Question:
Given the assumptions of the classical linear regression model, the ordinary least square estimators possess some optimum properties-given in the Gauss-Markov theorem. Which of the following is not a part of this theorem?
Given the assumptions of the classical linear regression model, the ordinary least square estimators possess some optimum properties-given in the Gauss-Markov theorem. Which of the following is not a part of this theorem?
Updated On: June 02, 2025
- The slope estimator \(\hat{\beta}_2\) is a linear function of random variables
- The expected value of \(\hat{\beta}_2\) is equal to zero
- No linear unbiased estimator has lower variance than that of \(\hat{\beta}_2\)
- The estimator \(\hat{\beta}_2\) is an unbiased estimator of \(\hat{\beta}_2\)
Hide Solution
Verified By Collegedunia
The Correct Option is B
Solution and Explanation
The correct answer is (B) : The expected value of \(\hat{\beta}_2\) is equal to zero.
Was this answer helpful?
0
0
Top Questions on Linear regression
The annual profit of a company depends on its annual marketing expenditure. The information of the preceding 3 years' annual profit and marketing expenditure is given in the table. Based on linear regression, the estimated profit (in units) of the 4th year at a marketing expenditure of 5 units is ............ (Rounded off to two decimal places)
- GATE PI - 2025
- Engineering Mathematics
- Linear regression
- Consider a two-variables (x, y) linear regression model
\[ y = \alpha + \beta x + \epsilon \] where x and y are the parameters, and \( \epsilon \) is the error term. The parameters are estimated using the Ordinary Least Squares (OLS) method. Let \( \hat{\beta} \) denote the estimated value of \( \beta \). If \( \hat{\beta} = 0 \), then which one of the following statements is CORRECT?- GATE XH-C1 - 2025
- Mathematics for Economy
- Linear regression
- In a linear regression, a line of best fit can be obtained by
- GATE EY - 2025
- Mathematics
- Linear regression
Let \[ A = \begin{bmatrix} 1 & 1 & 1 \\ 1 & 3 & 1 \\ -2 & -3 & -3 \end{bmatrix}, \quad b = \begin{bmatrix} b_1 \\ b_2 \\ b_3 \end{bmatrix}. \] For \( Ax = b \) to be solvable, which one of the following options is the correct condition on \( b_1, b_2, \) and \( b_3 \)?
- GATE CE - 2025
- Mathematics
- Linear regression
- Line of Regression of y on x
- AP PGECET - 2024
- Engineering Mathematics
- Linear regression
View More Questions
Questions Asked in CUET PG exam
- What is the one-word synonym for connotation?
- CUET (PG) - 2025
- Synonyms
- What is the antonym of eradicate?
- CUET (PG) - 2025
- Antonyms
- Who was the first Secretary-General of the UN?
- CUET (PG) - 2025
- United Nations and its Organizations
- What is the correct verb form: He, as well as his friends, ?
- Which preposition is correct: Chanakya lived ?
- CUET (PG) - 2025
- Prepositions
View More Questions
