Question

(By Hand) For the dependent variable Y and the independent variables X1 and X2, the linear regression model is given by: Y=0.08059*X1-0.16109*X2+5.26570. Complete the following table:

Actual Y |
X1 |
X2 |
Predicted Y |
Prediction Error |

6 |
6.8 |
4.7 |
||

3.1 |
5.3 |
5.5 |
||

5.8 |
4.5 |
6.2 |
||

4.5 |
8.8 |
7 |
||

4.5 |
6.8 |
6.1 |
||

3.7 |
8.5 |
5.1 |
||

5.4 |
8.9 |
4.8 |
||

5.1 |
6.9 |
5.4 |
||

5.8 |
9.3 |
5.9 |
||

5.7 |
8.4 |
5.4 |
||

Answer #1

For each of X1, X2 value ,

Predicted : Y = =0.08059*X1-0.16109*X2+5.26570.

And

Prediction error = Actual Y - Predicted Y

Actual Y | X1 | X2 | Predicted Y: | Predicted Y | Prediction Error | Prediction Error |

6 | 6.8 | 4.7 | =0.08059*6.8 - 0.16109*4.7 + 5.262570 = 5.056589 | 5.056589 | = 6 - 5.056589 = 0.943411 | 0.943411 |

3.1 | 5.3 | 5.5 | =0.08059*5.3 - 0.16109*5.5 + 5.262570 = 4.806832 | 4.806832 | = 3.1 - 4.806832 = -1.706832 | -1.706832 |

5.8 | 4.5 | 6.2 | =0.08059*4.5 - 0.16109*6.2 + 5.262570 = 4.629597 | 4.629597 | = 5.8 - 4.629597 = 1.170403 | 1.170403 |

4.5 | 8.8 | 7 | =0.08059*8.8 - 0.16109*7 + 5.262570 = 4.847262 | 4.847262 | = 4.5 - 4.847262 = -0.347262 | -0.347262 |

4.5 | 6.8 | 6.1 | =0.08059*6.8 - 0.16109*6.1 + 5.262570 = 4.831063 | 4.831063 | = 4.5 - 4.831063 = -0.331063 | -0.331063 |

3.7 | 8.5 | 5.1 | =0.08059*8.5 - 0.16109*5.1 + 5.262570 = 5.129156 | 5.129156 | = 3.7 - 5.129156 = -1.429156 | -1.429156 |

5.4 | 8.9 | 4.8 | =0.08059*8.9 - 0.16109*4.8 + 5.262570 = 5.209719 | 5.209719 | = 5.4 - 5.209719 = 0.190281 | 0.190281 |

5.1 | 6.9 | 5.4 | =0.08059*6.9 - 0.16109*5.4 + 5.262570 = 4.951885 | 4.951885 | = 5.1 - 4.951885 = 0.148115 | 0.148115 |

5.8 | 9.3 | 5.9 | =0.08059*9.3 - 0.16109*5.9 + 5.262570 = 5.064756 | 5.064756 | = 5.8 - 5.064756 = 0.735244 | 0.735244 |

5.7 | 8.4 | 5.4 | =0.08059*8.4 - 0.16109*5.4 + 5.262570 = 5.07277 | 5.07277 | = 5.7 - 5.07277 = 0.62723 | 0.62723 |

Actual Y | X1 | X2 | Predicted Y | Prediction Error |

6 | 6.8 | 4.7 | 5.056589 | 0.943411 |

3.1 | 5.3 | 5.5 | 4.806832 | -1.706832 |

5.8 | 4.5 | 6.2 | 4.629597 | 1.170403 |

4.5 | 8.8 | 7 | 4.847262 | -0.347262 |

4.5 | 6.8 | 6.1 | 4.831063 | -0.331063 |

3.7 | 8.5 | 5.1 | 5.129156 | -1.429156 |

5.4 | 8.9 | 4.8 | 5.209719 | 0.190281 |

5.1 | 6.9 | 5.4 | 4.951885 | 0.148115 |

5.8 | 9.3 | 5.9 | 5.064756 | 0.735244 |

5.7 | 8.4 | 5.4 | 5.07277 | 0.62723 |

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