Читать книгу Introduction to Linear Regression Analysis - Douglas C. Montgomery - Страница 40

We construct 95% CIs on β₁ and σ² using the rocket propellant data from Example 2.1. The standard error of is and t_0.025,18 = 2.101. Therefore, from Eq. (2.35), the 95% CI on the slope is

or

In other words, 95% of such intervals will include the true value of the slope.

If we had chosen a different value for α, the width of the resulting CI would have been different. For example, the 90% CI on β₁ is −42.16 ≤ β₁ ≤ −32.14, which is narrower than the 95% CI. The 99% CI is −45.49 ≤ β₁ ≤ 28.81, which is wider than the 95% CI. In general, the larger the confidence coefficient (1 − α) is, the wider the CI.

The 95% CI on σ² is found from Eq. (2.41) as follows:

From Table A.2, and . Therefore, the desired CI becomes

or