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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. GivenΣx = 6, Σy = 21, Σx2 = 14 and Σxy = 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?
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Three values of x and y are to be fitted in a straight line in the for...
Given:
Three values of x and y are given: x = 6, y = 21, x^2 = 14, and xy = 46.

Objective:
We need to find the values of a and b in the equation y = a + bx using the method of least squares.

Solution:
The equation of a straight line in the form y = a + bx can be written as:

y = a + bx

To find the values of a and b, we need to solve the following equations:

∑y = na + b∑x
∑xy = a∑x + b∑x^2

Here, n is the number of data points, which is 3 in this case.

Step 1: Calculate the required values:

∑y = 21 + 21 + 21 = 63
∑x = 6 + 6 + 6 = 18
∑x^2 = 14 + 14 + 14 = 42
∑xy = 46 + 46 + 46 = 138

Step 2: Substitute the values into the equations:

63 = 3a + 18b (Equation 1)
138 = 18a + 42b (Equation 2)

Step 3: Solve the equations simultaneously:

Multiply Equation 1 by 6 and Equation 2 by 3 to make the coefficients of 'a' equal:

378 = 18a + 108b (Equation 3)
414 = 54a + 126b (Equation 4)

Subtract Equation 3 from Equation 4:

414 - 378 = 54a + 126b - 18a - 108b
36 = 36a + 18b

Divide the equation by 18:

2 = 2a + b (Equation 5)

Step 4: Solve Equation 5 for 'a' in terms of 'b':

a = (2 - b)/2

Step 5: Substitute the value of 'a' in terms of 'b' into Equation 1:

63 = 3((2 - b)/2) + 18b

Simplify the equation:

63 = 3(2 - b) + 18b
63 = 6 - 3b + 18b
63 = 6 + 15b
57 = 15b
b = 57/15
b = 3.8

Step 6: Substitute the value of 'b' into Equation 5 to find 'a':

a = (2 - 3.8)/2
a = -1.8/2
a = -0.9

Therefore, the values of a and b are -0.9 and 3.8, respectively.

Conclusion:
The values of a and b in the equation y = a + bx are -0.9 and 3.8, respectively. Therefore, the correct answer is option 'D' (a = -0.9 and b = 3.8).
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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. GivenΣx = 6, Σy = 21, Σx2 = 14 and Σxy = 46, the values of a and b are respectively. a)2 and 3 b)1 and 2 c)2 and 1 d)3 and 2Correct answer is option 'D'. Can you explain this answer?
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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. GivenΣx = 6, Σy = 21, Σx2 = 14 and Σxy = 46, the values of a and b are respectively. a)2 and 3 b)1 and 2 c)2 and 1 d)3 and 2Correct answer is option 'D'. Can you explain this answer? for Mechanical Engineering 2025 is part of Mechanical Engineering preparation. The Question and answers have been prepared according to the Mechanical Engineering exam syllabus. Information about 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. GivenΣx = 6, Σy = 21, Σx2 = 14 and Σxy = 46, the values of a and b are respectively. a)2 and 3 b)1 and 2 c)2 and 1 d)3 and 2Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for Mechanical Engineering 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for 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. GivenΣx = 6, Σy = 21, Σx2 = 14 and Σxy = 46, the values of a and b are respectively. a)2 and 3 b)1 and 2 c)2 and 1 d)3 and 2Correct answer is option 'D'. Can you explain this answer?.
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