import numpy as np import pandas as pd from sklearn.linear_model import LinearRegression

Data

data = { "x": [3, 4, 5, 6, 7, 8, 9, 10], "y": [36.01, 35.98, 29.95, 29.92, 25.09, 21.76, 22.33, 18.1] }

Create dataframe

df = pd.DataFrame(data)

Perform linear regression

X = np.array(df["x"]).reshape(-1, 1) y = np.array(df["y"])

model = LinearRegression() model.fit(X, y)

Regression coefficients

slope = model.coef_[0] intercept = model.intercept_

slope, intercept(-2.6550000000000002, 44.650000000000006)(-2.6550000000000002, 44.650000000000006)successThe regression line is:

$y = -2.66x + 44.65$

Let me know if you would like details on how this was calculated or if you have further questions.

Related Questions:

1. How do we calculate the slope of a regression line manually?
2. What is the significance of the intercept in a regression equation?
3. How can we interpret the slope value in this specific context?
4. What is the R-squared value for this regression, and what does it indicate?
5. How would the regression line change if additional data points were added?

Tip: Always plot the data points with the regression line to visually assess the fit!