Site Loader
Rock Street, San Francisco

By and large, there are two groups of salmon. One is the Atlantic salmon. It lives in the North Atlantic Ocean between North America and Europe. The others are species of Pacific salmon that live in the North Pacific Ocean. Like the Atlantic salmon, they live in the ocean and besides in the rivers of western North America and eastern Asia. The salmon is an anadromous ( uh-NAD-droh-muhss ) fish. This means that it spawns in fresh water but spends much of its life at sea. When an Atlantic salmon reaches the age of two, it leaves its place in the North Atlantic. It begins a migration to the same topographic point in the river or watercourse where it was born. It spawns and so returns to the ocean for two old ages. After constructing up its strength, it leaves the ocean and returns to the rivers to engender yet once more.

The growing of pink-orange fish graduated table has been studied and their growing were measured by breadth for first twelvemonth when they were remaining in ocean environment. The pink-orange fish graduated tables have been enlarged 100 times, so that the ratings are made in hundredths of an inch. In this assignment, we were given a undertaking that consists of a set of measuring which was gathered by the Alaska Department of Fish and Game as given in Table A. ( Courtesy of K. Jensen and B. Van Alen. ) The content of assignment is to carry on an analysis on a spread diagram, a fitted line and a finding if I?1 differs from nothing. Furthermore, we were asked to happen a 95 % of assurance interval for the population mean when the fresh water growing is 100.Three types of arrested development analyses have been completed in this assignment, viz. all pink-orange fish arrested development analysis, male pink-orange fish arrested development analysis, and last but non least, female salmon fish arrested development analysis. All the analysis shows the arrested development of the marine growing over the freshwater growing.

Empirical Models

Today, many jobs in technology and the scientific discipline involve a survey or analysis of the relationship between or more variables. There are two types of empirical theoretical accounts that are deterministic and non deterministic. Deterministic theoretical accounts are those are able to foretell the supplanting absolutely, such as the force per unit area of a gas container is related to the temperature and yet most of the state of affairss are deterministic in existent word analysis. Therefore, there is a nondeterministic mode called arrested development theoretical account is used to pattern and research the relationships between these variables. However, there are some premises need to be made in our analysis for the empirical theoretical accounts that we are traveling to utilize. We assume that there is merely independent or forecaster variable ten and the relationship with the response Y are additive. The information aggregation of the informations are represented utilizing a spread diagram which is a graph on which each ( xi, yi ) brace is represented as a point plotted in a planar co-ordinate system. Base on the spread diagram, it is likely sensible to presume that the mean of the random variable Y is related to x by the undermentioned straight-line relationship:

where the incline and intercept of the line are called arrested development coefficients. Since the mean of Y is non precisely a additive map of x, therefore it ‘s more appropriate to show it as in the undermentioned equation:

, where is the random error term.

This theoretical account is besides known as the simple additive arrested development theoretical account, because it has merely one independent variable or regressor. Since there is no theoretical cognition of the relationship between ten and Y, and the pick of the theoretical account is based on review of a spread diagram, therefore it can be said that the arrested development theoretical account as an empirical theoretical account.

Simple Linear Regression

The instance of simple additive arrested development considers a individual regressor variable or forecaster variable ten and a dependant or response variable Y. Thus, Y can be described by the theoretical account

where is a random mistake with average mistake and ( unknown ) discrepancy. The random mistakes matching to different observations and are besides assumed to be uncorrelated random variables. Suppose that we have n braces of observations, an estimated arrested development line with the “ best tantrum ” is needed to be drawn in the spread diagram. The German scientist Karl Gauss ( 1777 – 1855 ) proposed gauging the parametric quantities and in Equation 1-1 to minimise the amount of the squares of the perpendicular divergence. We call this standard for gauging the arrested development coefficients the method of least squares. Using Equation 1-2, we may show the n looks in the sample as

( 1-3 )

and the amount of the squares of the divergences of the observations from the true arrested development line is

( 1-4 )

The least squares estimations of the intercept and incline in the simple additive arrested development theoretical account are

( 1-5 )

( 1-6 )

where and.

