A research laboratory was developing a new compound for the relief of severe cases of hay fever. In an experiment with 36 volunteers, the amounts of the two active ingredients (A & B) in the compound were varied at three levels each. Randomization was used in assigning four volunteers to each of the nine treatments. The data on hours of relief can be found in the following .csv file: Fever.csv

[Assume all of the ANOVA assumptions are satisfied]

1.1) State the Null and Alternate Hypothesis for conducting one-way ANOVA for both the variables ‘A’ and ‘B’ individually. [both statement and statistical form like Ho=mu, Ha>mu]

1.2) Perform one-way ANOVA for variable ‘A’ with respect to the variable ‘Relief’. State whether the Null Hypothesis is accepted or rejected based on the ANOVA results.

1.3) Perform one-way ANOVA for variable ‘B’ with respect to the variable ‘Relief’. State whether the Null Hypothesis is accepted or rejected based on the ANOVA results.

1.4) Analyse the effects of one variable on another with the help of an interaction plot.
What is the interaction between the two treatments?
[hint: use the ‘pointplot’ function from the ‘seaborn’ function]

1.5) Perform a two-way ANOVA based on the different ingredients (variable ‘A’ & ‘B’ along with their interaction ‘A*B’) with the variable ‘Relief’ and state your results.

1.6) Mention the business implications of performing ANOVA for this particular case study.

The dataset Education – Post 12th Standard.csv is a dataset that contains the names of various colleges. This particular case study is based on various parameters of various institutions. You are expected to do Principal Component Analysis for this case study according to the instructions given in the following rubric. The data dictionary of the ‘Education – Post 12th Standard.csv’ can be found in the following file: Data Dictionary.xlsx.

2.1) Perform Exploratory Data Analysis [both univariate and multivariate analysis to be performed]. The inferences drawn from this should be properly documented.

2.2) Scale the variables and write the inference for using the type of scaling function for this case study.

2.3) Comment on the comparison between covariance and the correlation matrix.

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

2.5) Build the covariance matrix, eigenvalues, and eigenvector.

2.6) Write the explicit form of the first PC (in terms of Eigen Vectors).

2.7) 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.

2.8) Mention the business implication of using the Principal Component Analysis for this case study. [Hint:Write Interpretations of the Principal Components Obtained