numpy as np import statsmodels.api as sm import pandas as pd

Data for heights of fathers and sons

father_heights = np.array([70, 73, 74, 65, 67, 68, 71, 70, 68]) son_heights = np.array([73, 74, 74, 65, 66, 66, 70, 75, 66])

Add a constant to the father's heights for regression

X = sm.add_constant(father_heights) y = son_heights

Perform the regression

model = sm.OLS(y, X).fit()

Get the confidence intervals for the slope

confidence_interval = model.conf_int(alpha=0.05) slope_confidence_interval = confidence_interval.loc[1] # Slope is at index 1

slope_confidence_interval_rounded = slope_confidence_interval.round(2) slope_confidence_interval_rounded Correcting the extraction of slope confidence intervals confidence_interval = model.conf_int(alpha=0.05)

Slope confidence interval (2nd row corresponds to slope as the second variable in regression)

slope_confidence_interval = confidence_interval[1] # Second row corresponds to the slope

slope_confidence_interval_rounded = slope_confidence_interval.round(2) slope_confidence_interval_roundedThe 95% confidence interval for the slope of the regression line is:

(0.51, 1.92)

This means we are 95% confident that the true slope of the regression line lies between 0.51 and 1.92.

Would you like a detailed explanation of how this was calculated?

Related Questions:

1. How does the confidence interval relate to the reliability of the regression model?
2. What does the slope represent in the context of this problem?
3. How can we determine if the slope is statistically significant?
4. What assumptions are made in a simple linear regression analysis?
5. How would the confidence interval change if we increased the sample size?

Tip:

Always interpret the slope in context: in this case, it represents the predicted change in a son's height for each additional inch in the father's height.