PIL import Image import pytesseract

Load the uploaded image to extract text

image_path = "/mnt/data/1733371492956wspg1f4a.jpg" extracted_text = pytesseract.image_to_string(Image.open(image_path))

extracted_textThe text extraction appears to be incomplete. I'll manually focus on reconstructing the relevant elements from the image data for accurate processing.

Steps to Solve:

1. Use the provided foot length and height data.
2. Calculate the regression equation (find slope $b_1$ and intercept $b_0$).
3. Predict the height for a foot length of 272.8 mm.
4. Compare the predicted height to the actual height of 1776 mm.

Let me calculate these steps. numpy as np import pandas as pd

Data from the table in the image

foot_lengths = np.array([282.2, 278.3, 253.0, 258.6, 279.1, 258.1, 274.1, 262.3]) heights = np.array([1784.8, 1771.2, 1675.6, 1646.3, 1858.9, 1709.8, 1788.8, 1737.0])

Calculate regression coefficients

n = len(foot_lengths) x_mean = np.mean(foot_lengths) y_mean = np.mean(heights)

Calculate slope (b1) and intercept (b0)

b1 = np.sum((foot_lengths - x_mean) * (heights - y_mean)) / np.sum((foot_lengths - x_mean)**2) b0 = y_mean - b1 * x_mean

Predict the height for a foot length of 272.8 mm

predicted_height = b0 + b1 * 272.8

Results

b0, b1, predicted_heightThe regression equation is:

$\hat{y} = 355.92 + 5.18x$

where:

• $\hat{y}$ is the predicted height,
• $x$ is the foot length.

For a foot length of 272.8 mm, the predicted height is approximately $1770.34 \, \text{mm}$.

Comparison with the actual height:

The actual height is $1776 \, \text{mm}$. The difference between the predicted and actual heights is:

$1776 - 1770.34 = 5.66 \, \text{mm}.$

Would you like a detailed explanation of the steps, or do you have any specific questions?

Follow-Up Questions:

1. How is the slope ($b_1$) calculated in a regression analysis?
2. What does the intercept ($b_0$) represent in the regression equation?
3. How can we test if the regression equation is statistically significant?
4. What is the importance of the $R^2$ value in regression analysis?
5. How would using a different significance level ($\alpha$) affect the conclusions?

Tip:

Always check the residuals (differences between actual and predicted values) to evaluate the fit of your regression model.