Regression Final

8/19/2019 Regression Final

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Data for building regression:

Factors GDP Agriculture and Allied sect

Year At 1999-2000 Prices (Rs Crore

1970-71 209842.98

1971-72 205903.46

1972-73 195570.241973-74 209655.02

1974-75 206461.23

1975-76 233073.63

1976-77 219606.21

1977-78 241646.45

1978-79 247210.37

1979-80 215630.01

1980-81 243420.90

1981-82 254622.33

1982-83 253907.261983-84 279605.15

1984-85 284037.15

1985-86 284929.80

1986-87 283763.06

1987-88 279257.48

1988-89 322932.36

1989-90 326772.53

1990-91 339892.76

1991-92 333256.39

1992-93 355421.301993-94 367230.91

1994-95 384549.44

1995-96 381875.38

1996-97 419758.56

Data for forecasting ! regression:

1997-98 409039.06

1998-99 434892.19

1999-00 446515.30

2000-01 445402.59

2001-02 473248.49

2002-03 438966.26

2003-04 482676.52

2004-05 482910.17

2005-06 511113.98

2006-07 531315.45


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AGR%C&'"&R ! A''%D #C")R %nstitutional Rural Credit

GR)## ARA &*DR %RR%GA"%)*(+000 ,ectares 'ong "er$ (in billlion Rs

33880 5.22

33675 6.38

34465 7.9235318 9.85

36689 11.50

38538 17.72

38847 21.60

40562 25.20

42489 29.08

43053 35.68

42932 42.89

43934 48.43

44453 59.9546249 71.85

46262 86.70

46128 103.77

47723 116.45

46826 137.42

50808 152.39

51313 181.60

52134 193.13

53432 207.23

54744 225.7656135 240.37

58035 263.78

58062 282.27

61409 309.11

62271 329.50

65341 338.86

66247 497.24

64183 373.02

66109 452.34

61722 542.24

65176 704.54

66298 862.59

67968 1079.88

70493 1324.77

"ractors #ales "i$e- #eries


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Rainfall "ractors

Annual ($$ #ales

92.6 1./0

127.8 1/.

120.9 1151.2 19.

124.4 2/.

148.0 2./

95.6 .

167.4 9//.

117.8 12

142.4 02.

92.4 /0.

86.6 01

111.5 /.1119.7 .2

92.0 02/

161.4 .22

152.7 ..9

160.7 9010

87.7 10/20

89.4 11.00

165.3 1.12

106.8 1/00

112.0 1/..0134.9 190.2

130.9 1/0.

123.9 191200

130.9 22/12

167.0 22./

157.0 2/

141.0 2/0./2

66.4 2.19

125.8 2100

77.6 1/.02

120.5 191/..

119.2 2.1

136.4 290/

100.8 2.1


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C,ec3 for Collinearit4:

GDP Agriculture and Allied sect

GDP Agriculture and Allied sector 1

GR)## ARA &*DR %RR%GA"%)*%nstitutional Rural Credit

Annual Rainfall

Fro$ t,e abo5e collinearit4 table6 7e get to 3no7 t,at factors- GDP6correlated to eac, ot,er8 ",erefore6 7e can run regression 7it,


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GR)## ARA &*DR %RR%GA"%) %nstitutional Rural Credi Annual Rainfall

0.9784348241 0.9825617815 0.0197360004

1 0.9648101376 0.01117886431 0.0503492988

1

ross area under irrigaton ! %nstitutional rural credit are ,ig,l4nl4 one factor a$ong t,ese t,ree and t,e annual rainfall8


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#&ARY )&"P&"

Regression Statistics Regression uMultiple R 0.9761805924

R Square 0.9529285489

Adjusted R Square 0.949005928Standard Errr 12896.01952731

!"ser#atins 27

A$!%A

df SS MS

Re&ressin 2 80802604135.1 40401302068

Residual 24 3991375671.57 166307319.65

'tal 26 84793979806.7

Coecients Standard Error t Stat

(nter)ept 39960.49672733 12548.3060018 3.184533173%nstitutional Rural Credi572.0504063365 25.9534372783 22.041412095

