Financial Risk Manager Part 1
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The return on a stock R exhibits the following relationship with the market return (MR).
Where is the slope coefficient and is the intercept. After gathering 36 observations, an analyst computed the estimated slope coefficient as 0.6 with a standard error of 0.2. Determine whether the estimated slope coefficient is different from 0 at a 95% confidence level with reference to the critical t-value. Click here to see critical values of the t-distribution.
Explanation:
Explanation
To determine if the slope coefficient is statistically different from zero at a 95% confidence level, we perform a hypothesis test:
Null Hypothesis: ( b = 0 )
Alternative Hypothesis: ( b \ne 0 )
Test Type: Two-tailed test
Step 1: Calculate the t-statistic
[ t = \frac{\text{Sample statistic} - \text{Hypothesized value}}{\text{Standard error of the sample statistic}} = \frac{0.6 - 0}{0.2} = 3 ]
Step 2: Determine the critical t-value
- Confidence level: 95% (α = 0.05)
- Two-tailed test: α/2 = 0.025
- Degrees of freedom: n - 2 = 36 - 2 = 34
- Critical t-value: ±2.03
Step 3: Compare and conclude
Since the calculated t-statistic (3) is greater than the critical t-value (2.03), we reject the null hypothesis.
Conclusion: The slope coefficient is statistically significant at the 95% confidence level with a t-statistic of 3.