Please find the questions below for PCA.

Problem Statement: The 'Hair Salon.csv' dataset contains various variables used for the

context of Market Segmentation. This particular case study is based on various parameters of a

salon chain of hair products. You are expected to do Principal Component Analysis for this case

study according to the instructions given in the following rubric.

Note: This particular dataset contains the target variable satisfaction as well. Please do drop this

variable before doing Principal Component Analysis.

Questions:

1) Perform Exploratory Data Analysis [both univariate and multivariate analysis to be

performed]. The inferences drawn from this should be properly documented. - 5 points

2) Scale the variables and write the inference for using the type of scaling function for this case

study. - 3 points

3) Comment on the comparison between covariance and the correlation matrix after scaling. - 2

points

4) Check the dataset for outliers before and after scaling. Draw your inferences from this

exercise. - 3 points

5) Build the covariance matrix, eigenvalues and eigenvector. - 4 points

6) Write the explicit form of the first PC (in terms of Eigen Vectors) - 5 points

7) Discuss the cumulative values of the eigenvalues. How does it help you to decide on the

optimum number of principal components? What do the eigenvectors indicate? Perform PCA

and export the data of the Principal Component scores into a data frame. - 10 points

8) Mention the business implication of using the Principal Component Analysis for this case

study. - 5 points

The data file Hair Salon :csv contains 12 variables used for Market Segmentation in the context of Product Service Management. Variable Expansion ProdQual Product Quality Ecom E-Commerce TechSup Technical Support CompRes Complaint Resolution Advertising Advertising ProdLine Product Line SalesFImage Salesforce Image ComPricing Competitive Pricing WartyClaim Warranty & Claims OrdBilling Order & Billing DelSpeed Delivery Speed Satisfaction Customer SatisfactionID ProdQual Ecom TechSup CompRes Advertising ProdLine SalesFImage ComPricing WartyClaim OrdBilling |DelSpeed Satisfaction 8.5 3.9 2.5 5.5 4.8 4.9 6 6.8 4.7 8.2 2.7 3.7 5.1 7.2 8.2 3.4 7.9 3.1 5.3 5.5 3.9 4.9 9.2 3.4 5.6 5.7 5.6 5.4 7.4 5.8 4.5 6.2 5.4 4.5 6.4 3.3 3.7 8.9 4.7 4.7 4.5 8.8 7 4.3 3 9 3.4 4.8 5.2 4.6 2.2 6 4.5 6.8 6.1 4.5 3.5 5.5 7.1 2.8 3.1 4.1 4 1.3 3.7 3.5 5.1 3.6 6.9 3.3 3.7 5 4.7 2.6 2.1 2.3 5.4 8.9 4.8 2.1 LD CO 6.2 21 3.3 3.9 4.8 5.7 4.6 3.6 5.1 6.9 5.4 1.3 5.8 3.7 3.6 5.1 6.7 6.3 3.7 5.9 5.8 9.3 5.9 4.4 10 4.6 5.4 4.5 5.1 7 6.1 4.7 5.7 5.7 8.4 5.4 11 4.1 4.4 3.7 3.2 4.6 5.5 4.8 2.7 5.8 4.6 5.8 5.8 3.8 12 4 6.1 7.4 4.9 6.3 3.9 4.4 3.9 6.4 8.2 5.8 13 3 9.5 5.6 3.2 6 1.6 6.9 5 6.9 5.6 7.6 6.5 5.1 14 4.4 9.2 3.9 5.7 8.4 5.5 2.4 8.4 4.8 7.1 6.7 15 4.5 5.3 4.5 4.2 4.7 6.9 7.6 4.5 6.8 5.9 3.8 6 4.8 16 5.2 3.7 8 3.2 4 6.8 3.2 7.8 3.8 1.9 6.1 4.3 4.5 17 5.7 4 6.6 6.7 6 3.3 5.5 5.1 5.2 6.7 18 4.2 4.5 5.9 1.1 5.5 6.4 7.2 3.5 6.4 5.5 3.4 6.2 5.7 19 4.8 5.6 3.4 7.4 5.1 6.4 3.7 5.7 5.6 9.1 5.4 5 20 9.1 4.5 4.5 3.6 6.8 6.4 5.3 5.3 7.1 3.4 5.8 4.5 21 5.2 4.4 3.8 7.1 7.6 5.2 3.9 4.3 5 8.4 7.1 3.3 22 5.7 3.3 3.6 5.8 5.4 5.9 5.4 8.3 7.8 1.5 6.4 1.3 23 3.6 4.3 3.6 9.9 7.4 5.1 3.5 7.3 4.7 3.7 6.7 24 4.8 9.3 4 2.4 2.6 7 7.2 2.2 7.2 1.5 5.2 6.4 6.7 25 4.5 6 4.1 5.3 8.6 4.7 3.5 5.3 5.3 8 6.5 26 4.7 4 5.4 3.6 6.6 6.1 4.8 4 3.9 5.3 7.1 6.1 5.6 27 3.9 8.5 3 7.2 6.6 5.8 1.1 7.6 3.7 4.8 6.9 5.3 4.4 28 7 3.3 5.4 5.5 6.3 2.6 1.8 1.2 9 6.5 4.3 29 3.7 3 5.4 8.5 5.7 6 2.3 7.6 3.7 4.8 5.8 5.7 30 7.6 4.4 3.6 6.3 3 4 5.1 4.2 4.6 7.7 4.9 31 4.7 5.9 3.5 3.4 3.5 5.4 4.3 4.5 5.4 4.7 5.2 7.7 3.7 3.3 32 3.1 2.5 6.1 7.2 4.5 2.3 5.1 3.8 6.6 6.8 33 3 3 6.7 3.7 5.5 6.4 5.3 5.3 5.1 1.9 9.2 5.7 3.5 34 3.4 8 3.3 6.1 5.4 5.7 5.5 4.6 4.7 8.7 35 5.9 4.7 5.7 4 4.2 5.2 7.3 3.9 5.4 5.8 3.4 6.2 2.5 36 8.7 3.5 6.3 3.2 6.1 4.3 3.5 6.1 2.9 5.6 6.1 3.1 2.5 5.4\f\fThe staff of a service center for electrical appliances include three technicians who specialize in repairing three widely used electrical appliances by three different manufacturers. It was desired to study the effects of Technician and Manufacturer on the service time. Each technician was randomly assigned five ropair jobs on each manufacturer's appliance and the time to complete each job (in minutes) was recorded. The data for this particular experiment is thus attached. Questions: 1) State the Nuli and Alternate Hypothesis for conducting one-way ANOVA for both the variables 'Manufacturer' and 'Technician individually. 3 points 2) Perform one-way ANOVA for variable 'Manufacturer' with respect to the variable 'Servioe Time'. State whether the Null Hypothesis is accepted or rejected based on the ANOVA results. - 3 points 3) Perform one-way ANOVA for variable 'Technician' with respect to the variable 'Service Time'. State whether the Null Hypothesis is accepted or rejected based on the ANOVA results. - 3 points 4) Analyse the effects of one variable on another with the help of an interaction plot. What is an interaction between two treatments? [hint use the 'pointplot' function from the 'seabom' graphical subroutine in Python] - 4 points 5) Perform a two-way ANOVA based on the variables 'lvlanufacturer' & 'Technician' with respect to the variable 'Service Time' and state your results. - 5 points a) Mention the business implications of performing ANOVA for this particular case study. - 5 points