The following data give the height in inches (X) and the weight in lb. (Y) of a random sample of 10 students from a large group of students of age 17 years:

X |
61 | 68 | 68 | 64 | 65 | 70 | 63 | 62 | 64 | 67 |

Y |
112 | 123 | 130 | 115 | 110 | 125 | 100 | 113 | 116 | 125 |

Estimate weight of the student of a height 69 inches.

#### Solution

Height(X) |
Weight(Y) |
dx = X − 65 |
dy = Y − 117 |
dx^{2} |
dy^{2} |
dxdy |

61 | 112 | − 4 | − 5 | 16 | 25 | 20 |

68 | 123 | 3 | 6 | 9 | 36 | 18 |

68 | 130 | 3 | 13 | 9 | 169 | 39 |

64 | 115 | − 1 | − 2 | 1 | 4 | 2 |

65 | 110 | 0 | − 7 | 0 | 49 | 0 |

70 | 125 | 5 | 8 | 25 | 64 | 40 |

63 | 100 | − 2 | − 17 | 4 | 289 | 34 |

62 | 113 | − 3 | − 4 | 9 | 16 | 12 |

64 | 116 | − 1 | − 1 | 1 | 1 | 1 |

67 | 125 | 2 | 8 | 4 | 64 | 16 |

652 |
1169 |
2 |
− 1 |
78 |
717 |
182 |

N = 10, ∑X = 652, ∑Y = 1169, ∑dx = 2, ∑dy = − 1, ∑dx^{2} = 78, ∑dy^{2} = 717, ∑dxdy = 182, `bar"X" = 652/10` = 65.2, `bar"Y" = 1169/10` = 116.9

b_{yx} = `("N"sum"dxdy" - (sum"dx")(sum"dy"))/("N"sum"dx"^2 - (sum"dx")^2)`

= `(10(182) - (2)(-1))/(10(78) - (2)^2)`

= `1822/776`

= 2.3479

Regression equation of Y on X

`"Y" - bar"Y" = "b"_"yx"("X" - bar"X")`

Y – 117 = 2.3479 (X – 65.2)

Y – 117 = 2.3479X – (2.3479)(65.2)

Y = 2.3479X – 153.08308 + 117

Y = 2.3479 – 36.08308

When the height X = 69 inches

Weight, Y = 2.3479(69) – 36.08308

= 162.0051 – 36.08308

= 125.92202

= 125.92 lb