The fitted or estimated arrested development line is hence

( 1-7 )

Note that each brace of observations satisfies the relationship

where is called the remainder. The residuary describes the mistake in the tantrum of the theoretical account to the ith observation. The remainders are used to obtain the information about the adequateness of the fitted theoretical account.

Notational, it is on occasion convenient to give particular symbols to the numerator and denominator of Equation 1-6. Given informations, ,aˆ¦ , , allow

( 1-8 )

and

( 1-9 )

Another unknown parametric quantity in the arrested development theoretical account, ( the discrepancy of the error term, ) . The remainders are used to obtain an estimation of. The amount of squares of the remainders, or known as the mistake amount of squares, is

( 1-10 )

It ‘s so showed that the expected value of the mistake amount of squares is. Therefore an indifferent calculator of is

( 1-11 )

By replacing into Equation 1-10, and simplifying,

( 1-12 )

where is the entire amount of squares of the response variable Y.

Hypothesis Trials in Simple Linear Regression

3.3.1 Use of t-Tests

Suppose we wish to prove the hypothesis that the incline equals a changeless, . The appropriate hypotheses are

Holmium:

H1: ( 1-13 )

where we assumed a reversible option. Since the mistakes are, it follows straight that the observations Yi are. Now is a additive combination of independent normal random variables, and accordingly, is, utilizing the prejudice and discrepancy belongingss of the incline discussed earlier. Besides, has a chi-square distribution with n-2 grade of freedom, and is independent of. As a consequence of those belongingss, the statistic

( 1-14 )

follows the t-distribution with n -2 grade of freedom under Ho: . We would reject Ho: if

( 1-15 )

A similar process can be used to prove hypotheses about the intercept. To prove

Holmium:

H1: ( 1-16 )

We would utilize the statistic

( 1-17 )

and reject the void analysis if computed value of this trial statistic, , is such that.

A really of import particular instance of hypotheses of Equation 1-13 is

Holmium:

H1: ( 1-18 )

These hypotheses relate to the significance of arrested development. Failure to reject Ho: is tantamount to reasoning that there is no additive relationship between ten and Y.

3.3.2 Analysis of Variance Approach to Test Significance of Regression

To prove significance of arrested development, the analysis of discrepancy can be used. The process partitions the entire variableness in the response variable into meaningful constituents as the footing for the trial. The analysis of discrepancy individuality is as follows:

( 1-19 )

The two constituents on the right-hand-side of Equation 1-19 step, severally, the sum of variableness in accounted for by the arrested development line and the residuary fluctuation left unexplained by the arrested development line. Using the Equation 1-10 ( the mistake amount of squares ) and the the arrested development amount of squares, we can calculate the undermentioned equation:

( 1-20 )

where is the entire corrected amount of squares of Y.

Since, and that and are independent chi-square random variables with n-2 and 1 grades of freedom, severally. Therefore, if the void hypothesis Ho: is true, the statistic,

( 1-21 )

follows the distribution, and we would reject Ho if. The measures and are called average squares. This trial process is normally arranged in an analysis of discrepancy tabular array.

Assurance Time intervals

3.4.1 Assurance Time intervals on Slope and Intercept

Under the premise that the observations are usually and independently distributed, a assurance interval on the incline in simple additive arrested development is

( 1-22 )

Similarly, a assurance interval on the intercept is

( 1-23 )

3.4.2 Assurance Time intervals on the Mean Response

A assurance interval about the average response at the value of, say, is given by

( 1-24 )

where is computed from the fitted arrested development theoretical account.

Adequacy of the Regression Model

Suiting a arrested development theoretical account requires several premises. Appraisal of the theoretical account parametric quantities requires the premise that the mistakes are uncorrected random variables with average nothing and changeless discrepancy. Trials of hypotheses and interval appraisal require that the mistakes be usually distributed. In add-on, we assume that the order of the theoretical account is right ; that is, if we fit a simple additive arrested development theoretical account, we are presuming that the phenomenon really behaves in a additive or first-order mode.

3.5.1 Residual Analysis

The remainders from a arrested development theoretical account are, where is existent observation and is the matching fitted value from the arrested development theoretical account. Analysis of the remainders is often helpful in look intoing the premise that the mistakes are about usually distributed with changeless discrepancy, and in finding whether extra footings in the theoretical account would be utile.

