In the multiple regression of the previous question, the F-statistic for the overall significance of the model has an

Question

BlackTom AI · Accepted Answer

To evaluate the F-statistic for the overall significance of a multiple regression model, we need to know the degrees of freedom used in the F distribution.
Option a: 'a. F4,40F_{4,40} distribution under the null' implies there are 4 regressors being tested (df1 = 4) and 40 degrees of freedom for error (df2 = 40). If the model actually has 3 predictors plus an intercept, df1 would be 3, not 4, so this option misstates the numerator df.
Option b: 'b. F_{3,41} distribution under the null' uses df1 = 3 but df2 = 41. The df2 value should reflect the total sample size minus the number of estimated parameters (including the intercept). If there are 3 predictors and an intercept, and with n observations such that df2 = n − 3 − 1 = n − 4, 41 would require n = 45. Unless the sample size is exactly 45, this is inconsistent with the common setup.
Option c: 'c. F_{4,44} distribution under the null' has df1 = 4 and df2 = 44. This would correspond to 4 estimated parameters plus an intercept (i.e., 4 predictors) and n such that df2 = n − 4 − 1 = 44, which would give n = 49. If the model only has 3 predictors, this is not correct.
Option d: 'd. F_{3,40} distribution under the null' uses df1 = 3 and df2 = 40. This matches the typical case where the model has 3 predictors (k = 3) and the error degrees of freedom equal n − k − 1. If the sample size is n = 44, then df2 = 44 − 3 − 1 = 40, which is a standard configuration for a model with three regressors and an intercept.
Option e: 'e. F_{3,44} distribution under the null' would imply df2 = 44, which would require n = 48 (since df2 = n − k − 1 = n − 3 − 1). If the sample size is not 48, this would be inconsistent with the model’s degrees of freedom.
In summary, each option assigns a pair of degrees of freedom to the F-distribution that must align with the number of predictors in the model (k) and the total sample size (n) via df1 = k and df2 = n − k − 1. The most conventional and internally consistent pairing for a model with 3 predictors and a typical sample size that yields df2 = 40 is df1 = 3 and df2 = 40, i.e., F_{3,40}.
Thus, option d aligns with the standard formula df1 = number of regressors and df2 = n − k − 1 under the null hypothesis that all regression coefficients (except the intercept) are zero, while the other options either misstate the numerator degrees of freedom (df1) or require a sample size that does not fit the assumed model structure. In particular, misalignments such as df1 = 4 or df2 values that imply incompatible n values lead to incorrect characterizations of the F-statistic under the null.

In the multiple regression of the previous question, the F-statistic for the overall significance of the model has anSingle choice

Similar Questions

In a regression model involving 30 observations, the following estimated regression equation was obtained: For this model SSR = 700 and SSE = 100. The critical F value at 95% confidence is

In a regression model involving 30 observations, the following estimated regression equation was obtained: For this model SSR = 700 and SSE = 100. The computed F statistic for testing the significance of the above model is

________________ is used to test the hypothesis that the values of the regression parameters B1, B2, ... Bq are all zero.

When evaluating a new project, firms should include in the projected cash flows all of the following EXCEPT:

Provide the best rationale for what's wrong with supply chains today?

More Practical Tools for Students Powered by AI Study Helper

Homework AI Solver

Stylized AI Paper Writer

Plagiarism Checker Assistant

Citation AI Academic Writing Tool

In-Class Translation Assistant

AI Note Generator

AI Quiz Answers

Past Exam Questions from University Test Bank

Smart Practice Assistant

Adaptive Practice

Making Your Study Simpler