For 4 data points of two correlated variables x and y, it is given that

∑ x = 24, ∑ y = 11, ∑ x2 = 202, ∑ xy = 84, ∑ y2 = 39

Fit a least squares line to this data using x as independent variable.

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DSSSB TGT Maths Male Subject Concerned - 23 Sep 2018 Shift 2
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  1. y=1116(36+103x)
  2. x=1116(36+103y)
  3. x=1116(103+36y)
  4. y=1116(103+36x)

Answer (Detailed Solution Below)

Option 4 : y=1116(103+36x)
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Detailed Solution

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Concept:

To solve this type of problems we need to follow several steps:

1) Calculate the slope m:

m=N(xy)xyN(x2)(x)2

N is the number of points. 

2) Calculate the intercept b:

b=ymxN

3) The equation of the line is: y = mx + b

Given:

∑ x = 24, ∑ y = 11, ∑ x2 = 202, ∑ xy = 84, ∑ y2 = 39 

and N = 4

Analysis:

m=N(xy)xyN(x2)(x)2

m=(4×84)(24×11)(4×202)(24)2

m = 72/232

Now, 

b=ymxN

b=1124 m4

b=11(72×24)2324

b=824232×4

The equation of the line is:

y=72232x + 8244×232

y=1116(103+36x)

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