Annual Rainfall -127.903507655 97.7961991988 -1.307857654

RES(*+A, !+'+'

Observation Predicted Sales Residuals

1 31102.73503954 -15342.7350395

2 27264.11004143 -10689.11004143 29027.60187001 -10673.60187

4 26256.18287229 -6381.18287229

5 30627.8800479 -4049.8800479

6 31167.51079465 1597.48920535

7 40089.21017237 -6616.21017237

8 32965.11978554 6701.88021446

9 41528.68934182 9899.31065818

10 42157.79573533 15869.2042647

11 52677.45454777 15409.5454522

12 56588.45414327 26712.5458567

13 59993.67748366 3720.3225163414 65752.26855629 8485.73144371

15 77790.14425243 2472.85574757

16 78678.54125733 -446.54125733

17 87044.90092628 -9155.90092628

18 98017.56988591 -7507.56988591

19 115918.1205276 -9668.12052759

20 132410.2769337 -15110.2769337

21 129298.1418877 7824.8581123

'on


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22 144846.4078149 1953.59218513

23 154781.4036045 -8011.40360448

24 160210.0697158 -21138.0697158

25 174113.3837587 -10038.3837587

26 185585.9203255 5614.07967454

27 200044.4286779 28567.5713221


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sing factors- %nstitutional Rural Credit and Annual Rainfall8

F Signicance F

242.93159287 1.183290E-016

P-value Lower 9! "##er 9! Lower 9$%! "##er 9$%!

0.003987124 14062.066019 65858.927435 14062.066019 65858.9274351.95188E-017 518.48514447 625.6156682 518.48514447 625.6156682

0.2033111226 -329.74494251 73.937927204 -329.74494251 73.937927204

"er$ (in billlion Rs Residual Plot

nnual ($$ Residual Plot


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#&ARY )&"P&"

Regression Statistics

Multiple R 0.9741572254

R Square 0.9489822999


!"ser#atins 27

A$!%A

df

Re&ressin 2

Residual 24

'tal 26

Coecients

(nter)ept -228432.660146GR)## ARA &*DR %RR%GA"%)*(+000 ,ectare 6.9613727891

Rainall Annual / -43.3900890989

RES(*+A, !+'+'

Observation Predicted Sales

1 3400.727698316

2 446.31514026943 6245.191258445

4 10868.52254786

5 21575.41902957

6 33422.99121389

7 37847.6960745

8 46671.04201052

9 62237.75579443

10 65096.57385565

11 66423.75220311

12 73650.71025457

13 76183.2495135514 88330.07631218

15 89622.47962647

16 85678.38348927

17 97159.26686305

18 90567.79475844

19 121455.4577089

20 124897.1878159

21 127319.1671132


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22 138893.3492057

23 147801.0418417

24 156490.678351

25 169890.8470067

26 170382.5346957

27 193379.7886173


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Regression using factors- Gross Area under irrigati

SS MS F Signicance F

80467985973 40233992986 223.21248453 3.109213E-016

4325993833.71 180249743.07

84793979806.7

Standard Error t Stat P-value Lower 9! "##er 9!

19738.0270946 -11.573226597 2.63511E-011 -269169.94588 -187695.374420.3294870183 21.127912186 5.13857E-017 6.281345006 7.6414005723

101.690312291 -0.42668852240.6734093896 -253.26857837 166.48840017

Residuals

12359.2723017

16128.684859712108.8087416

9006.47745214

5002.58097043

-657.99121389

-4374.6960745

-7004.04201052

-10809.7557944

-7069.57385565

1663.24779689

9650.28974543

-12469.2495136-14092.0763122

-9359.47962647

-7446.38348927

-19270.2668631

-57.7947584358

-15205.4577089

-7597.1878159

9803.83288685

GR)## ARA &*DR %RR%GA"%)*(+000 ,ectares Resi

Annual ($$ Residual Pl


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7906.65079431

-1031.04184168

-17418.678351

-5815.84700666

20817.4653043

35232.2113827


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on and Annual Rainfall8

Lower 9$%! "##er 9$%!

