Using the Cook's distance statistic Dᵢ to determine influential points in a multiple regression model with k independent variable and n observations and letting Fᵥ₁ᵥ₂ denote the critical value of an F distribution with v₁ and v₂ degrees of freedom at a 0.50 level of significance, Xᵢ is an influential point if A) Dᵢ Fk₊₁,n₋k₋₁. C) Dᵢ Fn₋k₋₁, k₊₁.

Question

Using the Cook's distance statistic Dᵢ to determine influential points in a multiple regression model with k independent variable and n observations and letting Fᵥ₁ᵥ₂ denote the critical value of an F distribution with v₁ and v₂ degrees of freedom at a 0.50 level of significance, Xᵢ is an influential point if A) Dᵢ < Fk₊₁,n₋k₋₁. B) Dᵢ > Fk₊₁,n₋k₋₁. C) Dᵢ < Fn₋k₋₁, k₊₁. D) Dᵢ > Fn₋k₋₁, k₊₁.

Quizplus · Accepted Answer

Cook's distance measures the influence of each observation on the regression coefficients, and points with high Cook's distance are considered to be influential. The critical value for Cook's distance depends on the number of independent variables and the sample size, and can be approximated by an F distribution. Specifically, an observation is considered influential if its Cook's distance is greater than the critical value of an F distribution with k+1 and n-k-1 degrees of freedom at a 0.5 level of significance. Therefore, the correct choice is B, since Dᵢ > Fk₊₁,n₋k₋₁ indicates that observation i is influential. Choices A, C, and D are incorrect, either because they use the wrong F distribution or because they have the wrong sign.

Using the Cook's Distance Statistic Dᵢ to Determine Influential Points