Math 141: Readings for November 24, 2025

Reading

Before coming to lecture today, please read the following material:

• no new reading today.

Homework Assignment

After you’ve completed the reading, but before coming to class, please complete the following homework assignment. Bring your responses to this assignment (handwritten or typed) to class on a piece of paper:

Explain how to do the following inference tasks both with the CLT-based method and the simulation-based method:

• Creating and interpreting a 90% confidence interval for \(\beta_1\) in the regression equation \(y = \beta_o + \beta_1 x_1 + \beta_2 x_2 + \epsilon\),
• Carrying out the hypothesis test \(H_o: \beta_1 = 0\), \(H_A: \beta_1 \neq 0\) at the \(\alpha = 0.1\) in the same regression model,
• Finally, connect the results from the hypothesis test to the bounds of the interval you described. What will be true about the bounds of the interval if we fail to reject \(H_o\)?