-269169.94588 -187695.374426.281345006 7.6414005723

-253.26857837 166.48840017

ual Plot

t


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#&ARY )&"P&"


Multiple R 0.9741635832

R Square 0.9489946869


!"ser#atins 27

A$!%A

df SS

Re&ressin 2 80469036316.9

Residual 24 4324943489.76

'tal 26 84793979806.7

Coecients Standard Error

(nter)ept -149598.605552 17080.4388752GDP- Agricultural ! Allied acti5iti 0.8643826045 0.0409066459

Rainall Annual / -61.7810175675 101.691419857

RES(*+A, !+'+'


1 26065.09456053 -10305.0945605

2 20485.14818062 -3910.148180623 11979.57865059 6374.42134941

4 22282.25745432 -2407.25745432

5 21177.32851039 5400.67148961

6 42722.59680192 -9957.59680192

7 34318.9180686 -845.918068602

8 48934.23826911 -9267.23826911

9 56807.93743036 -5379.93743036

10 27990.61052359 30036.3894764

11 55101.61641988 12985.3835801

12 65142.27134222 18158.7286578

13 62985.8312696 728.16873039914 84692.03443062 -10454.0344306

15 90234.31222529 -9971.31222529

16 86718.30319528 -8486.30319528

17 86247.28549306 -8358.28549306

18 81858.49220113 8651.50779887

19 124120.317606 -17870.317606

20 127334.6621579 -10034.6621579

21 133986.381632 3136.61836805


24/55

22 131864.2116978 14935.7883022

23 150701.9090472 -3931.90904724

24 159495.1432923 -20423.1432923

25 174712.109169 -10637.109169

26 172833.1578698 18366.8421302

27 205146.2525009 23465.7474991


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Regression using factors- GDP ! Annual Rainfall8

MS F Signicance F

40234518158 223.26960759 3.100166E-016

180205978.74

t Stat P-value Lower 9! "##er 9! Lower 9$%!

-8.7584755079 6.12280E-009 -184850.89878 -114346.31233 -184850.8987821.130615482 5.12359E-017 0.7799554369 0.9488097721 0.7799554369

-0.60753422120.5492022802 -271.66179274 148.09975761 -271.66179274

At 1999-2000 Prices (Rs Crore Residual

Annual ($$ Residual Plot


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"##er 9$%!

-114346.312330.9488097721

148.09975761

Plot


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#&ARY )&"P&"


Multiple R 0.9744607451

R Square 0.9495737438


!"ser#atins 27

A$!%A

df SS MS

Re&ressin 1 80518136854.6 80518136855

Residual 25 4275842952.03 171033718.08

'tal 26 84793979806.7


%nterce=t 24288.80750722 3777.4018228 6.430030123%nstitutional Rural Credi570.3413798686 26.286265612721.697314798

RES(*+A, !+'+'


1 27265.98951014 -11505.9895101

2 27927.58551079 -11352.5855108

3 28805.91123578 -10451.91123584 29906.67009893 -10031.6700989

5 30847.73337571 -4269.73337571

6 34395.2567585 -1630.2567585

7 36608.18131239 -3135.18131239

8 38661.41027991 1005.58972009

9 40874.3348338 10553.6651662

10 44638.58794094 13388.4120591

11 48750.74928979 19336.2507102

12 51910.44053426 31390.5594657

13 58480.77323035 5233.22676965

14 65267.83565079 8970.1643492115 73737.40514184 6525.59485816

16 83473.13249619 -5241.13249619

17 90705.06119293 -12816.0611929

18 102665.1199288 -12155.1199288

19 111203.1303854 -4953.13038541

20 127862.8020914 -10562.8020914

21 134438.8382013 2684.16179875

22 142480.6516574 4319.3483426

%n all t,e t,rrunning singl

'ong


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23 153049.0774264 -6279.07742637

24 161381.7649863 -22309.7649862

25 174733.456689 -10658.456689

26 185279.0688027 5920.93119725

27 200587.0314384 28024.9685616


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"ractor #ales 2281 ; .08< %nstitutional Rural Credit