As an approximative cheque of normalcy, the experimenter can build a frequence histogram of the remainders or a normal chance secret plan of remainders. We may besides standardise the remainders by calculating. If the mistakes are usually distributed, approximated 95 % of the standardised remainders should fall in the interval ( -2, +2 ) . Remainders that are far outside this interval may bespeak the presence of an outlier, that is, an observation that is non typical of the remainder of the informations. Assorted regulations have been propose for flinging outlier, but outliers sometimes provide of import information about unusual fortunes of involvement to experimenters and hence should non be automatically discarded.

3.5.2 Coefficient of Determination ( R2 )

The coefficient of finding is

( 1-25 )

The coefficient is frequently used to judge the adequateness of a arrested development theoretical account. However the statistic R2 should be usage with cautiousness, because it is ever possible to do R2 integrity by merely adding adequate footings to the theoretical account. For illustration, we can obtain a “ perfect ” tantrum to n informations points with a multinomial of grade n – 1. In add-on, R2 will ever increase if we add a variable to the theoretical account, but this does non needfully connote that the new theoretical account is superior to the old 1. Unless the mistake amount of squares in the new theoretical account is reduced by an sum equal to the original mistake mean square, the new theoretical account will hold a larger mistake mean square than the old one, because of the loss of one mistake grade of freedom. Therefore, the new theoretical account will really be worse than the old one.

4.0 METHODS

In this subdivision, we discuss about the methods used to execute arrested development analysis. The methods used to calculate all the consequences are shown. Microsoft Office Excel 2007 is used as our chief analyses package to carry on the analysis. Our analyses include obtaining spread diagram, linear fitted line, trial hypotheses and the assurance interval. All these analyses can be done by utilizing one of the maps of Microsoft Excel that is ‘Regression ‘ in ‘Data Analysis ‘ .

4.1 Stairss of Using ‘Data Analysis ‘ in Microsoft Excel

First of wholly, there is an of import measure to make before we can get down to analyse our informations that is make certain the handiness of map ‘Data Analysis ‘ in our Microsoft Excel. ‘Data ‘ from the bill of fare check is chosen to look into the handiness of the map. If ‘Analysis ‘ column is non found, so add in map is needed to obtain the map of informations analysis. Function ‘Data Analysis ‘ can be retrieved by custom-making the speedy entree toolbar utilizing the check of ‘Add-Ins ‘ . After finish the ‘Add- Ins ‘ procedure, so merely we can continue to analyse our informations.

Then, ‘Data Analysis ‘ is clicked and an direction box ( Data Analysis ) is popped out. Following, ‘Regression ‘ is chosen and another direction box ( Regression ) . We started our input procedure by first input the ‘Input Y Range ‘ , which the information of dependent / response variables is keyed in ; and 2nd is ‘Input X Range ‘ , which the information of independent / regressor variables is keyed in. The ‘Input Y Range ‘ is the information of First Year Marine Growth, while the ‘Input X Range ‘ is the information of Freshwater Growth. For our assignment, merely ‘Label ‘ and ‘Line Fit Plot ‘ is ticked and any of the end product options can be selected based on the users. Last, the drumhead end product is shown after the ‘OK ‘ button is pressed.

2.4 Trial Hypothesiss

In order to find whether the fitted line follows additive relationship, trial hypotheses is done by comparing the value of F in ANOVA with fI±,1, n-2. The value of F in ANOVA can be obtained straight from the arrested development drumhead end product. The appropriate hypotheses are H0: I?1=0 ( there is no additive relationship between X and Y ) and H1: I?1a‰ 0 ( there is additive relationship between X and Y ) . Therefore, H0 is rejected if F & gt ; fI±,1, n-2 and Ho is failed to reject if F & lt ; fI±,1, n-2. When H0 is rejected, it means that the dependant and independent variable has linear relationship.

2.5 Assurance Time interval

In order to happen the 95 % assurance interval for the population mean when the when the fresh water growing is 100, the expression of assurance interval about the average response is used. The unknown values are obtained from arrested development sum-up end product and applying of equation as shown below in order to obtain the consequences.

