Mathematics · Probability and Statistics
An analyst fits a multiple linear regression model Yi = β0 + β1 X1i + ... + β4 X4i + εi, i = 1, 2, ..., n, using the method of least squares. However, his coordinator insists that the intercept and two regressors Z1 = X1 + X3 and Z2 = X2 - X4 are enough to represent the model. Suppose the coordinator's claim can be tested in the form of a general linear hypothesis H0: LTβ = 0 against HA: H0 is not true, where βT = (β0, β1, ..., β4). Suppose we have n observations on the response Y and each regressor. Assuming standard normal errors, which of the following statements is true?
Verified Solution4 OptionsUpdated: October 2026👁️1 View
Share:
- 1Sum of squares residuals without the restrictions LTβ = 0 follows a non-central σ2χ2n-4 distribution
- 2Sum of squares residuals under the restrictions LTβ = 0 follows σ2χ2n-3 distribution
- 3The test statistic for testing H0 against HA follows an F-distribution with (2, n-4) degrees of freedom under H0
- 4A possible choice of LT is [β1 - β3, β2 + β4]expressed in matrix form as LT = 010-1000101✓
Correct answer
A possible choice of LT is [β1 - β3, β2 + β4]expressed in matrix form as LT = 010-1000101
Download Single Question PDF
Save this question and verified answer as a clean study sheet with live clickable link.
👥
Share with Friends & Study Groups
Challenge your peer aspirants on WhatsApp or Telegram to solve this question!
Online Test Series
Start Free Mock Test →Preparing for Mathematics?
Practice full-length mock tests with real exam timers, instant score analysis, and all-India ranking.
Chapter Practice
Practice Probability and Statistics MCQs →Want more practice questions on Probability and Statistics?
Solve complete topic-wise tests with detailed solutions on GkGet.
Related Practice Questions
Recommended practice questions in Mathematics · Probability and Statistics