Hello, good to see you here! I'm here to help you understand some of the advanced concepts of statistics.

Today's quiz would be based on the concept of Factor Analysis. I quess you will find it clear and interesting.

Factor analysis is a statistical procedure used to draw inferences on quantities that cannot be quantified numerically. Quantities such as intelligence, friendliness and patroitism.

The objective a factor analysis is to describe the correlation between p measured attributes in terms of variation in few underlying unobservable factors.

These explains the variation caused by the different factors under consideraion. The portion of the variance that is contributed by the k common factors is the communality and the portion that is not explained by the common factor is the uniqueness also known as specific variance

Rotation is the process of obtaining a different set of loadings by multiplying the loadings by an orthogonal matrix chosen based on a specific criteria.

The KMO is a measure of how suitable the available data is to be used for Factor Analysis. The value of the KMO statistic ranges from 0 to 1.

PCA is a variance-maximation procedure that aims are transforming a set of features into few principal components

Bartlett's test is a measure of sampling adequacy and relates to the significance of the study and just like the KMO, test how suitable the data is.

Take some time to get used to these concepts in your own word and I would like to thank you or reading!

Today's quiz would be based on the concept of Factor Analysis. I quess you will find it clear and interesting.

**Question 1: Briefly explain Factor Analysis?**Factor analysis is a statistical procedure used to draw inferences on quantities that cannot be quantified numerically. Quantities such as intelligence, friendliness and patroitism.

**Question 2: What is the goal of Factor Analysis?**The objective a factor analysis is to describe the correlation between p measured attributes in terms of variation in few underlying unobservable factors.

**Question 3: Explain Communality and Uniqueness in Factor Analysis**These explains the variation caused by the different factors under consideraion. The portion of the variance that is contributed by the k common factors is the communality and the portion that is not explained by the common factor is the uniqueness also known as specific variance

**Question 4: Outline the various methods of carrying ouf Factor Analysis problem**- Maximum Likelihood Method
- Least Squares Method
- Principal Components
- Alpha Factoring
- Image Factoring

**Question 5: What is the concept of Rotation in Factor Analysis?**Rotation is the process of obtaining a different set of loadings by multiplying the loadings by an orthogonal matrix chosen based on a specific criteria.

**Question 6: Outline and explain the types of rotations you know?***Varimax*: Orthogonal rotation that minimizes the number of variables that have high loadings on each other. It simplifies interpretation of factors*Quartimax*: A rotation mentod that minimizes the number of factors needed to explain each variable. It simplifies interpretation of observed variable*Equamax*:A mixed rotation method which is a combination of the Varimax and the Quatimax methods.*Direct Oblimin*: Non-orthogonal rotation*Promax Rotation*: Non-orthogonal rotation that allows correlation of factors.**Question 7: What is Keiser-Meyer-Olkin(KMO) Test used for?**The KMO is a measure of how suitable the available data is to be used for Factor Analysis. The value of the KMO statistic ranges from 0 to 1.

**Question 8: What is Principal Component Analysis(PCA)?**PCA is a variance-maximation procedure that aims are transforming a set of features into few principal components

**Question 9: How if Principal Component Analysis Performed?**- Compute teh sample covariance matrix
- Compute the eigenvalues
- Choose a dimension k
- Define the dimension reduced data

**Question 10: Briefly Explain Bartlett's Test of Sphericity**Bartlett's test is a measure of sampling adequacy and relates to the significance of the study and just like the KMO, test how suitable the data is.

Take some time to get used to these concepts in your own word and I would like to thank you or reading!