5.0 Consequences

5.1 Consequences for All Fishs:

Freshwater Growth

Marine Growth

147

131

444

405

139

113

446

422

160

137

438

428

99

121

437

469

120

139

405

424

151

144

435

402

115

161

394

440

121

107

406

410

109

129

440

366

119

123

414

422

130

148

444

410

110

129

465

352

127

119

457

414

100

134

498

396

115

139

452

473

117

140

418

398

112

126

502

434

116

116

478

395

98

112

500

334

98

117

589

455

83

97

480

439

85

134

424

511

88

88

455

432

98

99

439

381

74

105

423

418

58

112

411

475

114

98

484

436

88

80

447

431

77

139

448

515

86

97

450

508

86

103

493

429

65

93

495

420

127

85

470

424

91

60

454

456

76

115

430

491

44

113

448

474

42

91

512

421

50

109

417

451

57

122

466

442

42

Table 5.1: Datas for All Fishs

68

496

363

SUMMARY End product:

Arrested development Statisticss

Multiple R

0.172822174

R Square

0.029867504

Adjusted R Square

0.017429908

Standard Error

40.7184312

Observations

80

Analysis of variance

A

df

United states secret service

Multiple sclerosis

F

Significance F

Arrested development

1

3981.480125

3981.480125

2.401388784

0.125275736

Residual

78

129323.2699

1657.990639

Entire

79

133304.75

A

A

A

A

Coefficients

Standard Error

T Stat

P-value

Intercept

469.6160571

18.31507653

25.64095521

9.42156E-40

FreshM

-0.257920086

0.166438551

-1.549641502

0.125275736

Lower 95 %

Upper 95 %

Lower 95.0 %

Upper 95.0 %

433.1535413

506.078573

433.1535413

506.078573

-0.589273781

0.07343361

-0.58927378

0.07343361

Figure 5.1: Scatter Diagram & A ; Fitted Line of All Fish

RESIDUAL OUTPUT:

