Financial Risk Manager Part 1

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Suppose that the following regression is estimated using 25 quarterly observations:

y_t = \beta_1 + \beta_2 x_{2t} + \beta_3 x_{3t} + u_t

What is the appropriate critical value for a 2-sided 5% size of test of $H_0 : \beta_3 = 1$ ?

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NNikitesh

Last updated: February 2, 2026 at 10:22

1.72

2.06

2.07

1.64

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.

In this case, $n = 25$ , $k = 3$

Also, this is a two-tailed test.

Thus, we would be interested in $t_{0.025,22}$ . We would be looking in the t-tables in the degrees of freedom = 22 rows and the 2.5% column (so that 2.5% is in each tail for a 5% 2-tailed test). The critical value would be 2.07.

Option A is incorrect. 1.72 would be the critical value for a 5% one-tailed test or a 10% two-tailed test.

Option B is incorrect. This is the critical value obtained if you forget to subtract the number of parameters estimated (3) from the number of observations to get the degrees of freedom, i.e., $t_{0.025,25} = 2.06$ .

Option D is incorrect. 1.64 is the 5% one-sided critical value from the normal distribution.

Note: the fact that observations are quarterly is irrelevant in our calculations.

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