F Signicance F

470.77346945 9.822514E-018


9.85544E-007 16509.102824 32068.512191 16509.102824 32068.5121919.82251E-018 516.20380243 624.47895731 516.20380243 624.47895731

e 'R6 =-5alue for Annual Rainfall factor is $ore t,an 0806 ,ence re>ected8e factor linear regression:

"er$ (in billlion Rs Residual Plot


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n


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"ractor #ales 2281

Year %nstitutional Rural Credit

1970-71 5.22 157601971-72 6.38 16575

1972-73 7.92 18354

1973-74 9.85 19875

1974-75 11.50 26578

1975-76 17.72 32765

1976-77 21.60 33473

1977-78 25.20 39667

1978-79 29.08 51428

1979-80 35.68 58027

1980-81 42.89 68087

1981-82 48.43 83301

1982-83 59.95 63714

1983-84 71.85 74238

1984-85 86.70 80263

1985-86 103.77 78232

1986-87 116.45 77889

1987-88 137.42 90510

1988-89 152.39 106250

1989-90 181.60 117300

1990-91 193.13 137123

1991-92 207.23 1468001992-93 225.76 146770

1993-94 240.37 139072

1994-95 263.78 164075

1995-96 282.27 191200

1996-97 309.11 228612

199.-9 329.50 22./

199-99 338.86 2/

1999-00 497.24 2/0./2

2000-01 373.02 2.19

2001-02 452.34 2100

2002-0 542.24 1/.02

200-0 704.54 191/..

200-0 862.59 2.1

200-0/ 1079.88 290/

200/-0. 1324.77 2.1

"ractors Actual#ales

Forecast Calculations:


36/55

.08< %nstitutional Rural Credit

"ractors Forcasted #ales

2726627928

28806

29907

30848

34395

36608

38662

40875

44639

48751

51911

58481

65268

73738

83474

90706

102666

111204

127864

134441

142482153051

161384

174736

185282

200590

rror

?-A @@ @@A AP

212219 41057 41057 0.162103 /82

21. 39000 39000 0.152014

0.90 -47128 47128 0.18073

2.01 148 148 0.000625

2221 -67276 67276 0.312904

-167853 167853 1.012984

2/12 -234446 234446 1.223132

1/2/. -268736 268736 1.085666

/019 -349652 349652 1.203432

..9.1 -427090 427090 1.210639


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#&ARY )&"P&"


Multiple R 0.9739585625

R Square 0.9485952815


!"ser#atins 27

A$!%A

df

Re&ressin 1

Residual 25

'tal 26

Coecients

(nter)ept -233739.19632GR)## ARA &*DR %RR%GA"%)*(+000 ,ectare 6.9598011713


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"ractor #ales -2.982 ; /89

SS MS F Signicance F

80435169146.8 80435169147 461.33667773 1.249561E-017

4358810659.84 174352426.39

84793979806.7

Standard Error t Stat P-value Lower 9! "##er 9!

15074.3395837 -15.505766937 2.47372E-014 -264785.37985 -202693.012790.3240319549 21.478749445 1.24956E-017 6.2924448678 7.6271574747

%n all t,e t,ree 'R6 =-5alue for Annual Rainfall factor isingle factor linear regression:


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"ractor #ales -2.982

Year GR)## ARA &*DR %RR%GA"%)

1970-71 33880 157601971-72 33675 16575

1972-73 34465 18354

1973-74 35318 19875

1974-75 36689 26578

1975-76 38538 32765

1976-77 38847 33473

1977-78 40562 39667

1978-79 42489 51428

1979-80 43053 58027

1980-81 42932 680871981-82 43934 83301

1982-83 44453 63714

1983-84 46249 74238

1984-85 46262 80263

1985-86 46128 78232

1986-87 47723 77889

1987-88 46826 90510

1988-89 50808 106250

1989-90 51313 117300

1990-91 52134 137123

1991-92 53432 146800

1992-93 54744 146770

1993-94 56135 139072

1994-95 58035 164075

1995-96 58062 191200

1996-97 61409 228612

199.-9 62271 22./

199-99 65341 2/

1999-00 66247 2/0./2

2000-01 64183 2.19

2001-02 66109 2100

2002-0 61722 1/.02

200-0 65176 191/..

