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Sum

Find the equation of the regression line of y on x, if the observations (x, y) are as follows :

(1,4),(2,8),(3,2),(4,12),(5,10),(6,14),(7,16),(8,6),(9,18)

Also, find the estimated value of y when x = 14.

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#### Solution

x |
y |
xy |

1 | 4 | 4 |

2 | 8 | 16 |

3 | 2 | 6 |

4 | 12 | 48 |

5 | 12 | 50 |

6 | 14 | 84 |

7 | 16 | 112 |

8 | 6 | 48 |

9 | 18 | 162 |

n = 9

Σx = 45

Σy = 90

x = 5 , y = 10

Σx^{2 }= 285

Σ_{xy} = 530

`b = b_xy = (Sigma_Xy - n bar x bary )/(Σx^2 n(bar x)`2)'

`= (530 - 9xx5xx10)/(285- 9 xx 25) = 80/60 = 4/3`

`= bary - barx`

`a = 10-4/3 xx 5`

`a =10/3`

Therefore the regression equation of y on x is y= a + bx

y = `10/3 + 4/3 x`

3y = 4x × 14 + 10

3y = 4 × 14 + 10

3y = 66

y = 22

Concept: Lines of Regression of X on Y and Y on X Or Equation of Line of Regression

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