12.2.2.2 - Example: Body Correlation Matrix

Construct 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...

  1. Open the Minitab file: StudentSurvey.mpx
  2. Select Stat > Basic Statistics > Correlation
  3. 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
  4. Select the Graphs... button and select Correlations and p-values from the dropdown
  5. Select the Results... button and verify that the Correlation matrix and Pairwise correlation table boxes are checked
  6. 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 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.