### 1. Main problem

Sometimes you have a huge amount of variables. So, to make your data profitable you need to reduce number of variables saving without losing the precious information.

- Principal component analysis (PCA)
- Linear discriminant analysis (LDA)
- Multidimensional scaling (MDS)
- â€¦

### 2. Data

I will use a dataset from [Huttenlocher, Vasilyeva, Cymerman, Levine 2002]. Authors analysed 46 pairs of mothers and children (aged from 47 to 59 months, mean age â€“ 54). They recorded and trinscribed 2 hours from each child per day. During the study they collected number of noun phrases per utterance in mother speech to the number of noun phrases per utterance in child speech.

### 3. PCA

PCA is essentially a rotation of the coordinate axes, chosen such that each successful axis captures as much variance as possible. We can reduce 2 dementions to one using a regression:

We used regression for predicting value of one variable by another variable.

In PCA we change coordinate system and start predicting variablesâ€™ values using less variables.