Introduction

This blog mainly focuses on finding out the relationship between height (in cm) and metacarpal bone length (in mm). Based on the sample data collection of nine individuals, to implement the linear regression model which can predict the height based on the length of the metacarpal bone.

Figure 1 Illustration of Metacarpal bones. (‘Metacarpal bones’, 2013)

Exploratory Data Analysis

Table 1 gives a brief about the measurements of height and metacarpal bone length data.

Table 1Measurements of metacarpal and height

Create scatterplot to find out the relation between metacarpal and height and calculate the correlation coefficient (Figure 1 Scatterplot graph).

Figure 2 Scatterplot graph

Now, let’s just calculate the correlation coefficient using excel formula:

=CORREL (bone length, Height)

Based on the above formula, the value of correlation coefficient is 0.855968284268897, which indicates a very strong linear relationship between metacarpal and height. Based on this, we can say that it’s ready to perform a liner regression analysis.

Performing the Linear Regression Analysis

Let’s just perform linear regression analysis in excel using below steps:

Step1: Go to the 'Data' tab.

Step 2: Select 'Data Analysis' (you might need to enable the Analysis Tool Pak add-in) and Choose 'Regression'.

Step 3: Select the data ranges for the dependent variable (Height) and the independent variable (Metacarpal Bone Length).

Based on above steps it will give us the below output (Figure 3 Linear Regression).

Figure 3 Linear Regression

The linear regression equation based on the model is:

Y(Height) = 1.6996 * X (Metacarpal Bone Length) + 94.428

Let’s just find out Interpretation of the Linear Regression Equation based on example:

For every 1 mm increase in metacarpal bone length, the predicted height increases by 1.6996 cm.

Predicted Height (cm)= 1.6996 * 42 (Metacarpal Bone Length) + 94.428 = 165.8112

Conclusion

This study explains about linear regression model to predict human height based on metacarpal bone length. The model indicates a strong positive linear relationship, with the equation Y(Height) = 1.6996 * X (Metacarpal Bone Length) + 94.428.