Lab3_PojiltovOlga_EMREI286

8/7/2019 Lab3_PojiltovOlga_EMREI286

1/19

Laboratory work no.3:

1) Initial data:

Cost:1 60679.50

2 49069.50

3 107885.0

4 95191.00

5 119836.0

6 45158.00

7 111255.5

8 102450.5

9 44925.00

10 110205.0

11 84383.00

12 77397.00

13 27661.00

14 185558.0

15 74937.50

16 213922.5

17 273743.518 51052.00

19 60285.50

20 62255.00

21 100130.0

22 160020.0

23 81860.00

24 63036.00

25 82253.50

26 71179.50

27 107115.0

28 225585.0

29 87733.50

30 165043.531 224350.5

32 79189.00

33 170152.5

34 81332.00

35 193484.5

36 91005.00

37 95280.00

38 115875.0

39 175651.5

40 99325.00

41 241165.5

42 340909.5

43 322422.544 111050.0

45 111608.5

46 103729.0

47 225175.5

48 194600.0

49 85670.00

50 232461.0

51 100132.5

52 192550.0

53 97084.50

54 117622.0

55 106815.0

56 344529.0

57 566136.5

58 512913.0

59 537137.0


2/19

60 525826.0

61 204450.5

62 387874.5

63 200763.0

64 444725.0

65 169285.5

66 359547.0

67 174170.5

68 293233.5

69 255670.0

70 257588.0

71 335007.0

72 560110.0

73 596982.0

74 132534.0

N:

1 99.00000

2 102.0000

3 131.0000

4 135.00005 146.0000

6 173.0000

7 173.0000

8 185.0000

9 199.0000

10 205.0000

11 208.0000

12 211.0000

13 236.0000

14 253.0000

15 255.0000

16 258.0000

17 269.000018 275.0000

19 276.0000

20 276.0000

21 280.0000

22 307.0000

23 309.0000

24 322.0000

25 347.0000

26 348.0000

27 350.0000

28 355.0000

29 363.0000

30 371.0000

31 384.0000

32 395.0000

33 400.0000

34 424.0000

35 434.0000

36 450.0000

37 451.0000

38 461.0000

39 472.0000

40 474.0000

41 493.0000

42 506.0000

43 513.0000

44 513.0000

45 515.0000

46 529.0000


3/19

47 532.0000

48 538.0000

49 544.0000

50 551.0000

51 563.0000

52 567.0000

53 592.0000

54 605.0000

55 609.0000

56 623.0000

57 632.0000

58 643.0000

59 653.0000

60 663.0000

61 679.0000

62 690.0000

63 711.0000

64 724.0000

65 736.0000

66 751.0000

67 769.0000

68 826.000069 920.0000

70 1017.000

71 1079.000

72 1163.000

73 1200.000

74 1267.000

COST=COST+10000*Z

N=N+10*Z, where Z =1

Result:Cost:

1 61679.50

2 50069.50

3 108885.0

4 96191.00

5 120836.0

6 46158.00

7 112255.5

8 103450.5

9 45925.00

10 111205.011 85383.00

12 78397.00

13 28661.00

14 186558.0

15 75937.50

16 214922.5

17 274743.5

18 52052.00

19 61285.50

20 63255.00

21 101130.0

22 161020.0

23 82860.0024 64036.00

25 83253.50

26 72179.50


4/19

27 108115.0

28 226585.0

29 88733.50

30 166043.5

31 225350.5

32 80189.00

33 171152.5

34 82332.00

35 194484.5

36 92005.00

37 96280.00

38 116875.0

39 176651.5

40 100325.0

41 242165.5

42 341909.5

43 323422.5

44 112050.0

45 112608.5

46 104729.0

47 226175.5

48 195600.049 86670.00

50 233461.0

51 101132.5

52 193550.0

53 98084.50

54 118622.0

55 107815.0

56 345529.0

57 567136.5

58 513913.0

59 538137.0

60 526826.0

61 205450.562 388874.5

63 201763.0

64 445725.0

65 170285.5

66 360547.0

67 175170.5

68 294233.5

69 256670.0

70 258588.0

71 336007.0

72 561110.0

73 597982.0

74 133534.0

N:

1 109.0000

2 112.0000

3 141.0000

4 145.0000

5 156.0000

6 183.0000

7 183.0000

8 195.0000

9 209.0000

10 215.000011 218.0000

12 221.0000

13 246.0000


5/19

14 263.0000

15 265.0000

16 268.0000

17 279.0000

18 285.0000

19 286.0000

20 286.0000

21 290.0000

22 317.0000

23 319.0000

24 332.0000

25 357.0000

26 358.0000

27 360.0000

28 365.0000

29 373.0000

30 381.0000

31 394.0000

32 405.0000

33 410.0000

34 434.0000

35 444.000036 460.0000

37 461.0000

38 471.0000

39 482.0000

40 484.0000

41 503.0000

42 516.0000

43 523.0000

44 523.0000

45 525.0000

46 539.0000

47 542.0000

48 548.000049 554.0000

50 561.0000

51 573.0000

52 577.0000

53 602.0000

54 615.0000

55 619.0000

56 633.0000

57 642.0000

58 653.0000

59 663.0000

60 673.0000

61 689.000062 700.0000

63 721.0000

64 734.0000

65 746.0000

66 761.0000

67 779.0000

68 836.0000

69 930.0000

70 1027.000

71 1089.000

72 1173.000

73 1210.000

74 1277.000


6/19

2)

