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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
Managerial Economics Final Project Report September 2009
FORE School of Management – FMG XVIII A – Trimester 1
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
Managerial Economics Final Project Report September 2009
FORE School of Management – FMG XVIII A – Trimester 1
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
Managerial Economics Final Project Report September 2009
FORE School of Management – FMG XVIII A – Trimester 1
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
Managerial Economics Final Project Report September 2009
FORE School of Management – FMG XVIII A – Trimester 1
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.
Managerial Economics Final Project Report September 2009
FORE School of Management – FMG XVIII A – Trimester 1
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
Managerial Economics Final Project Report September 2009
FORE School of Management – FMG XVIII A – Trimester 1
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
Managerial Economics Final Project Report September 2009
FORE School of Management – FMG XVIII A – Trimester 1
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:
2009: 4,30,058.2 GWH Root Mean Square Error = 39384
Managerial Economics Final Project Report September 2009
FORE School of Management – FMG XVIII A – Trimester 1
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
2009: 4,44,535.0 GWH Root Mean Square Error = 29597
b. Dumping Factor/ Weight: 0.5
2009: 4,31,461.7 GWH Root Mean Square Error = 31517
Managerial Economics Final Project Report September 2009
FORE School of Management – FMG XVIII A – Trimester 1
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.
Managerial Economics Final Project Report September 2009
FORE School of Management – FMG XVIII A – Trimester 1
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
Estimated Demand for Power in MWH
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
Managerial Economics Final Project Report September 2009
FORE School of Management – FMG XVIII A – Trimester 1
13
f. 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 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.
Managerial Economics Final Project Report September 2009
FORE School of Management – FMG XVIII A – Trimester 1
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
Managerial Economics Final Project Report September 2009
FORE School of Management – FMG XVIII A – Trimester 1
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
Managerial Economics Final Project Report September 2009
FORE School of Management – FMG XVIII A – Trimester 1
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.
Managerial Economics Final Project Report September 2009
FORE School of Management – FMG XVIII A – Trimester 1
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
Managerial Economics Final Project Report September 2009
FORE School of Management – FMG XVIII A – Trimester 1
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
Managerial Economics Final Project Report September 2009
FORE School of Management – FMG XVIII A – Trimester 1
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
Managerial Economics Final Project Report September 2009
FORE School of Management – FMG XVIII A – Trimester 1
20
Forecasting Per Capita Income Annually In India
Regression Statistics
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
Managerial Economics Final Project Report September 2009
FORE School of Management – FMG XVIII A – Trimester 1
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
Managerial Economics Final Project Report September 2009
FORE School of Management – FMG XVIII A – Trimester 1
22
population
SUMMARY
OUTPUT
Regression Statistics
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
Managerial Economics Final Project Report September 2009
FORE School of Management – FMG XVIII A – Trimester 1
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
Managerial Economics Final Project Report September 2009
FORE School of Management – FMG XVIII A – Trimester 1
24
Predicted Price
Regression Statistics
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
Managerial Economics Final Project Report September 2009
FORE School of Management – FMG XVIII A – Trimester 1
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
Managerial Economics Final Project Report September 2009
FORE School of Management – FMG XVIII A – Trimester 1
26
Gross National Product
SUMMAR
Y
OUTPUT
Regression Statistics
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
Managerial Economics Final Project Report September 2009
FORE School of Management – FMG XVIII A – Trimester 1
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
Managerial Economics Final Project Report September 2009
FORE School of Management – FMG XVIII A – Trimester 1
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
DEMAND IN 2010 AFTER SEASONAL
ADJUST 35659.83
DEMAND IN 2011 37841.5
DEMAND IN 2011 AFTER SEASONAL
ADJUST 37834.95
Managerial Economics Final Project Report September 2009
FORE School of Management – FMG XVIII A – Trimester 1
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
forecasted value using
regression value actual/forecasted
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
ACTUAL/FORECASTED 1.000020694
Intercept -4566994.6
X Variable 1 2292.1
DEMAND IN 2009 37834.3
DEMAND IN 2009 AFTER SEASONAL
ADJUST 37835.08
DEMAND IN 2010 40126.4
DEMAND IN 2010 AFTER SEASONAL
ADJUST 40127.23
DEMAND IN 2011 42418.5
DEMAND IN 2011 AFTER SEASONAL
ADJUST 42419.38
Managerial Economics Final Project Report September 2009
FORE School of Management – FMG XVIII A – Trimester 1
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
forecasted value using
regression value actual/forecasted
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
ACTUAL/FORECASTED 0.999840982
Intercept -3826470
X Variable 1 1921.9
DEMAND IN 2009 34627.1
DEMAND IN 2009 AFTER SEASONAL
ADJUST 34621.59
DEMAND IN 2010 36549
DEMAND IN 2010 AFTER SEASONAL
ADJUST 36543.19
DEMAND IN 2011 38470.9
DEMAND IN 2011 AFTER SEASONAL
ADJUST 38464.78
Managerial Economics Final Project Report September 2009
FORE School of Management – FMG XVIII A – Trimester 1
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
ACTUAL/FORECASTED 0.999969226
Intercept -4202801.8
X Variable 1 2109.7
DEMAND IN 2009 35585.5
DEMAND IN 2009 AFTER SEASONAL
ADJUST 35584.4
DEMAND IN 2010 37695.2
DEMAND IN 2010 AFTER SEASONAL
ADJUST 37694.04
DEMAND IN 2011 39804.9
DEMAND IN 2011 AFTER SEASONAL
ADJUST 39803.68
TOTAL ELECTRICITY CONSUMPTION FROM 1950-51 TO 2006-07
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