## 1.1 Visualization

The first 5 rows of `dat_recs`

can be visualized:

y | x2 | x3 | x4 | x5 | x6 | x7 | x8 |
---|---|---|---|---|---|---|---|

7.540 | 5 | 3 | 8 | 1 | 39 | 5 | 15 |

8.193 | 1 | 2 | 2 | 0 | 85 | 5 | 14 |

8.678 | 3 | 1 | 1 | 0 | 71 | 5 | 8 |

7.846 | 4 | 3 | 5 | 1 | 39 | 5 | 8 |

9.755 | 1 | 3 | 3 | 0 | 57 | 0 | 10 |

### 1.1.1 Box Plot

For each level of `x2`

a box indicating three quantiles (25%, 50%, 75%) of `y`

is given. It shows that there is a tendency for `y`

to decrease with `x2`

by looking at the median. The sizes of different boxes seem to vary with different values of `x2`

. Besides, there are many observations when `x2`

is small. But it is assumed for now that the conditional variance is constant, which will be tested section 4. Three dat_recsa points with extreme values `36`

, `241`

and `163`

is discussed in sections 3 and 5.

The box plot of `y`

by `x6`

is given. It can be seen that the tendency is not strictly linear and the condition variance is not stable. So we will regress `y`

on `x2`

first and use `x6`

as the second regressor in section 6.