Question: Please do not just copy someone else's answer. They are incorrect and not complete. What is the predictive density of a new observation at the
Please do not just copy someone else's answer. They are incorrect and not complete.

What is the predictive density of a new observation at the predictor vector x = (1,0.12.0.56)?
| y | x1 | x2 | x3 |
| -1.47196 | 1 | -0.62645 | -0.38342 |
| 4.585642 | 1 | 1.595281 | 1.215549 |
| 3.113337 | 1 | 0.487429 | 0.562698 |
| 1.018829 | 1 | -0.30539 | 0.239762 |
| -0.21683 | 1 | -0.62124 | -1.09928 |
| 1.817658 | 1 | -0.04493 | -0.03631 |
| 4.314445 | 1 | 0.821221 | 0.753025 |
| 1.144786 | 1 | 0.782136 | 0.569865 |
| 2.500895 | 1 | 0.619826 | 0.417039 |
| -2.69653 | 1 | -1.47075 | -1.17297 |
| 5.02527 | 1 | 1.35868 | 0.920239 |
| 0.026614 | 1 | -0.05381 | -0.45078 |
| 1.017648 | 1 | -0.39429 | -0.2938 |
| 2.757856 | 1 | 0.763176 | 0.484866 |
| 2.360044 | 1 | 0.696963 | 0.654873 |
| -0.03233 | 1 | -0.7075 | -0.38587 |
| 1.359103 | 1 | -0.11235 | 0.18569 |
| -1.6795 | 1 | -0.61203 | -0.32608 |
| 5.096062 | 1 | 1.433024 | 1.597237 |
| -1.7833 | 1 | -1.04413 | -0.55998 |
| 8.162335 | 1 | 2.401618 | 1.66936 |
| 1.041416 | 1 | 0.028002 | -0.20338 |
| -3.28047 | 1 | -1.80496 | -0.8238 |
| 6.298758 | 1 | 2.172612 | 1.663481 |
| 1.115098 | 1 | 0.610726 | 0.147279 |
| 1.655023 | 1 | 0.291446 | 0.071025 |
| 0.455197 | 1 | 0.074341 | -0.12482 |
| -0.53512 | 1 | -0.13518 | 0.258801 |
| 3.76664 | 1 | 0.593946 | 0.515647 |
| 0.556808 | 1 | -0.30418 | -0.10192 |
y = XB + 0, assuming o = 1 is known, and 3 has a multivariate normal prior with mean 0 and covariance matrix 100(X'X)-. y = XB + 0, assuming o = 1 is known, and 3 has a multivariate normal prior with mean 0 and covariance matrix 100(X'X)
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