# 12.2.2.2 - Example: Body Correlation Matrix

12.2.2.2 - Example: Body Correlation MatrixConstruct a correlation matrix using the variables age (years), weight (Kg), height (cm), hip girth, navel (or abdominal girth), and wrist girth.

This example is using the body dataset. These data are from the *Journal of Statistics Education* data archive.

For this example, you can use the following Minitab file: body.dat.mpx

To construct a correlation matrix in Minitab...

- Open the Minitab file: StudentSurvey.mpx
- Select
*Stat > Basic Statistics > Correlation* - Enter the variables
*Age(years), Weight (Kg), Height (cm)**, Hip girth at level of bitrochan, Navel (or "Abdominal") girth,*and*Wrist minimum girth*into the*Variables*box - Select the
*Graphs...*button and select*Correlations and p-values*from the dropdown - Select the
*Results...*button and verify that the*Correlation matrix*and*Pairwise correlation table*boxes are checked - Click
*OK*and*OK*

This should result in the following partial output:

##### Pairwise Pearson Correlations

Sample 1 | Sample 2 | N | Correlation | 95% CI for ρ | P-Value |
---|---|---|---|---|---|

Weight (Kg) | Age (years) | 507 | 0.207 | (0.122, 0.289) | 0.000 |

Height (cm) | Age (years) | 507 | 0.068 | (-0.019, 0.154) | 0.127 |

Hip girth at level of bitrochan | Age (years) | 507 | 0.227 | (0.143, 0.308) | 0.000 |

Navel (or "Abdominal") girth at | Age (years) | 507 | 0.422 | (0.348, 0.491) | 0.000 |

Wrist minimum girth | Age (years) | 507 | 0.192 | (0.107, 0.275) | 0.000 |

Height (cm) | Weight (Kg) | 507 | 0.717 | (0.672, 0.757) | 0.000 |

Hip girth at level of bitrochan | Weight (Kg) | 507 | 0.763 | (0.724, 0.797) | 0.000 |

Navel (or "Abdominal") girth at | Weight (Kg) | 507 | 0.712 | (0.666, 0.752) | 0.000 |

Wrist minimum girth | Weight (Kg) | 507 | 0.816 | (0.785, 0.844) | 0.000 |

Hip girth at level of bitrochan | Height (cm) | 507 | 0.339 | (0.259, 0.413) | 0.000 |

Navel (or "Abdominal") girth at | Height (cm) | 507 | 0.313 | (0.232, 0.390) | 0.000 |

Wrist minimum girth | Height (cm) | 507 | 0.691 | (0.642, 0.734) | 0.000 |

Navel (or "Abdominal") girth at | Hip girth at level of bitrochan | 507 | 0.826 | (0.796, 0.852) | 0.000 |

Wrist minimum girth | Hip girth at level of bitrochan | 507 | 0.459 | (0.387, 0.525) | 0.000 |

Wrist minimum girth | Navel (or "Abdominal") girth at | 507 | 0.435 | (0.362, 0.503) | 0.000 |

Cell contents grouped by Age, Weight, Height, Hip Girth, and Abdominal Girth; First row: Pearson correlation, Following row: P-Value

Cell contents grouped by Age, Weight, Height, Hip Girth, and Abdominal Girth; First row: Pearson correlation, Following row: P-Value

This correlation matrix presents 15 different correlations. For each of the 15 pairs of variables, the 'Correlation' column contains the Pearson's r correlation coefficient and the last column contains the p value.

The correlation between age and weight is \(r=0.207\). This correlation is statistically significant (\(p=0.000\)). That is, there is evidence of a relationship between age and weight in the population.

The correlation between age and height is \(r=0.068\). This correlation is not statistically significant (\(p=0.127\)). There is not enough evidence of a relationship between age and height in the population.

The correlation between weight and height is \(r=0.717\). This correlation is statistically significant (\(p<0.000\)). That is, there is evidence of a relationship between weight and height in the population.

And so on.