I'm trying to understand how JMP centers polynomials. Here’s an example with two independent variables, x1 and x2, and a response variable y:

x1 | x2 | y |

2 | 12 | 80 |

4 | 14 | 85 |

6 | 16 | 90 |

8 | 18 | 95 |

10 | 20 | 100 |

12 | 22 | 105 |

When using the Analyze->Fit Model option in JMP with x1, x2, x1*x1, and x2*x2 (keeping the "Center Polynomials" checkbox checked), I get the following parameter estimates:

- **Intercept: 75.375**

- x1: 3.0714286

- x2: 0

- (x1-7)*(x1-7): -0.089286

- (x2-17)*(x2-17): 0

I wanted to test what happens if I center manually by subtracting the mean from each value of x1 and x2.

The mean of x1 is 7, and the mean of x2 is 17. So, for the x1 column, I subtracted 7 from each value (2, 4, 6, etc.). Here’s the resulting table:

x1 | x2 | y |

-5 | -5 | 80 |

-3 | -3 | 85 |

-1 | -1 | 90 |

1 | 1 | 95 |

3 | 3 | 100 |

5 | 5 | 105 |

Using these new centered values for x1 and x2 in the Fit Model option with "Center Polynomials" unchecked, I get the following parameter estimates:

- **Intercept: 96.875**

- x1: 3.0714286

- x2: 0

- (x1-7)*(x1-7): -0.089286

- (x2-17)*(x2-17): 0

As you can see, all parameter estimates are correct except for the intercept. Why is the intercept different? Could someone please explain how it is calculated?