Statistical modelling

Assignment 1:

Scatter plots show the relationship between two variables by displaying data points on a two-dimensional graph. The variable that might be considered an explanatory variable is plotted on the x axis, and the response variable is plotted on the y axis.

Scatter plots are especially useful when there is a large number of data points. They provide the following information about the relationship between two variables:

* Strength

* Shape - linear, curved, etc.

* Direction - positive or negative

* Presence of outliers

A correlation between the variables results in the clustering of data points along a line. The following is an example of a scatter plot suggestive of a positive linear relationship.

Question 1:

Scatter Plot (Before Insulate)

As it can be seen there is linear relation between the two given variables.

Scatter plot (After Insulate)

As it can be seen there is linear relation between the two given variables

Question 2:

The ANalysis Of VAriance (or ANOVA) is a powerful and common statistical procedure in the social sciences. It can handle a variety of situations. We will talk about the case of one between groups factor here and two between groups factor.

ANOVA

Sum of Squares

df

Mean Square

F

Sig.

Temp

Between Groups

68.562

1

68.562

11.473

.002

Within Groups

250.983

42

5.976

Total

319.544

43

Gas

Between Groups

7.887

1

7.887

8.809

.005

Within Groups

37.603

42

.895

Total

45.490

43

as it can be seen there is a significance difference in temp.

Question 3:

Regression

ANOVAb

Model

Sum of Squares

df

Mean Square

F

Sig.

1

Regression

14.912

1

14.912

20.482

.000a

Residual

30.578

42

.728

Total

45.490

43

a. Predictors: (Constant), Temp

b. Dependent Variable: Gas

Question 4:

Coefficientsa

Model

Unstandardized Coefficients

Standardized Coefficients

t

Sig.

B

Std. Error

Beta

1

(Constant)

5.329

.243

21.959

.000

Temp

-.216

.048

-.573

-4.526

.000

a. Dependent Variable: Gas

Question 5:

Question 6:

Residuals Statisticsa

Minimum

Maximum

Mean

Std. Deviation

N

Predicted Value

3.1256

5.5019

4.3977

.58889

44

Std. Predicted Value

-2.160

1.875

.000

1.000

44

Standard Error of Predicted Value

.129

.309

.176

.048

44

Adjusted Predicted Value

3.2051

5.5570

4.3942

.57997

44

Residual

-1.45941

1.69810

.00000

.84328

44

Std. Residual

-1.710

1.990

.000

.988

44

Stud. Residual

-1.734

2.103

.002

1.012

44

Deleted Residual

-1.50040

1.89623

.00350

.88545

44

Stud. Deleted Residual

-1.778

2.197

.006

1.025

44

Mahal. Distance

.000

4.666

.977

1.154

44

Cook's Distance

.000

.258

.025

.046

44

Centered Leverage Value

.000

.109

.023

.027

44

a. Dependent Variable: Gas

Assignment 5:

Variables Entered/Removedb

Model

Variables Entered

Variables Removed

Method

1

Site a

.

Enter

a. All requested variables entered.

b. Dependent Variable: Distance

Model Summaryb

Model

R

R Square

Adjusted R Square

Std. Error of the Estimate

1

.000a

.000

-.007

17.054

a. Predictors: (Constant), Site

b. Dependent Variable: Distance

ANOVAb

Model

Sum of Squares

df

Mean Square

F

Sig.

1

Regression

.000

1

.000

.000

1.000a

Residual

41300.000

142

290.845

Total

41300.000

143

a. Predictors: (Constant), Site

b. Dependent Variable: Distance

Coefficientsa

Model

Unstandardized Coefficients

Standardized Coefficients

t

Sig.

B

Std. Error

Beta

1

(Constant)

19.167

7.215

2.657

.009

Site

.002

.832

.000

.000

1.000

a. Dependent Variable: Distance

Residuals Statisticsa

Minimum

Maximum

Mean

Std. Deviation

N

Predicted Value

19.17

19.17

19.17

.000

144

Residual

-19.167

30.833

.000

16.994

144

Std. Predicted Value

.000

.000

.000

.000

144

Std. Residual

-1.124

1.808

.000

.996

144

a. Dependent Variable: Distance

The required linear regression model is

Distance= 0.002 Site+ 19.167

Spatial modeling of line-transect survey data collected from ships of opportunity yielded abundance estimates and predicted density maps for three baleen whale species in the Antarctic. Our looped animations of predicted animal density represent a novel way to illustrate uncertainty in estimates of both abundance and distribution to interested stakeholders who are non-scientists. This study demonstrates that there is merit in collecting reliable distance sampling data from a non-randomized survey with reasonable coverage, modeling heterogeneity along the trackline, and using the model to predict density throughout the study area. The framework outlined here is an appropriate way to gain useful information on frequently seen cetacean species in other areas from expedition-style cruise ships, fishing boats, freighters, or other ships of opportunity in understudied areas, or where lack of research funding prevents researchers from conducting design-unbiased surveys.

But identification of high-density areas also plays an important iterative role in cetacean research itself. Studies that do not require a randomized sampling design routinely benefit from identifying high-density areas that can be targeted in future. This would increase the efficiency of photo-identification and biopsy studies. Identifying core areas, and directing ...