Financial Risk Manager Part 1

Explanation

When we have a total of k "regressors" (including a constant) and n observations, the t-test statistic will follow a t-distribution with n - k degrees of freedom.

Given:

• n = 25 observations
• k = 3 regressors (β₁, β₂, β₃)
• Degrees of freedom = n - k = 25 - 3 = 22

Test Details:

• This is a two-tailed test
• Significance level = 5%
• Each tail has 2.5% of the distribution
• We need the critical value for t_{0.025, 22}

Critical Value:

Looking up the t-distribution table with 22 degrees of freedom and 2.5% in each tail gives us a critical value of 2.07.

Key Points:

• The fact that observations are quarterly is irrelevant for the calculation
• When testing a hypothesis about a single coefficient in a model with multiple regressors, we use a t-test
• The t-test is NOT suitable for testing hypotheses that involve more than one parameter (those require F-tests)
• The correct critical value is 2.07, which corresponds to option C_