Using the Studentized residuals tᵢ to determine influential points in a multiple regression model with k independent variable and n observations and letting tn₋k₋₂ denote the upper critical value of a two-tail t test with a 0.10 level of significance, Xᵢ is an influential point if A) |tᵢ| tn₋k₋₁. C) |tᵢ| tn₋k₋₂.

Question

Using the Studentized residuals tᵢ to determine influential points in a multiple regression model with k independent variable and n observations and letting tn₋k₋₂ denote the upper critical value of a two-tail t test with a 0.10 level of significance, Xᵢ is an influential point if A) |tᵢ| < tn₋k₋₁. B) |tᵢ| > tn₋k₋₁. C) |tᵢ| < tn₋k₋₂. D) |tᵢ| > tn₋k₋₂.

Quizplus · Accepted Answer

According to the definition of influential point, an observation is considered influential if it significantly affects the estimates or predictions of the regression model. In multiple regression, one way to identify influential points is to use the Studentized residuals, which are the residuals divided by their estimated standard errors.

The Studentized residuals follow a t-distribution with n-k-1 degrees of freedom, where n is the sample size and k is the number of independent variables in the regression model. Therefore, we can compare the absolute value of each Studentized residual to a critical value from the t-distribution to determine if the point is influential.

The upper critical value of a two-tail t test with a 0.10 level of significance and n-k-1 degrees of freedom is denoted tn₋k₋₂. So, an observation Xᵢ is considered influential if |tᵢ| > tn₋k₋₂, which is choice D. Therefore, the correct answer is D.

Using the Studentized Residuals Tᵢ to Determine Influential Points in a Multiple