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

Data from the table in the image

data = { "Temperature (°F)": [66, 73, 72, 63, 52, 39, 33, 30, 33, 37, 48, 57], "Crawling Age (Weeks)": [29.84, 30.52, 29.70, 31.84, 28.58, 31.44, 33.64, 32.82, 33.83, 33.35, 33.38, 32.32] }

Create a DataFrame

df = pd.DataFrame(data)

Separate independent (X) and dependent (y) variables

X = np.array(df["Temperature (°F)"]).reshape(-1, 1) y = np.array(df["Crawling Age (Weeks)"])

Perform linear regression

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

Get the slope and intercept

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

slope, intercept(-0.07773916191510544, 35.67805955290071)(-0.07773916191510544, 35.67805955290071)successThe equation of the least-squares regression line is:

$\hat{y} = -0.08x + 35.68$

where:

• $x$ represents the temperature (in °F),
• $\hat{y}$ represents the predicted crawling age (in weeks).

Do you have any questions or need further explanation?

Here are 5 related questions to expand understanding:

1. How is the slope of the regression line interpreted in this context?
2. How does temperature influence crawling age based on the regression equation?
3. What is the significance of the y-intercept in this scenario?
4. How could the correlation between temperature and crawling age be quantified?
5. Can this regression line be used to make predictions for temperatures outside the provided range?

Tip: When interpreting regression results, always consider the context and whether the relationship is causal or merely correlational.