To predict the height of a person as an adult based on their height at age 2 (25.00 inches), we first need to determine the regression equation. Let’s calculate it using the given data.

The general regression equation is:
$y = a + b x$ Where:

• $y$ is the predicted adult height,
• $x$ is the height at age 2,
• $a$ is the y-intercept,
• $b$ is the slope.

The slope $b$ is calculated as: $b = \frac{n \sum (x y) - \sum x \sum y}{n \sum x^2 - (\sum x)^2}$ The y-intercept $a$ is calculated as: $a = \bar{y} - b \bar{x}$

Let me extract the data from the table and perform the calculations. numpy as np

Data from the table

height_age_2 = np.array([33.00, 35.75, 31.50, 34.00, 29.75, 37.00, 32.50, 36.25]) height_age_22 = np.array([64.50, 69.25, 63.25, 68.00, 57.50, 72.25, 67.50, 74.00])

Calculate necessary sums for regression

n = len(height_age_2) sum_x = np.sum(height_age_2) sum_y = np.sum(height_age_22) sum_xy = np.sum(height_age_2 * height_age_22) sum_x2 = np.sum(height_age_2 ** 2)

Calculate slope (b) and intercept (a)

b = (n * sum_xy - sum_x * sum_y) / (n * sum_x2 - sum_x ** 2) a = (sum_y / n) - b * (sum_x / n)

Regression equation: y = a + b * x

Predict height for x = 25.00 inches

x_new = 25.00 predicted_height = a + b * x_new

a, b, predicted_heightThe regression equation is:
$y = 0.437 + 1.975x$ Where $y$ is the predicted adult height, and $x$ is the height at age 2.

Using this equation, the predicted adult height for a person who was 25.00 inches tall at age 2 is approximately: $49.81 \, \text{inches}$

Would you like further clarification or additional details?

Here are 5 related questions to explore further:

1. How is the slope of a regression line interpreted in this context?
2. What is the significance of the y-intercept in this scenario?
3. How accurate is the prediction, and what measures can verify its reliability?
4. How could we improve the model with more data points?
5. What assumptions are made in linear regression, and are they reasonable here?

Tip: Always check for outliers or unusual patterns in data before performing regression analysis, as they can significantly affect the results.