Financial Risk Manager Part 1
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The following table presents regression results for a linear regression model with 3 independent random variables:
| Variable | Coefficient | Standard error | t-statistic | p-value |
|---|---|---|---|---|
| Intercept | 2.0 | 2.0 | 1.0 | 0.3215 |
| X | -1.8 | 0.56 | -3.2 | 0.0022 |
| Y | 16.4 | 4.10 | 4.0 | 0.0002 |
| Z | 0.12 | 0.54 | 0.22 | 0.0319 |
Determine the regression parameters that are significantly different from zero at the 1% level of significance, assuming .
Other
Community
NNikitesh
A
X and Y
B
X only
C
Y and Z
D
All of X, Y, and Z
Explanation:
The p-value is the smallest level of significance for which the null hypothesis can be rejected. At the 1% significance level (α = 0.01), we compare each variable's p-value:
- X: p-value = 0.0022 < 0.01 → Statistically significant
- Y: p-value = 0.0002 < 0.01 → Statistically significant
- Z: p-value = 0.0319 > 0.01 → Not statistically significant
- Intercept: p-value = 0.3215 > 0.01 → Not statistically significant
Therefore, only X and Y are significantly different from zero at the 1% level of significance.
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