To compute the residual for the observed head circumference of the 25.25-inch-tall child:

Steps:

1. Fit a Linear Regression Model: We'll use the provided data points $(x, y)$, where $x$ is height (in inches), and $y$ is head circumference (in inches), to derive the regression equation $y = mx + b$.

2. Compute the Predicted Value: Use the regression equation to find the predicted head circumference for $x = 25.25$.

3. Calculate the Residual: Residual = Observed Value $-$ Predicted Value.

Let’s perform the calculations.import numpy as np import pandas as pd from sklearn.linear_model import LinearRegression

Data

data = { "Height (inches)": [27.5, 24.75, 25.5, 25.75, 25, 28, 26.25, 27, 26, 26, 28], "Head Circumference (inches)": [17.8, 17