a$.$Describe the basic concept behind the factor analysis model and approach of principal component analysis used for factor extraction. Write the preconditions. Develop the linear equation for estimating the factors score on factor $3$ and describe the symbols used.

b$.$ Check for the interdependence between the seven statements. Formulate the appropriate null hypothesis that needs to be tested. Also, comment on the adequacy of sample, quote the relevant statistic.

c$)$ How many factors have been determined based on eigenvalue, how much total variance of the data is explained by these factors is it satisfactory?

d$)$ Identify the major constituents of each factor and label $($name$)$ the factors extracted, appropriately explaining the rationale behind.