200-0 66298 2.1

200-0/ 67968 290/




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200/-0. 70493 2.1


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/89/< Area under %rrigation


2066639

6137

12074

21616

34485

36636

48572

61984

65910

6506872041

75654

88154

88244

87312

98413

92170

119884

123399

129113

138148

147279

156960

170184

170372

193669

rror

?-A @@ @@A AP

199// 53608 53608 0.211658 1890/.

22102 35526 35526 0.138472

22.1 33421 33421 0.128169

2129.2 24217 24217 0.102101

22/1 -11376 11376 0.052912

19 -30143 30143 0.181909

219/ -28209 28209 0.147171

22./9. 19834 19834 0.080129

291 51228 51228 0.176317


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2/91 95890 95890 0.271811


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#&ARY )&"P&"


Multiple R 0.9737608907

R Square 0.9482102723

Adjusted R Square 0.9461386832 Standard Errr 13253.614036

!"ser#atins 27

A$!%A

df SS MS

Re&ressin 1 80402522681.2 80402522681

Residual 25 4391457125.45 175658285

'tal 26 84793979806.7


%nterce=t -157119.23927 11619.2855258 -13.5222806GDP 0.8638921217 0.0403793194 21.394420056

%n all t,e t,rsingle factor


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"ractor #ales -1.119 ; 08/< GDP(Agricultural ! Allied Acti5ities

F Signicance F

457.72120952 1.371977E-017


5.32846E-013 -181049.60577 -133188.87278 -181049.60577 -133188.872781.37198E-017 0.7807293566 0.9470548869 0.7807293566 0.9470548869

e 'R6 =-5alue for Annual Rainfall factor is $ore t,an 0806 ,ence re>ected8 )linear regression:


49/55

running


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"ractor #ales -1.119 ; 08/<

Year GDP Agriculture and Allied sect

1970-71 209842.98 157601971-72 205903.46 16575

1972-73 195570.24 18354

1973-74 209655.02 19875

1974-75 206461.23 26578

1975-76 233073.63 32765

1976-77 219606.21 33473

1977-78 241646.45 39667

1978-79 247210.37 51428

1979-80 215630.01 58027

1980-81 243420.90 680871981-82 254622.33 83301

1982-83 253907.26 63714

1983-84 279605.15 74238

1984-85 284037.15 80263

1985-86 284929.80 78232

1986-87 283763.06 77889

1987-88 279257.48 90510

1988-89 322932.36 106250

1989-90 326772.53 117300

1990-91 339892.76 137123

1991-92 333256.39 146800

1992-93 355421.30 146770

1993-94 367230.91 139072

1994-95 384549.44 164075

1995-96 381875.38 191200

1996-97 419758.56 228612

199.-9 409039.06 22./

199-99 434892.19 2/

1999-00 446515.30 2/0./2

2000-01 445402.59 2.19

2001-02 473248.49 2100

2002-0 438966.26 1/.02

200-0 482676.52 191/..

200-0 482910.17 2.1

200-0/ 511113.98 290/




51/55

200/-0. 531315.45 2.1


52/55

DP(Agricultural ! Allied Acti5ities


2418520782

11854

24023

21263

44257

32621

51664

56471

29185

5319762875

62257

84460

88289

89060

88052

84159

121895

125212

136548

130815

149965

160169

175132

172821

205552

rror

?-A @@ @@A AP

19/291 56985 56985 0.224993 1/819

21/2 37930 37930 0.147842

22/.0 32092 32092 0.123069

22..09 9480 9480 0.039969

21./ -36763 36763 0.170985

2221 -56446 56446 0.340647

2991 -68237 68237 0.355997

2/011 -12584 12584 0.05084

2 6063 6063 0.020866


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019 50843 50843 0.144122


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Documents

Regression Final