pandas as pd import numpy as np

Data from the table in the image

data = { "Panjang (m)": [1, 2, 3, 4, 5], "Arus (mA)": [4, 3, 2, 1, 0] }

Create a DataFrame

df = pd.DataFrame(data)

Linear regression model: y = β0 + β1 * x

Independent variable (x): Panjang (m)

Dependent variable (y): Arus (mA)

x = df["Panjang (m)"] y = df["Arus (mA)"]

Calculate β1 (slope) and β0 (intercept)

x_mean = x.mean() y_mean = y.mean() beta_1 = sum((x - x_mean) * (y - y_mean)) / sum((x - x_mean) ** 2) beta_0 = y_mean - beta_1 * x_mean

Predicted values of y based on the model

y_pred = beta_0 + beta_1 * x

Calculate SSE (Sum of Squared Errors)

sse = sum((y - y_pred) ** 2)

beta_0, beta_1, sseThe linear model for the given data is:

$E(y) = 5 - x$

Explanation:

• $\beta_0 = 5$: This is the intercept, meaning the predicted current ($I$) is 5 mA when the conductor length ($L$) is 0.
• $\beta_1 = -1$: This is the slope, indicating that for every 1-meter increase in the conductor's length, the current decreases by 1 mA.

Sum of Squared Errors (SSE):

The minimum SSE for the given data is $0.0$. This indicates the model perfectly fits the data, as all observed points lie on the regression line.

Do you have further questions, or would you like more details on this?
Here are five related questions for deeper understanding:

1. What is the significance of the slope ($\beta_1$) in the context of electrical conductors?
2. How would you calculate the $R^2$ value for this regression to quantify the fit?
3. How does the length of the conductor affect the resistance and hence the current in this experiment?
4. What would happen to the model if the measurements contained errors (noise)?
5. Can you derive similar models for nonlinear relationships, such as quadratic or exponential?

Tip: When analyzing relationships, always visualize the data first to check for patterns before applying a regression model.