Part D and E

Part D and E



Part D and E

Fit a linear relationship between density and space mean speed and assess the coefficient of correlation of the relationship..

Variables Entered/Removedb

Model

Variables Entered

Variables Removed

Method

1

space mean speeda

.

Enter

a. All requested variables entered.

b. Dependent Variable: density

Model Summary

Model

R

R Square

Adjusted R Square

Std. Error of the Estimate

1

.178a

.032

-.056

63.53360

a. Predictors: (Constant), space mean speed

ANOVAb

Model

Sum of Squares

df

Mean Square

F

Sig.

1

Regression

1446.989

1

1446.989

.358

.561a

Residual

44401.708

11

4036.519

Total

45848.697

12

a. Predictors: (Constant), space mean speed

b. Dependent Variable: density

Coefficientsa

Model

Unstandardized Coefficients

Standardized Coefficients

t

Sig.

B

Std. Error

Beta

1

(Constant)

69.090

52.367

1.319

.214

space mean speed

.014

.024

.178

.599

.561

a. Dependent Variable: density

Coefficients value is 0.014

b:) fit an exponential relationship between density and space mean hasten and assess the coefficient of association of the relationship.

Model Description

Model Name

MOD_1

Dependent Variable

1

density

Equation

1

Linear

2

Exponentiala

Independent Variable

space mean speed

Constant

Included

Variable Whose standards mark facts in Plots

Unspecified

a. The model requires all non-missing standards to be positive.

Case Processing Summary

N

Total Cases

13

Excluded Casesa

0

Forecasted Cases

0

Newly Created Cases

0

a. Cases with a missing worth in any variable are excluded from the analysis.

Variable Processing Summary

Variables

Dependent

Independent

density

space mean speed

Number of Positive Values

13

13

Number of Zeros

0

0

Number of Negative Values

0

0

Number of Missing Values

User-Missing

0

0

System-Missing

0

0

Model abstract and Parameter Estimates

Dependent Variable:density

Equation

Model Summary

Parameter Estimates

R Square

F

df1

df2

Sig.

Constant

b1

Linear

.032

.358

1

11

.561

69.090

.014

Exponential

.264

3.950

1

11

.072

19.109

.001

The independent variable is space mean speed.

c:) using the fundamental connection, determine the connection between q and us for situations a) and b) respectively.

To check the validity of the relationship between any two variables, the best option is correlation test. Correlation is a assess of connection between two variables. It has broad submission in enterprise and statistics. And there are two types of correlations.

Bivariate Correlation

Partial Correlation

Bivariate Correlation

Bivariate correlation checks the strength of the connection between two variables without giving any concern to the interference some other variable might origin to the connection between the two variables being tested.

Aassociation coefficient is an index number that measures…

The magnitude and

The direction of the connection between two variables

It is conceived to variety in worth between

0.0 And 1.0

-1.0-0.8-0.6-0.4-0.2 0.0+0.2+0.4+0.6+0.8+1.0

NegativePositive

Relationship Relationship

(X (Y(X (Y

(X (Y(X (Y

No relationship

In the given data, we want to know the relationship between Time Mean Speed and Space Mean Speed variables. The best result would be Bivariate Correlation test. Following results are showing the correlations between the two.

Correlations

space mean speed

density

space mean speed

Pearson Correlation

1

.178

Sig. (2-tailed)

.561

N

13

13

density

Pearson Correlation

.178

1

Sig. (2-tailed)

.561

N

13

13

d) based on the model fitting parameteres of the two us-k models (linear and exponential), find the maximum flow volume qmax and the respective densities and space mean speeds..

Variables Entered/Removedb

Model

Variables Entered

Variables Removed

Method

1

density, space mean speeda

.

Enter

a. All requested variables entered.

b. Dependent Variable: flow

Model Summary

Model

R

R Square

Adjusted R Square

Std. Error of the Estimate

1

.978a

.956

.948

4.025801

a. Predictors: (Constant), density, space mean speed

Coefficientsa

Model

Unstandardized Coefficients

Standardized Coefficients

t

Sig.

B

Std. Error

Beta

1

(Constant)

64.205

3.571

17.979

.000

space mean speed

-.003

.002

-.149

-2.221

.051

density

-.268

.019

-.940

-14.012

.000

a. Dependent Variable: flow

e:) plot the measured data in three graghs, representing us-k, q-k and us-q relationships respectively.

In statistics, a histogram is a graphical representation, displaying a visual effect of the circulation of untested data. It is an approximate of the likelihood circulation of a relentless variable and was first presented by Karl Pearson. A histogram comprises of tabular frequencies, shown as adjacent rectangles, erected over discrete gaps (bins), with an locality identical to the frequency of the facts in the interval. The size of a rectangle is furthermore identical to the frequency density of the interval, ...