEMAND IN 2009 35585.5


ADJUST 35584.4

DEMAND IN 2010 37695.2


ADJUST 37694.04

DEMAND IN 2011 39804.9


ADJUST 39803.68

TOTAL ELECTRICITY CONSUMPTION FROM 1950-51 TO 2006-07

Documents

Indian Power Sector Demand and supply