obs COST N

1 61679.50 109.0000

2 50069.50 112.0000

3 108885.0 141.0000

4 96191.00 145.0000

5 120836.0 156.0000

6 46158.00 183.0000

7 112255.5 183.0000

8 103450.5 195.0000

9 45925.00 209.0000

10 111205.0 215.0000

11 85383.00 218.0000

12 78397.00 221.0000

13 28661.00 246.0000

14 186558.0 263.0000

15 75937.50 265.0000

16 214922.5 268.0000

17 274743.5 279.0000

18 52052.00 285.0000

19 61285.50 286.0000

20 63255.00 286.0000

21 101130.0 290.0000

22 161020.0 317.0000

23 82860.00 319.0000

24 64036.00 332.0000

25 83253.50 357.0000

26 72179.50 358.0000

27 108115.0 360.0000

28 226585.0 365.0000

29 88733.50 373.0000

30 166043.5 381.0000

31 225350.5 394.000032 80189.00 405.0000

33 171152.5 410.0000

34 82332.00 434.0000

35 194484.5 444.0000

36 92005.00 460.0000

37 96280.00 461.0000

38 116875.0 471.0000

39 176651.5 482.0000

40 100325.0 484.0000

41 242165.5 503.0000

42 341909.5 516.0000

43 323422.5 523.0000

44 112050.0 523.000045 112608.5 525.0000

46 104729.0 539.0000

47 226175.5 542.0000

48 195600.0 548.0000

49 86670.00 554.0000

50 233461.0 561.0000

51 101132.5 573.0000

52 193550.0 577.0000

53 98084.50 602.0000

54 118622.0 615.0000

55 107815.0 619.0000

56 345529.0 633.0000

57 567136.5 642.000058 513913.0 653.0000

59 538137.0 663.0000

60 526826.0 673.0000


7/19

61 205450.5 689.0000

62 388874.5 700.0000

63 201763.0 721.0000

64 445725.0 734.0000

65 170285.5 746.0000

66 360547.0 761.0000

67 175170.5 779.0000

68 294233.5 836.0000

69 256670.0 930.0000

70 258588.0 1027.000

71 336007.0 1089.000

72 561110.0 1173.000

73 597982.0 1210.000

74 133534.0 1277.000

3)

Initial:

Variable Coefficient Std. Error t-Statistic Prob.

C 21562.87 27604.71 0.781130 0.4373

N 339.0432 49.55144 6.842248 0.0000

R-squared 0.394023 Mean dependent var 188418.0

Adjusted R-squared 0.385606 S.D. dependent var 141969.9

S.E. of regression 111280.6 Akaike info criterion 26.10415

Sum squared resid 8.92E+11 Schwarz criterion 26.16642

Log likelihood -963.8536 Hannan-Quinn criter. 26.12899

F-statistic 46.81636 Durbin-Watson stat 1.352470

Prob(F-statistic) 0.000000


8/19

a)log(COST) against N (regression LS log(cost) c n )


C 11.05178 0.132866 83.17981 0.0000

N 0.001726 0.000238 7.235675 0.0000




Sum squared resid 20.65540 Schwarz criterion 1.678115Log likelihood -57.78618 Hannan-Quinn criter. 1.640684



Cost1=log(cost)

b)COST against log(N) (regression LS cost c log(n) )


C -725686.2 144087.7 -5.036420 0.0000

N1 151023.3 23703.92 6.371236 0.0000




Sum squared resid 9.41E+11 Schwarz criterion 26.22023Log likelihood -965.8443 Hannan-Quinn criter. 26.18280



N1=log(n)


9/19

c) inverse(COST) against N (regression LS 1/cost c n)


C 1.48E-05 1.20E-06 12.32222 0.0000

N -1.27E-08 2.15E-09 -5.918251 0.0000

R-squared 0.327264 Mean dependent var 8.50E-06

Adjusted R-squared 0.317921 S.D. dependent var 5.85E-06

S.E. of regression 4.83E-06 Akaike info criterion -21.61707

Sum squared resid 1.68E-09 Schwarz criterion -21.55480

Log likelihood 801.8317 Hannan-Quinn criter. -21.59223



Cost2=1/cost


10/19

d)COST against inverse(N) (regression LS cost c 1/n)


C 298329.4 26833.51 11.11779 0.0000

N2 -39608368 8154473. -4.857256 0.0000


Adjusted R-squared 0.236345 S.D. dependent var 141969.9S.E. of regression 124063.7 Akaike info criterion 26.32163





N2=1/n

e)COST against POWER(2, N) (regression LS cost c n^2)