Observation

Predicted Marine Growth

Remainders

1

431.7018

12.2982

2

433.7652

12.23483

3

428.3488

9.651157

4

444.082

-7.08197

5

438.6656

-33.6656

6

430.6701

4.329876

7

439.9552

-45.9552

8

438.4077

-32.4077

9

441.5028

-1.50277

10

438.9236

-24.9236

11

436.0864

7.913554

12

441.2448

23.75515

13

436.8602

20.13979

14

443.824

54.17595

15

439.9552

12.04475

16

439.4394

-21.4394

17

440.729

61.27099

18

439.6973

38.30267

19

444.3399

55.66011

20

444.3399

144.6601

21

448.2087

31.79131

22

447.6928

-23.6928

23

446.9191

8.08091

24

444.3399

-5.33989

25

450.53

-27.53

26

454.6567

-43.6567

27

440.2132

43.78683

28

446.9191

0.08091

29

449.7562

-1.75621

30

447.4349

2.56507

31

447.4349

45.56507

32

452.8513

42.14875

33

436.8602

33.13979

34

446.1453

7.854671

35

450.0141

-20.0141

36

458.2676

-10.2676

37

458.7834

53.21659

38

456.7201

-39.7201

39

454.9146

11.08539

40

458.7834

37.21659

41

435.8285

-30.8285

42

440.4711

-18.4711

43

434.281

-6.28101

44

438.4077

30.59227

45

433.7652

-9.76517

46

432.4756

-30.4756

47

428.0909

11.90908

48

442.0186

-32.0186

49

436.3444

-70.3444

50

437.8919

-15.8919

51

431.4439

-21.4439

52

436.3444

-84.3444

53

438.9236

-24.9236

54

435.0548

-39.0548

55

433.7652

39.23483

56

433.5072

-35.5072

57

437.1181

-3.11813

58

439.6973

-44.6973

59

440.729

-106.729

60

439.4394

15.56059

61

444.5978

-5.59781

62

435.0548

75.94523

63

446.9191

-14.9191

64

444.082

-63.082

65

442.5344

-24.5344

66

440.729

34.27099

67

444.3399

-8.33989

68

448.9825

-17.9825

69

433.7652

81.23483

70

444.5978

63.40219

71

443.0503

-14.0503

72

445.6295

-25.6295

73

447.6928

-23.6928

74

454.1409

1.859148

75

439.9552

51.04475

76

440.4711

33.52891

77

446.1453

-25.1453

78

441.5028

9.497232

79

438.1498

3.850193

80

452.0775

-89.0775

5.2 Consequences for Males ‘ Fish:

Freshwater Growth

Marine Growth

147

83

444

480

139

85

446

424

160

88

438

455

99

98

437

439

120

74

405

423

151

58

435

411

115

114

394

484

121

88

406

447

109

77

440

448

119

86

414

450

130

86

444

493

110

65

465

495

127

127

457

470

100

91

498

454

115

76

452

430

117

44

418

448

112

42

502

512

116

50

478

417

98

57

500

466

98

42

589

496

Table 5.2: Datas for Males Fish

SUMMARY End product:

Arrested development Statisticss

Multiple R

0.190576376

R Square

0.036319355

Adjusted R Square

0.010959338

Standard Error

37.05170732

Observations

40

Analysis of variance

A

df

United states secret service

Multiple sclerosis

F

Significance F

Arrested development

1

1966.097431

1966.097431

1.43215026

0.238826934

Residual

38

52167.50257

1372.829015

Entire

39

54133.6

A

A

A

A

Coefficients

Standard Error

T Stat

P-value

Intercept

478.3539243

20.29522918

23.569772

2.77485E-24

Freshwater Growth

-0.236440512

0.197573001

-1.196724806

0.238826934

Lower 95 %

Upper 95 %

Lower 95.0 %

Upper 95.0 %

437.2683812

519.4394675

437.2683812

519.4394675

-0.636406139

0.163525116

-0.636406139

0.163525116

Figure 5.2: Scatter Diagram & A ; Fitted Line of Males Fish

RESIDUAL OUTPUT:

Observation

Predicted Marine Growth

Remainders

1

443.5971691

0.402830894

2

445.4886932

0.511306801

3

440.5234425

-2.523442454

4

454.9463137

-17.94631367

5

449.9810629

-44.98106292

6

442.6514071

-7.651407059

7

451.1632655

-57.16326548

8

449.7446224

-43.74462241

9

452.5819086

-12.58190855

10

450.2175034

-36.21750343

11

447.6166578

-3.616657805

12

452.345468

12.65453196

13

448.3259793

8.67402066

14

454.7098732

43.29012684

15

451.1632655

0.83673452

16

450.6903845

-32.69038446

17

451.872587

50.12741298

18

450.926825

27.07317503

19

455.1827542

44.81724582

20

455.1827542

133.8172458

21

458.7293619

21.27063815

22

458.2564808

-34.25648083

23

457.5471593

-2.547159296

24

455.1827542

-16.18275418

25

460.8573265

-37.85732646

26

464.6403746

-53.64037465

27

451.399706

32.60029401

28

457.5471593

-10.5471593

29

460.1480049

-12.14800492

30

458.0200403

-8.020040319

31

458.0200403

34.97995968

32

462.9852911

32.01470893

33

448.3259793

21.67402066

34

456.8378378

-2.837837761

35

460.3844454

-30.38444544

36

467.9505418

-19.95054181

37

468.4234228

43.57657717

38

466.5318987

-49.53189874

39

464.8768152

1.123184841

40

468.4234228

27.57657717

5.3 Consequences for Females ‘ Fish:

Freshwater growing

Marine growing

131

97

405

439

113

134

422

511

137

88

428

432

121

99

469

381

139

105

424

418

144

112

402

475

161

98

440

436

107

80

410

431

129

139

366

515

123

97

422

508

148

103

410

429

129

93

352

420

119

85

414

424

134

60

396

456

139

115

473

491

140

113

398

474

126

91

434

421

116

109

395

451

112

122

334

442

117

68

455

363

Table 5.3: Datas for Females Fish

SUMMARY OUTPUT

Arrested development Statisticss

Multiple R

0.040178762

R Square

0.001614333

Adjusted R Square

-0.024658974

Standard Error

41.54801703

Observations

40

Analysis of variance

A

df

United states secret service

Multiple sclerosis

F

Significance F

Arrested development

1

106.0666754

106.0666754

0.061443841

0.805562865

Residual

38

65597.03332

1726.237719

Entire

39

65703.1

A

A

A

A

Coefficients

Standard Error

T Stat

P-value

Intercept

420.6274808

35.00378835

12.01662736

1.63513E-14

Freshwater Growth

0.074221808

0.299427962

0.247878681

0.805562865

Lower 95 %

Upper 95 %

Lower 95.0 %

Upper 95.0 %

349.7660166

491.4889451

349.7660166

491.4889451

-0.531938406

0.680382023

-0.531938406

0.680382023

Figure 5.3: Scatter Diagram & A ; Fitted Line of Females Fish

RESIDUAL OUTPUT:

