import pandas as pd

Load the uploaded Excel file to examine its structure

file_path = '/mnt/data/1732116268097xwm3v2wh.xlsx' data = pd.ExcelFile(file_path)

Display the sheet names to understand its structure

data.sheet_names['Data', 'Sheet2', 'Sheet3']['Data', 'Sheet2', 'Sheet3']success# Load the main data sheet to inspect its contents main_data = data.parse('Data')

Display the first few rows to understand the structure

main_data.head() Line Speed Number of Defective\nParts Found 0 20 23 1 20 21 2 30 19 3 30 16 4 40 15 Line Speed Number of Defective\nParts Found 0 20 23 1 20 21 2 30 19 3 30 16 4 40 15successThe dataset consists of two columns:

1. Line Speed (independent variable $X$)
2. Number of Defective Parts Found (dependent variable $Y$)

I will now use the least squares method to develop the estimated regression equation.import numpy as np

Rename columns for easier reference

main_data.columns = ['Line_Speed', 'Defective_Parts']

Extract variables

X = main_data['Line_Speed'] Y = main_data['Defective_Parts']

Perform calculations for least squares regression

n = len(X) X_mean = X.mean() Y_mean = Y.mean()

Calculate slope (b1) and intercept (b0)

b1 = np.sum((X - X_mean) * (Y - Y_mean)) / np.sum((X - X_mean)**2) b0 = Y_mean - b1 * X_mean

Construct the regression equation

regression_equation = f"Y = {b0:.1f} + {b1:.1f}X"

b0, b1, regression_equation(27.5, -0.3, 'Y = 27.5 + -0.3X')(27.5, -0.3, 'Y = 27.5 + -0.3X')successThe estimated regression equation is:

$Y = 27.5 - 0.3X$

This equation indicates that for each unit increase in line speed ($X$), the number of defective parts ($Y$) decreases by 0.3 on average.

Would you like me to provide further details, such as a visualization or statistical analysis? Here are some related questions:

1. How is the regression equation applied in predictive analysis?
2. Would you like a visual representation of the regression line with the data points?
3. How do we interpret the slope ($-0.3$) in this context?
4. Can I calculate additional metrics such as $R^2$ or residuals for model accuracy?
5. How is the intercept ($27.5$) significant in this scenario?

Tip: Always ensure that the relationship between variables is approximately linear before relying on a simple regression model!