Analysis of Coefficient Correlation

Correlation Statistics

Select a data table from the article that best describes the use of the correlation and regression statistic

The table selected from the article is Table 3.

Age-adjusted correlation coefficients between HRR parameters and other variables

Boys

Girls

Correlation Coefficient

P

Correlation Coefficient

P

Waist circumference (cm)

DBP (mmHg)

Triglycerides (mg/dl)

Glucose (mg/dl)

Log-CRP

Identify and interpret the correlation coefficient and coefficient of determination in the data table

According to the data in the table illustrated above, the HRR parameters are negatively correlated with majority of the metabolic risk factors. These include the waist circumference, SBP, levels of serum triglycerides as well as the serum CRP levels. This is owing to the fact that the coefficient correlations of these parameters from the multiple linear regression analysis were negative, for both boys and girls. However, on the other hand, the coefficient correlations if serum HDL levels were positive which shows that this parameter is positively correlated with HRR (Lin et al., 2008).

Boys

R squared

Percentage

Girls

R squared

Correlation Coefficient

Coefficient of Determination

As a Percentage

Correlation Coefficient

Coefficient of Determination

As a Percentage

Waist circumference (cm)

1 min

-0.105

0.011025

1.10%

-0.078

0.006084

0.61%

2 min

-0.339

0.114921

11.49%

-0.308

0.094864

9.49%

3 min

-0.272

0.073984

7.40%

-0.352

0.123904

12.39%

SBP (mmHg)

1 min

0.004

0.000016

0.00%

-0.17

0.0289

2.89%

2 min

-0.138

0.019044

1.90%

-0.234

0.054756

5.48%

3 min

-0.118

0.013924

1.39%

-0.249

0.062001

6.20%

DBP (mmHg)

1 min

-0.045

0.002025

0.20%

-0.032

0.001024

0.10%

2 min

0.032

0.001024

0.10%

0.015

0.000225

0.02%

3 min

0.084

0.007056

0.71%

0.078

0.006084

0.61%

Triglycerides (mg/dl)

1 min

-0.11

0.0121

1.21%

-0.095

0.009025

0.90%

2 min

-0.23

0.0529

5.29%

-0.1

0.01

1.00%

3 min

-0.173

0.029929

2.99%

-0.055

0.003025

0.30%

HDL (mg/dl)

1 min

0.071

0.005041

0.50%

0.167

0.027889

2.79%

2 min

0.2

0.04

4.00%

0.226

0.051076

5.11%

3 min

0.28

0.0784

7.84%

0.084

0.007056

0.71%

Glucose (mg/dl)

1 min

0.055

0.003025

0.30%

-0.105

0.011025

1.10%

2 min

-0.078

0.006084

0.61%

-0.011

0.000121

0.01%

3 min

-0.055

0.003025

0.30%

-0.02

0.0004

0.04%

Log-CRP

1 min

0.032

0.001024

0.10%

-0.145

0.021025

2.10%

2 min

-0.164

0.026896

2.69%

-0.323

0.104329

10.43%

3 min

-0.055

0.003025

0.30%

-0.281

0.078961

7.90%

The coefficient of determination gives an indication of how many data points are placed within the results of the line that is formed by the regression equation. Therefore, a higher coefficient implies a higher percentage of points that lie within the regression line. In this particular case, the longer-term heart rate recoveries which are 2 minutes and 3 minutes have a stronger correlation with the metabolic risks. This is in comparison with the shorter period HRR of 1 minute. For instance, with respect to HDL levels, the coefficient of determination of boys for 1 minute was 0.50%, 4.00% for 2 minutes and even higher, 7.84% for 3 minutes. This is the same for the coefficient of determination of girls. The inference is that there is a better goodness of fit for longer term HRR (Andale, 2012).

Data Representation

This can be deemed the best way to present the data. The reason thereto being that there are numerous metabolic risk factors, which are linked to the heart rate recovery. Therefore, it was important to analyze how each of these factors correlate to HRR to understand which of them is strongly linked to heart rate recovery. Therefore, the presentation of the correlation coefficient of all these metabolic risk factors makes it much easier to gain an understanding of the correlation and the strength of such correlation. Through this presentation of data, it was possible to ascertain the inverse correlated factors such as serum CRP levels, systolic blood pressure (SBP) and waist circumference. In addition, it was easily apparent to perceive that serum HDL levels were positively correlated to heart rate recovery.

. "Correlation is not causation"