Читать книгу Introduction to Linear Regression Analysis - Douglas C. Montgomery - Страница 36

We will test for significance of regression in the model developed in Example 2.1 for the rocket propellant data. The fitted model is , SS_T = 1,693,737.60, and Sxy = −41,112.65. The regression sum of squares is computed from Eq. (2.34) as

The analysis of variance is summarized in Table 2.5. The computed value of F₀ is 165.21, and from Table A.4, F_0.01,1,18 = 8.29. The P value for this test is 1.66 × 10⁻¹⁰. Consequently, we reject H₀: β₁ = 0.

The Minitab output in Table 2.3 also presents the analysis-of-variance test significance of regression. Comparing Tables 2.3 and 2.5, we note that there are some slight differences between the manual calculations and those performed by computer for the sums of squares. This is due to rounding the manual calculations to two decimal places. The computed values of the test statistics essentially agree.