IGNOU MST 2 2015 - | IGNOU Academy

Question

Image ignouacademy-com--p-ignou-29739

24 Nov 2017

Answer :

Word Count : 486

Alright, let's go step-by-step. --- ## 1. Understanding the least squares method The method of least squares for fitting \( Y = a + bX \) minimizes the sum of squared errors: \[ S = \sum_{i=1}^{n} (Y_i - (a + b X_i))^2 \] Differentiate \( S \) w.r.t \( a \) and \( b \), set to zero: We get normal equations: \[ \sum Y = na + b \sum X \] \[ \sum XY = a \sum X + b \sum X^2 \] Solve these to find \( a \) and \( b \). --- ## 2. Given data \( X: 1, 3, 5, 7, 9, 10 \) \( Y: 5, 8, 12, 15, 18, 22 \) Number of points \( n = 6 \). --- ## 3. Compute sums \[ \sum X = 1 + 3 + 5 + 7 + 9 + 10 = 35 \] \[ \sum Y = 5 + 8 + 12 + 15 + 18 + 22 = 80 \] \[ \sum XY = (1\cdot 5) + (3\cdot 8) + (5\cdot 12) + (7\cdot 15) + (9\cdot 18) + (10\cdot 22) \] \[

_______ ________ __________ ___ __________ __________ ____ __________ ______ ______ ____ __________.
_____ _______ _____ _______ ______ ____ ________ _________ ______ ___.
________ __________ ___ _______ ____ _________ ______ ______ _____ _______.
____ ______ ________ ___ _______ ___ ________ ______ ______.
_____ _________ _________ ______ _____ ____ _________ ___ _______ ________ ___ __________.
____ _____ _______ ____ __________ ____ _______.
___ _________ _____ __________ ______ ______ __________ __________.
___ ____ _______ ___ ____ __________ ________ ___ ____ ___ _____.
___ ___ __________ ________ __________ _______ _____ ________ _________ ____.
___ ______ __________ ___ ________.
_______ __________ _______ ____ _______ ____.
_________ ______ ______ _________ __________ ____ ____ _______ ______ ___ ______ ____.
_______ _______ ____ _____ _________ _________ ___ ____.
________ _________ ____ _______ _______ _________ ___.
_________ ________ ____ ________ ___ _________ _____ _____ ______ ________.
_______ ____ ________ _______ _____ ______ ___ ___.
________ ___ ________ ______ ____ _____.
__________ ____ ________ _______ ___ ________ __________ ______ _____.
__________ __________ ___ ____ _________ _________ ______ __________ _________ ____.
______ ________ _______ ________ _____ _______ ________.
______ ________ ___ __________ ____ __________ _____ ______ _______.
______ _______ ___ _______ ______ _____ __________ ___ ________.
___ _______ _______ ________ ________ _____ _______ _______ __________ ________ _____ _______.
__________ ________ ________ ___ ______ _________ _________ _______.
_____ __________ _______ ____ ___ ______ ____ ___ __________ _________ _________.
_______ _________ __________ _______ __________ _______ _____ _________ ___ ________ ____.
_______ __________ ______ ______ _____ ____ ______ __________ _____.
_______ _______ ________ _________ ____ __________ ____ ____ _______ _________ _____ ________.
_____ ______ _______ ____ ____ ____ _____ _____.
_________ _________ __________ __________ __________ ____.
___ ___ ____ _____ _______ _____ ______ __________ _________.
______ ______ __________ _________ _________ _____ _____ ____ __________ __________ ________.
___ __________ ___ _________.

IGNOU ACADEMY

Your IGNOU journey, made easier.

Solved Assignments
Study Notes
Guess Papers
Question Papers

Call Us WhatsApp

STUDY • PREPARE • SUCCEED

Skip in 10

Marks	1	2	3	4	5	6	7	8	9	10
Mathematics	40	46	42	30	35	28	39	43	25	45
Statistics	35	41	36	32	42	48	29	38	28	40

Class	0-10	10-20	20-30	30-40	40-50
Frequency	05	15	30	12	08

Marks:	2.7- 7.5	7.5- 12.5	12.5- 17.5	17.5- 22.5	22.5- 27.5	27.5- 32.5	32.5- 37.5
Frequency:	06	13	23	39	19	15	05

Marks	1	2	3	4	5	6	7	8
Mathematics	76	80	85	80	78	65	85	80
Physics	91	78	82	78	86	80	88	92

X₁	10	20	30	40	50
X₂	20	30	40	50	60
X₃	30	40	50	60	70