Business Context
At NorthBridge Capital, an analyst wants to explain how regression analysis is used in financial data by modeling a stock's monthly return as a function of the market's monthly return. This is a standard way to estimate the stock's market sensitivity and test whether it tends to outperform after adjusting for market movement.
Problem Statement
Use simple linear regression to model the relationship between AlphaTech's monthly return and the market index return:
Rstock=α+βRmarket+ε
Estimate the regression coefficients, test whether the slope is statistically different from 0, and interpret the results in financial terms.
Given Data
You are given summary statistics from 24 monthly observations.
| Metric | Value |
|---|
| Number of months n | 24 |
| Mean market return xˉ | 0.008 |
| Mean stock return yˉ | 0.011 |
| Sum of squares of market returns Sxx=∑(xi−xˉ)2 | 0.0184 |
| Sum of cross products Sxy=∑(xi−xˉ)(yi−yˉ) | 0.0258 |
| Sum of squares of stock returns Syy=∑(yi−yˉ)2 | 0.0412 |
| Significance level α | 0.05 |
Requirements
- Estimate the slope β^ and intercept α^
- Compute R2 and explain what it means
- Test H0:β=0 versus H1:βeq0
- Construct a 95% confidence interval for β
- Interpret the regression in plain financial language
Assumptions
- The linear relationship between market and stock returns is appropriate over this period
- Monthly observations are treated as independent
- Regression residuals have constant variance and are approximately normal for inference
