Financial Risk Manager Part 1

Explanation

The test statistic for the slope coefficient is calculated using the formula:

$t_{α,n−2} = \frac{β₁ - β₀}{se(β₁)}$

Where:

• $β₁$ = 0.2043 (estimated slope coefficient)
• $β₀$ = 0 (hypothesized value under H₀)
• $se(β₁)$ = 0.01828 (standard error of slope coefficient)
• $n$ = 6 (number of observations)
• Degrees of freedom = $n - 2 = 6 - 2 = 4$

Test statistic calculation: $t = \frac{0.2043 - 0}{0.01828} = 11.1761 ≈ 11.2$

Critical value: For a one-tailed test at 0.5% significance level with 4 degrees of freedom: $t_{0.005,4} = 4.604$

Decision: Since 11.2 > 4.604, we reject the null hypothesis H₀: β₁ = 0 and conclude that β₁ > 0.

Key points:

• This is a one-tailed test because the alternative hypothesis is Hₐ: β₁ > 0
• The test statistic (11.2) exceeds the critical value (4.604)
• Therefore, we have sufficient evidence to conclude that the slope coefficient is significantly greater than zero