Compute the appropriate regression equation for the following data: x (Dependent Variable) 10 12 13 17 18 y (Independent Variable) 5 6 7 9 13 - Mathematics and Statistics

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Compute the appropriate regression equation for the following data:

x (Dependent Variable) 10 12 13 17 18
y (Independent Variable) 5 6 7 9 13
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Solution

  X = xi Y = yi xi2 yi2 xiyi
  10 5 100 25 50
  12 6 144 36 72
  13 7 169 49 91
  17 9 289 81 153
  18 13 324 169 234
Total 70 40 1026 360 600

From the table, we have,

n = 5, Σxi = 70, Σyi = 40, Σxiyi = 600, Σxi2 = 1026, Σyi2 = 360

`barx = (sumx_"i")/"n" = 70/5` = 14, `bary = (sumy_"i")/"n" = 40/5` = 8

Now, for regression equation of X on Y

bxy = `(sumx_"i"y_"i" - "n"bar(x)  bar(y))/(sumy_"i"^2 - "n" bar(y)^(-2))`

= `(600 - 5 xx 14 xx 8)/(360 - 5(8)^2)`

= `(600 - 560)/(360 - 320)`

= `40/40`

= 1

Also, a' = `barx - "b"_(xy)  bary` = 14 – 1 (8)

= 14 – 8

= 6

∴ The regression equation of X on Y is

X = a' + bxy Y

∴ X = 6 + Y

Concept: Types of Linear Regression
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Chapter 2.3: Linear Regression - Q.4

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