Question: STATISTICAL LEARNING - Chapter 2

[minirandom95]

Good morning,
can someone explain to me what does it mean?
and is there any materials that I can study beside this book? (I find it is pretty difficult for me to understand)
*I have watched several videos on Youtube however it seems that they only explain not for the whole chapter.
Thank you very much.

 

[BigBeachBanana]

Consider the following data set. You wish to predict commute time to work using windspeed and temperature.

Observation #	Windspeed (mph)	Temperature (F)	Commute Time (minutes)
1	9.0	77	20
2	10.3	89	60
3	8.3	60	30

Notice, there are 3 observations, so you have $i=1,2,3$. Whereas you have 2 predictors i.e. windspeed and temperature so you have $j=1,2$.

The value of $x_{11}=9.0$. The first observation, of the first variable (windspeed).
Another example, $x_{3,2}=60$ -- the third observation of the second variable (temperature), and so on...
More formally, we represent the dataset with a matrix.
$$X=\begin{pmatrix} x_{11}& x_{12}\\ x_{21}&x_{22} \\ x_{31}&x_{32}\end{pmatrix}=\begin{pmatrix} 9 & 77\\ 10.3 &89 \\ 8.3 & 60\end{pmatrix}$$$$Y=\begin{pmatrix} y_1\\ y_2\\ y_3\end{pmatrix} =\begin{pmatrix} 20\\ 60\\ 30\end{pmatrix}$$
More general, we extend the matrix for $i=1,2,3,..n$ and $j=1,2,3,...p$, where you have $n$ observations and $p$ predictors.