LINEAR MODEL

The matrix notation can be: y = Xb + e => y = + ?_i + ?_j + e_ij

_{Where X = Matrix of Xij}

Get me the matrix X and it is all i need

the matrix will get the format : | Xij1 Xij2 Xij3 Xij4 | | | | e111 |

Y = | - ---- ------------------------------ --| | ?₁ | + | e112 |

| | | ?₂ | | e122 |

| | | ?₁ | | e211 |

| ?₂ | | ' |

| e22 |

Where X = | Xij1 Xij2 Xij3 Xij4 |

|-----------------------------------------|

| |

| |

| y112 |

Y = | y122 |

| y211 |

| ' |

| y22 |

Question 4 Consider the symbolic data below from a 2 factor factorial experiment with two observations per combination of the factor levels Factor 2 Factor ] 2 Vill, V1 12 V121, V122 )211, '212 )'221, )/222 (a) Write down the linear model for the data in terms of the main effects of Factor I (a, ) and Factor 2 (B, ), and the errors (E.,) 1 if observation is from level I of Factor 1 X71 = 0 otherwise 1 If observation is from level 2 of Factor I X712 = 0 otherwise I if observation is from level 1 of Factor 2 X13 = 0 otherwise I if observation is from level 2 of Factor 2 ) otherwise Rewrite the model in part (a) as a multiple regression on the above dummy (0,1) explanatory/independent variables