This document discusses residual mapping, which is used to analyze the relationship between two areal variables. It provides steps for calculating residual values, which indicate the difference between observed and estimated dependent variable (y) values. Positive residual values mean y is higher than estimated, while negative values mean y is lower. The document includes a calculation and data table applying this process to analyze the relationship between area and population in West Bengal districts. The resulting residual map shows major parts of several districts have well-distributed populations relative to their areas, while northern districts generally have negative residuals.

1. RESIDUAL MAPPING
Dr. Arindam Sarkar , Department of Geography
Purash Kanpur Haridas Nandi College Website: https://pkhnm.ac.in/
Email ID: arindam.srkr1@gmail.com
Dr. Arindam Sarkar
Department of Geography
Purash Kanpur Haridas Nandi College
arindam.srkr1@gmail.com

2. Dr. Arindam Sarkar , Department of Geography
Purash Kanpur Haridas Nandi College Website: https://pkhnm.ac.in/
Email ID: arindam.srkr1@gmail.com
Residual Mapping is an important analytical
techniques of areal pattern of data.
In context to areal pattern analysis , Residual
Mapping has been used to explain the inter relationship
between two variables.
When Z Score explains only one data association and
stated about only one variable.
In Residual Mapping one variable is independent (x)
and another variable is dependent (y).
The relationship status of x and y well explained
through residual value . That has been analysised on the
basis of observed and estimated value.
Value of residual may be (+) or (-).

3. Dr. Arindam Sarkar , Department of Geography
Purash Kanpur Haridas Nandi College Website: https://pkhnm.ac.in/
Email ID: arindam.srkr1@gmail.com
Calculation Procedure
1. Determine independent (x) and dependent (y) variable.
2. Calculate the value of x² of individual independent variable.
3. Do sum of all x² value.
4. Calculate the y² of individual dependent variable.
5. Do sum of all y² values.
6. Multiply dependent variable with independent variable(x.y).
7. Do calculate the x and y individual (all given administrative unit).
8. Do sum all x and y value.
9. Calculate yc = a + bx
Where , b =
a =
10. Calculate (y-yc ) value.
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)( xNx
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xby 

4. Dr. Arindam Sarkar , Department of Geography
Purash Kanpur Haridas Nandi College Website: https://pkhnm.ac.in/
Email ID: arindam.srkr1@gmail.com
Mapping Procedure
1. In the Residual Mapping context (y-yc ) value may
be appear in negative and positive both.
2. So, it is better to use continues line for positive
and broken line for negative value of (y-yc )
through choropleth.
3. Isoline has been generated on the basis of (y-yc ) .
4. ( Choropleth = Red , Isopleth = Brown ).

5. Dr. Arindam Sarkar , Department of Geography
Purash Kanpur Haridas Nandi College Website: https://pkhnm.ac.in/
Email ID: arindam.srkr1@gmail.com
SL No.Name Of District Area in SqKm. Total Population(,00000) x² y² xy yc=a+bx y-yc
1 Bardhaman 7024 68.95514 49336576 4754.811 484340.9 48.403 20.552
2 Birbhum 4545 30.15422 20657025 909.277 137050.93 41.859 -11.705
3 Bankura 6882 31.92695 47361924 1019.3 219721.27 48.028 -16.101
4 pur. Medinipur 4295 44.17377 18447025 1951.322 189726.34 41.199 2.975
5 Pas.Medinipur 9786 51.93411 95765796 2697.152 508227.2 55.695 -3.761
6 Hugli 3149 50.41976 9916201 2542.152 158771.82 38.173 12.247
7 Puruliya 6259 25.36516 39175081 643.391 158760.54 46.384 -21.019
8 N24Pargana 4094 89.34286 16760836 7982.147 365769.67 40.668 48.675
9 S 24 Pargana 9960 69.06689 99201600 4770.235 687906.22 56.154 12.913
10 Haora 1467 42.73099 2152089 1825.938 62686.36 33.733 8.998
11 Nadia 3927 46.04827 15420329 2120.443 180831.56 40.227 5.821
12 Mursidabad 5324 58.66569 28344976 3441.663 312336.13 43.915 14.751
13 U.Dinajpur 3140 24.41794 9859600 596.236 76672.33 38.15 -13.732
14 D.Dinajpur 2219 15.03178 4923961 225.954 33355.52 35.718 -20.686
15 Malda 3733 32.90468 13935289 1082.718 122833.17 39.715 -6.81
16 Jalpaiguri 6227 34.01173 38775529 1156.798 211791.04 46.299 -12.287
17 Darjeeling 3149 16.09172 9916201 258.943 50672.83 38.173 -22.081
18 Kooch Bihar 3387 24.79155 11471769 614.621 83968.98 38.8 -14.008
19 Kolkata 185 45.72876 34225 2091.119 8459.82 30.348 15.381
Total 88752 801.76 531457032 40684.25 4053882.6
Calculation And Data Table For Residual Map

6. Dr. Arindam Sarkar , Department of Geography
Purash Kanpur Haridas Nandi College Website: https://pkhnm.ac.in/
Email ID: arindam.srkr1@gmail.com
Calculation Of Residual Value
Formula - (y-yc )
Where , yc = a+bx
b = , b =
b = 0.00264
a = a = 42.198-0.00264(4671.158)
a = 29.85990
Sample Calculation For Bardhaman :
Residual Value = (y-yc )
= 68.95514-48.403 ( y = 68.95514 ) = 20.552
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)( xNx
yxNxy
2
)88752(19531457032
)198.42158.4671(1964.4053882
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xby 

7. Dr. Arindam Sarkar , Department of Geography
Purash Kanpur Haridas Nandi College Website: https://pkhnm.ac.in/
Email ID: arindam.srkr1@gmail.com
INTERPRETATION
Here map showing that spatial
relationship of area and population
through Residual Map of West Bengal. In
map major part of Maldah , western part
of Mursidabad , eastern part of Birbhum ,
middle part of Bardhman , eastern part
of Bankura , western part of Hooghly
,major part of Howrah and Paschim ,
Purba Medinipur is under very well
distributed population correspondence
with area.
And northern district of west Bengal and
Purulia and western par of Bankura is
under (-) residual value. Major eastern
part district are under (+) residual value.

8. Dr. Arindam Sarkar , Department of Geography
Purash Kanpur Haridas Nandi College Website: https://pkhnm.ac.in/
Email ID: arindam.srkr1@gmail.com