Civil Engineering (CE) Exam > Civil Engineering (CE) Questions > The parameter E which we use for least square...
Start Learning for Free
The parameter E which we use for least square method is called as ______
- a)Sum of residues
- b)Residues
- c)Error
- d)Sum of errors
Correct answer is option 'A'. Can you explain this answer?
Most Upvoted Answer
The parameter E which we use for least square method is called as ____...
E is given by
E = Σdi2 = Σ(yi – f(xi))2.
Where the term inside the summation is called as residues and the sum is said to be a sum of residues. Therefore, E is said to be the sum of residues.
E = Σdi2 = Σ(yi – f(xi))2.
Where the term inside the summation is called as residues and the sum is said to be a sum of residues. Therefore, E is said to be the sum of residues.
Free Test
FREE
| Start Free Test |
Community Answer
The parameter E which we use for least square method is called as ____...
Understanding the Least Squares Method
The least squares method is a statistical technique used to minimize the sum of the squares of the residuals, which are the differences between observed and predicted values. In this context, the parameter \( E \) is crucial.
Definition of Residues
- **Residues** are defined as the differences between the observed values (\( y_i \)) and the values predicted by the model (\( \hat{y}_i \)).
- Mathematically, it is expressed as:
\[
r_i = y_i - \hat{y}_i
\]
Sum of Residues
- The term **Sum of Residues** refers to the cumulative sum of these individual residues. However, in least squares, we are concerned with the square of these residues.
Why Option 'A' is Correct
- The parameter \( E \) specifically represents the **Sum of Squares of Residues**, which is calculated as:
\[
E = \sum_{i=1}^{n} (y_i - \hat{y}_i)^2
\]
- This minimization of \( E \) leads to the best-fitting line or curve for the given data points.
Importance in Civil Engineering
- In civil engineering, accurate predictions and models are essential for design and analysis. The least squares method provides a robust way to achieve these predictions by minimizing the discrepancies between observed and predicted values.
Conclusion
- Therefore, the correct answer is option 'A', as it accurately denotes the **Sum of Residues**, which is central to the least squares method.
The least squares method is a statistical technique used to minimize the sum of the squares of the residuals, which are the differences between observed and predicted values. In this context, the parameter \( E \) is crucial.
Definition of Residues
- **Residues** are defined as the differences between the observed values (\( y_i \)) and the values predicted by the model (\( \hat{y}_i \)).
- Mathematically, it is expressed as:
\[
r_i = y_i - \hat{y}_i
\]
Sum of Residues
- The term **Sum of Residues** refers to the cumulative sum of these individual residues. However, in least squares, we are concerned with the square of these residues.
Why Option 'A' is Correct
- The parameter \( E \) specifically represents the **Sum of Squares of Residues**, which is calculated as:
\[
E = \sum_{i=1}^{n} (y_i - \hat{y}_i)^2
\]
- This minimization of \( E \) leads to the best-fitting line or curve for the given data points.
Importance in Civil Engineering
- In civil engineering, accurate predictions and models are essential for design and analysis. The least squares method provides a robust way to achieve these predictions by minimizing the discrepancies between observed and predicted values.
Conclusion
- Therefore, the correct answer is option 'A', as it accurately denotes the **Sum of Residues**, which is central to the least squares method.
|
Explore Courses for Civil Engineering (CE) exam
|
|
Similar Civil Engineering (CE) Doubts
Top Courses for Civil Engineering (CE)View all
The parameter E which we use for least square method is called as ______a)Sum of residuesb)Residuesc)Errord)Sum of errorsCorrect answer is option 'A'. Can you explain this answer?
Question Description
The parameter E which we use for least square method is called as ______a)Sum of residuesb)Residuesc)Errord)Sum of errorsCorrect answer is option 'A'. Can you explain this answer? for Civil Engineering (CE) 2025 is part of Civil Engineering (CE) preparation. The Question and answers have been prepared according to the Civil Engineering (CE) exam syllabus. Information about The parameter E which we use for least square method is called as ______a)Sum of residuesb)Residuesc)Errord)Sum of errorsCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for Civil Engineering (CE) 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The parameter E which we use for least square method is called as ______a)Sum of residuesb)Residuesc)Errord)Sum of errorsCorrect answer is option 'A'. Can you explain this answer?.
The parameter E which we use for least square method is called as ______a)Sum of residuesb)Residuesc)Errord)Sum of errorsCorrect answer is option 'A'. Can you explain this answer? for Civil Engineering (CE) 2025 is part of Civil Engineering (CE) preparation. The Question and answers have been prepared according to the Civil Engineering (CE) exam syllabus. Information about The parameter E which we use for least square method is called as ______a)Sum of residuesb)Residuesc)Errord)Sum of errorsCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for Civil Engineering (CE) 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The parameter E which we use for least square method is called as ______a)Sum of residuesb)Residuesc)Errord)Sum of errorsCorrect answer is option 'A'. Can you explain this answer?.
Solutions for The parameter E which we use for least square method is called as ______a)Sum of residuesb)Residuesc)Errord)Sum of errorsCorrect answer is option 'A'. Can you explain this answer? in English & in Hindi are available as part of our courses for Civil Engineering (CE).
Download more important topics, notes, lectures and mock test series for Civil Engineering (CE) Exam by signing up for free.
Here you can find the meaning of The parameter E which we use for least square method is called as ______a)Sum of residuesb)Residuesc)Errord)Sum of errorsCorrect answer is option 'A'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
The parameter E which we use for least square method is called as ______a)Sum of residuesb)Residuesc)Errord)Sum of errorsCorrect answer is option 'A'. Can you explain this answer?, a detailed solution for The parameter E which we use for least square method is called as ______a)Sum of residuesb)Residuesc)Errord)Sum of errorsCorrect answer is option 'A'. Can you explain this answer? has been provided alongside types of The parameter E which we use for least square method is called as ______a)Sum of residuesb)Residuesc)Errord)Sum of errorsCorrect answer is option 'A'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice The parameter E which we use for least square method is called as ______a)Sum of residuesb)Residuesc)Errord)Sum of errorsCorrect answer is option 'A'. Can you explain this answer? tests, examples and also practice Civil Engineering (CE) tests.
|
|
Explore Courses for Civil Engineering (CE) exam
|
|
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
|
© EduRev
|
Education Revolution
|
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup