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Three values of x and y are to be fitted in a straight line in the form y = a + bx by the method of least squares. Given : N=3, ∑x = 6, ∑y = 21, ∑x2 = 14 and ∑xy = 46, the values of a and b are respectively.
  • a)
    2 and 3
  • b)
    1 and 2
  • c)
    2 and 1
  • d)
    3 and 2
Correct answer is option 'D'. Can you explain this answer?
Verified Answer
Three values of x and y are to be fitted in a straight line in the fo...
Given,
N = 3, ∑x = 6, ∑y = 21, ∑x2 = 14 and ∑xy = 46
There are two normal equations to evaluate a and b of the equation
y = a + bx
∑y = Na + b∑x …(i)
and ∑xy = a∑x + b∑x2 …(ii)
From Eq. (i), 21 = 3a + 6b …(iii)
From Eq. (ii) 46 = 6a + 14b
⇒ 23 = 3a + 7b …(iv)
Now, Eq. (iv) – Eq. (iii),
3a + 7b = 23
3a + 6b = 21
- - -
b = 2
From Eq. (iii), 3a = 21 – 12
3a = 9 ⇒ a = 3
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Most Upvoted Answer
Three values of x and y are to be fitted in a straight line in the fo...
Given Data:
- N = 3
- Σx = 6
- Σy = 21
- Σx² = 14
- Σxy = 46

Finding the values of a and b:
1. Finding b:
- Using the formula for b:
b = (NΣxy - ΣxΣy) / (NΣx² - (Σx)²)
- Substituting the given values:
b = (3(46) - 6(21)) / (3(14) - 6²)
b = (138 - 126) / (42 - 36)
b = 12 / 6
b = 2
2. Finding a:
- Using the formula for a:
a = (Σy - bΣx) / N
- Substituting the given values and the calculated value of b:
a = (21 - 2(6)) / 3
a = (21 - 12) / 3
a = 9 / 3
a = 3
Therefore, the values of a and b are 3 and 2 respectively. Hence, the correct answer is option 'D' (3 and 2).
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Three values of x and y are to be fitted in a straight line in the form y = a + bx by the method of least squares. Given : N=3, ∑x = 6, ∑y = 21, ∑x2 = 14 and ∑xy = 46, the values of a and b are respectively.a)2 and 3b)1 and 2c)2 and 1d)3 and 2Correct answer is option 'D'. Can you explain this answer?
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