import pandas as pd import numpy as np

Data provided

data = { "y": [46, 40, 42, 37, 51, 40, 51, 44, 42, 35, 49, 44, 41, 42], "x1": [40, 31, 45, 43, 42, 48, 44, 42, 37, 40, 35, 39, 43, 53], "x2": [41, 41, 49, 41, 42, 40, 44, 39, 52, 47, 44, 40, 30, 34], "x3": [40, 35, 38, 40, 50, 43, 40, 38, 41, 39, 43, 45, 42, 35] }

Create a DataFrame

df = pd.DataFrame(data)

Calculate the correlation matrix

correlation_matrix = df.corr()

import ace_tools as tools; tools.display_dataframe_to_user(name="Correlation Matrix", dataframe=correlation_matrix)

Display the correlation matrix

correlation_matrix y x1 x2 x3 y 1.000000 -0.059575 0.030199 0.471198 x1 -0.059575 1.000000 -0.366454 -0.076318 x2 0.030199 -0.366454 1.000000 0.036857 x3 0.471198 -0.076318 0.036857 1.000000 y x1 x2 x3 y 1.000000 -0.059575 0.030199 0.471198 x1 -0.059575 1.000000 -0.366454 -0.076318 x2 0.030199 -0.366454 1.000000 0.036857 x3 0.471198 -0.076318 0.036857 1.000000successThe correlation matrix has been calculated and displayed for analysis. Use this to determine which variable has the strongest correlation with $y$ to predict the first step of a stepwise regression model at a significance level of $\alpha = 0.25$. Let me know if you need help interpreting the results or have additional questions.

1. What does each correlation value imply for the relationship between variables?
2. How does the significance level $\alpha = 0.25$ influence the variable selection?
3. Which variable seems most strongly correlated with $y$?
4. How can stepwise regression benefit from analyzing the correlation matrix?
5. Should multicollinearity among $x_1, x_2,$ and $x_3$ be considered?

Tip: When using stepwise regression, always examine how each predictor variable interacts to ensure they add meaningful insight.