Observation

Predicted Marine Growth

Remainders

1

430.3505378

-25.35053775

2

429.0145452

-7.0145452

3

430.7958686

-2.795868602

4

429.6083197

39.39168033

5

430.9443122

-6.944312219

6

431.3154213

-29.31542126

7

432.577192

7.422807995

8

428.5692143

-18.56921435

9

430.2020941

-64.20209413

10

429.7567633

-7.756763284

11

431.6123085

-21.6123085

12

430.2020941

-78.20209413

13

429.4598761

-15.45987605

14

430.5732032

-34.57320318

15

430.9443122

42.05568778

16

431.018534

-33.01853403

17

429.9794287

4.020571291

18

429.2372106

-34.23721062

19

428.9403234

-94.94032339

20

429.3114324

25.68856757

21

427.8269963

11.17300374

22

430.5732032

80.42679682

23

427.159

4.841000012

24

427.9754399

-46.97543988

25

428.4207707

-10.42077073

26

428.9403234

46.05967661

27

427.9012181

8.098781927

28

426.5652255

4.434774479

29

430.9443122

84.05568778

30

427.8269963

80.17300374

31

428.2723271

0.727672885

32

427.530109

-7.530109031

33

426.9363346

-2.936334563

34

425.0807894

30.91921065

35

429.1629888

61.83701118

36

429.0145452

44.9854548

37

427.3816654

-6.381665414

38

428.717658

22.28234203

39

429.6825415

12.31745852

40

425.6745638

-62.67456382

6.0 Discussion and Analysis

6.1 Discussion and analysis for All Fishs:

Figure 5.1 shows the spread diagram and fitted line of all fishes, while the drumhead end product of all fish calculated utilizing Microsoft Excel ( Data Analysis ) besides shown in subdivision 5.1. In Figure 5.1, we noticed that there is equation of consecutive line and its several coefficient of finding, R2. The value from the equation can be obtained from the drumhead end product every bit good, which is the coefficients of intercept and fresh water growing. The consecutive line equation is y = -0.2579x + 469.62 and the value of R2 = 0.0299.

In order to find if I?1 differs from nothing, a trial hypothesis is done where,

H0: I?1 = 0

H1: I?1 a‰ 0

From drumhead end product, the F in ANOVA tabular array is 2.4014. Therefore, we reject H0 if F & gt ; f0.05,1,78 a‰? 4 ( Value from brochure ) . Since F = 2.4014 & lt ; f0.05,1,78 a‰? 4, so we fail to reject H0. Therefore there is no strong grounds to find that I?1 differs from nothing.

To happen 95 % assurance interval for the population mean when the fresh water growing is 100. Therefore, the fresh water growing ( x0 ) is 100, hence

Where = 469.62 and = -0.2579. Substitute these values and = 443.83.

Then, by utilizing the expression

Where t0.025,78 a‰? 2.00, = 1657.99, n = 80, = 106.5875, = 59851.3875. All values are substituted into the equation and therefore the 95 % assurance interval for the population mean is

434.46 a‰¤ a‰¤ 453.20

6.2 Discussion and analysis for Males Fish:

Figure 5.2 shows the spread diagram and fitted line of males, while the drumhead end product of males fish calculated utilizing Microsoft Excel ( Data Analysis ) besides shown in subdivision 5.2. In Figure 5.2, we noticed that there is equation of consecutive line and its several coefficient of finding, R2. The value from the equation can be obtained from the drumhead end product every bit good, which the coefficient of intercept = I?0 while the coefficient of fresh water growing = I?1.The consecutive line equation is y = -0.2364x + 478.35 and R2 = 0.0363

Test hypothesis is done in order to find if I?1 differs from nothing. Therefore,

H0: I?1 = 0

H1: I?1 a‰ 0

From the drumhead end product, the F in ANOVA tabular array is 1.4322. Therefore, we reject H0 if F & gt ; f0.05,1,38 a‰? 4.08. Since F = 1.4322 & lt ; f0.05,1,78 a‰? 4.08, so fail to reject H0. Therefore there is no strong grounds to find that I?1 differs from nothing.

