This tutorial will help you implement a Principal Component Analysis (PCA) on a subset of particular observations.

## Dataset for running a Principal Component Analysis

#### Included in

XLSTAT-Base XLSTAT-Sensory XLSTAT-Marketing XLSTAT-Forecast XLSTAT-Biomed XLSTAT-Ecology XLSTAT-Psy XLSTAT-Quality XLSTAT-PremiumAn Excel sheet containing both the data and the results for use in this tutorial can be downloaded by clicking here.

The data are from the US Census Bureau and describe the changes in the population of 51 states between 2000 and 2001. The initial dataset has been transformed to rates per 1000 inhabitants, with the data for 2001 serving as the focus for the analysis. We are interested in studying large states (with a population greater than the average population). A size variable has been added (large/small).

## Goal of this Principal Component Analysis

Our goal is to analyze the correlations between the variables and to find out if the changes in population in some states are very different from the ones in other states. We focus on the large states by using the filter option of XLSTAT.

The only difference between this tutorial and the tutorial available here is that we decide to study only the large states.

## Setting up a Principal Component Analysis

Once XLSTAT-Pro is activated, select the **XLSTAT / Analyzing data / Principal components analysis** command, or click on the corresponding button of the **Analyzing Data** toolbar (see below).

The Principal Component Analysis dialog box will appear.

Select the data on the Excel sheet. The **Data format** chosen is **Observations/variables** because of the format of the input data.

The **PCA type** that will be used during the computations is the Pearson's correlation matrix, which corresponds to the classical correlation coefficient.

In the **Data options** tab, select the filter option and select the size column of the dataset.

In the **Charts** tab, we wish to have all large states displayed and thus do not activate the filter option.

Click on **OK**. A new dialog box asking you which group you want to keep is displayed. Select the large group and click Ok.

The computations begin once you have clicked on **OK**. You are asked to confirm the number of rows and columns.

Then you should confirm the axes for which you want to display plots. In this example, the percentage of variability represented by the first two factors is not very high (72.09%); to avoid a misinterpretation of the results, we have decided to complement the results with a second chart on axes 1 and 3.

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## Interpreting the results of a Principal Component Analysis applied on filtered data

The results for the largest states are displayed. The first table gives some descriptive statistics.

Then, eigenvalues are displayed.

We are interested in the maps for variables and observations. Regarding variables we have the following map:

We can see that on the first axis *older* states are opposed to *younger* states. The second axis opposes states with high domestic migration rates to states with lower domestic migration rates.

Regarding observations we have the following map.

This simple tool allows you to filter observations directly from your PCA dialog box and avoid complex data manipulation.