C 112849.2 18444.56 6.118293 0.0000

N3 0.243494 0.040349 6.034718 0.0000








N3=n^2


11/19

f) COST against POLYNOMINAL(3, N) (regression LS cost c n n^2 n^3)


C 120549.0 90917.40 1.325918 0.1892

N -453.2069 561.3389 -0.807368 0.4222

N3 1.611226 0.987547 1.631544 0.1073

N4 -0.000883 0.000497 -1.775264 0.0802








N4=n^3


12/19

g)POWER(COST) against N (regression LS cost^2 c n)


C -3.49E+10 1.73E+10 -2.017541 0.0474

N 1.84E+08 31082571 5.904483 0.0000

R-squared 0.326240 Mean dependent var 5.54E+10

Adjusted R-squared 0.316882 S.D. dependent var 8.45E+10

S.E. of regression 6.98E+10 Akaike info criterion 52.80245





cost3=cost^2

h) LS cost^2 n^2


13/19


C 1.26E+10 1.12E+10 1.123759 0.2648

N3 137780.7 24574.52 5.606649 0.0000

R-squared 0.303907 Mean dependent var 5.54E+10

Adjusted R-squared 0.294239 S.D. dependent var 8.45E+10

S.E. of regression 7.10E+10 Akaike info criterion 52.83505





LS cost3 c n3

i) LS 1/cost c 1/n


C 3.42E-06 1.06E-06 3.236099 0.0018

N2 0.001829 0.000321 5.691257 0.0000


Adjusted R-squared 0.300702 S.D. dependent var 5.85E-06

S.E. of regression 4.89E-06 Akaike info criterion -21.59214

Sum squared resid 1.72E-09 Schwarz criterion -21.52987Log likelihood 800.9092 Hannan-Quinn criter. -21.56730



LS cost2 c n2


14/19

4)Initial form: LS cost c n

Fitting forms:b)LS cost c log(n)cost=-725686.2+151023.3n


C -725686.2 144087.7 -5.036420 0.0000

N1 151023.3 23703.92 6.371236 0.0000









15/19

e) LS cost c n^2cost=112849.2+0.243494n


C 112849.2 18444.56 6.118293 0.0000

N3 0.243494 0.040349 6.034718 0.0000






F-statistic 36.41782 Durbin-Watson stat 1.246031Prob(F-statistic) 0.000000


16/19

i)LS 1/cost c 1/ncost=3.42E-06+0.001829n


C 3.42E-06 1.06E-06 3.236099 0.0018

N2 0.001829 0.000321 5.691257 0.0000


Adjusted R-squared 0.300702 S.D. dependent var 5.85E-06S.E. of regression 4.89E-06 Akaike info criterion -21.59214

Sum squared resid 1.72E-09 Schwarz criterion -21.52987

Log likelihood 800.9092 Hannan-Quinn criter. -21.56730



5)The best coefficient of determination is at the initial equationCost=21562.87+339.0432n


17/19

6)LS cost c n n^2 n^3


C 120549.0 90917.40 1.325918 0.1892

N -453.2069 561.3389 -0.807368 0.4222

N3 1.611226 0.987547 1.631544 0.1073

N4 -0.000883 0.000497 -1.775264 0.0802









18/19

Test t-student for b0

H0: b0 =0

H1: b0 0

0b

t =1.325918

tcrit (0.05;df)df=n-k-1=74-3-1=70tcrit (0.05;70)=1.96

if0

bt > tcrit the accept H1

Fisher test:

1) F calc =17.36989

2) F tab=(0.05;3;70)=2.76

df1=k=3

df2=n-k-1=703) If F calc > F tab, accept H1, there is a relation between the dependent variable and independent

variables or the equation is significant.

If finding the ariants best fitting the initial equation, we will choose the variant with the

equations:


19/19

LS cost c log(n)

( cost=-725686.2+151023.3n )

LS cost c n^2

(cost=112849.2+0.243494n )

LS 1/cost c 1/n(cost=3.42E-06+0.001829n )

From all three, the last has the smallest standard error, proving to be more efficient andhaving a smaller sum of residual. This standard error is even smaller than the initialequations standard error, proving the possibility of using this certain equation in theanalysis.

There is a medium intensity direct relationship between the variables of the equation.Due to a high standard error, the initial estimators are unreliable. I we are performingthe test at the 5% significance level, a p-value lower than .05 is taken as evidence to

reject the null hypothesis of a zero coefficient.

In the case of the equation: cost=120549.0-453.2069n+1.611226n3-0.000883n4(LS cost c n n^2 n^3)There is a positive low intensity linear relation between the variables.The standard error proves the estimators unreliable.The regression fits no better than the simple mean of the dependent variable( inpredicting the values of the dependent variable within the sample, based on the resultsof the R squared )Based on the t-statistic test, we accept the hypothesis H1, when b0 0.Based on the Fisher test, we accept the H1 hypothesis. There is a relation between thedependent variable and independent variables or the equation is significant

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Lab3_PojiltovOlga_EMREI286