To obtain the 95 % assurance interval for the population mean when the fresh water growing ( x0 ) is 100, by using expression

Where = 478.35 and = -0.2364. Substitute these values and = 454.71.

Then, by utilizing the expression

Where t0.025,38 a‰? 2.021, = 1372.83, n = 40, = 98.35, = 35169.1. All values are substituted into the equation and therefore the is within the assurance interval of

442.85 a‰¤ a‰¤ 466.57

6.3 Discussion and analysis for Females Fish:

Figure 5.3 shows the spread diagram and fitted line of males, while the drumhead end product of males fish calculated utilizing Microsoft Excel ( Data Analysis ) besides shown in subdivision 5.3. In Figure 5.3, we noticed that there is equation of consecutive line and its several coefficient of finding, R2. The value from the equation can be obtained from the drumhead end product every bit good, which the coefficient of intercept = I?0 while the coefficient of fresh water growing = I?1.The consecutive line equation is y = 0.0742x + 420.63 and R2 = 0.0016

Test hypothesis is done in order to find if I?1 differs from nothing. Therefore,

H0: I?1 = 0

H1: I?1 a‰ 0

From the drumhead end product, the F in ANOVA tabular array is 0.0614. Therefore, we reject H0 if F & gt ; f0.05,1,38 a‰? 4.08. Since F = 0.0614 & lt ; f0.05,1,78 a‰? 4.08, so we fail to reject H0. Therefore there is no strong grounds to find that I?1 differs from nothing.

The 95 % assurance interval for the population mean when the fresh water growing is 100 is found by following these stairss and by utilizing expression.

Where = 420.63 and = 0.0742. Substitute these values and = 428.05.

Then, by utilizing the expression

Where t0.025,38 a‰? 2.021, = 1726.24, n = 40, = 114.825, = 19253.775. All values are substituted into the equation and therefore the is within the assurance interval of

412.03 a‰¤ a‰¤ 444.07

7.0 Decision

In decision, arrested development analysis can be used to pattern the relationship between one or more response variables and one or more forecaster variables. Based on the undertaking given, it is a simple additive arrested development analysis which consists of a individual forecaster, or regressor which is the salmon ‘s growing in fresh H2O and a individual response variable which is the salmon ‘s growing in Marine. This simple additive arrested development analysis determines whether there is any relationship between the regressor and the response variable. The simple additive arrested development theoretical account besides gives a consecutive line relationship between a individual response ( dependent ) variable and a individual forecaster ( independent ) variable. In this undertaking arrested development analysis have been done individually for all fishes, males ‘ fish and females ‘ fish.

From the consequences obtained, the marine growing on fresh water growing for all fishes can be represented by a consecutive line equation: . We fail to reject H0 since there is no sufficient grounds to find that I?1 differs from nothing. This shows that there is no additive relationship between the Y and X. The 95 % assurance interval for the population mean when the fresh water is 100 is between 434.46 and 453.20.

On the other manus, for the males ‘ fish, is the consecutive line equation obtained from the spread diagram and fitted line secret plan. We fail to reject H0 and therefore we can statistically reason that there is no additive relationship between Y and X. The 95 % assurance interval for the population mean when the fresh water is 100 is between of 442.85 and 466.57.

Besides, for females ‘ fish, the consecutive line equation obtained is. Since the H0 is failed to reject, therefore we can statistically reason that there is no additive relationship between Y and X. The 95 % assurance interval for the population mean when the fresh water is 100 is 412.03 a‰¤ a‰¤ 444.07.

Last, from the consequences and analysis obtained, it is really obvious and we can therefore statically conclude that the fresh H2O growing and marine growing salmons do non hold direct relationship. This is because the informations obtained do non supply strong grounds to demo the being of one-dimensionality between fresh H2O growing and marine growing.

Post Author: admin