Consider the following data description for the data given in CSV file HW$3$DataBO::

Input Variables:

Hours Studied: The total number of hours spent studying by each student.

Previous Scores: The scores obtained by students in previous tests.

Extracurricular Activities: Whether the student participates in extracurricular activities $($Yes $(1)$ or No $(0)).$

Sleep Hours: The average number of hours of sleep the student had per day.

Sample Question Papers Practiced: The number of sample question papers the student practiced.

Output Variable:

Performance Index: A measure of the overall performance of each student. The performance index represents the student's academic performance and has been rounded to the nearest integer. The index ranges from $10$ to $100,$ with higher values indicating better performance.

Solve all the following questions using Python.

Use Pandas, Seaborn, Sklearn, etc. libraries for all the analysis.

B$-1$: $(5$ points$)$ Read the data and display the first $10$ records of HW$3$DataBO data. Identify the number of rows and columns. Does any column have missing data? Report any inconsistency? Display the statistical summaries of all the columns.

B$-2$: $(5$ points$)$ Normalization. For each column in HW$3$DataBO, apply the standard scaler, such that the mean is zero and standard deviation is one. Display the statistical summaries of all the columns.

B$-3$: $(5$ points$)$ Cross Normalization. For each column in HW$3$DataBN, apply the standard scaler fitted $($learned$)$ from HW$3$DataBO data. Display the statistical summaries of all the columns in HW$3$DataBN data.

B$-4$: $(5$ points$)$ OLS Regression $($Formula$).$ The hypothesis is that the $5$ input variables are linearly related to Performance Index. Use the following formula to calculate the OLS coefficient estimates of all HW$5$DataBO data. $.$

B$-5$: $(6$ points$)$ OLS Regression $($sklearn$).$ The hypothesis is that the $5$ input variables are linearly related to Performance Index. Do the following:

a$.$ Use the sklearn library to calculate the OLS coefficient estimates of all HW$5$DataBO data.

b$.$ Compare the coefficients obtained in Part B$-4$ with the above coefficients. Report any differences between the coefficients from Parts B$-4$ and B$-5.$

C$.$ Using the above OLS coefficient estimates, calculate the MSE for data given in HW$3$DataBN.

B$-6$: $(6$ points$)$ Ridge Regression. It may be possible that some input variables are not independent. Thus, the coefficients need regularization $($penalization$).$ Do the following:

a$.$ Do the Ridge analysis, taking all HW$3$DataBO data as the training data. Use $8-$fold cross validation, and pick the best value of alpha from $0\mathrm{.}01,0\mathrm{.}1,10,20,30.$ Print the best alpha and the resulting regression coefficients.

b$.$ Using the above coefficient estimates, calculate the MSE for data given in HW$3$DataBN.

B$-7$: $(6$ points$)$ LASSO Regression. It may be possible that not all input variables are helpful in predicting Performance Index. Thus, the coefficients need selection $($penalization$).$ Do the following:

a$.$ Do the LASSO analysis, taking all HW$3$DataBO data as the training data. Use $8-$fold cross validation and pick the best value of alpha from $0\mathrm{.}1,1,10,100,1000.$ Print the best alpha and the resulting regression coefficients.

b$.$ Using the above coefficient estimates, calculate the MSE for data given in HW$3$DataBN.

B$-8$: $(4$ points$)$ Regression Analysis. Compare and comment on the coefficients of the three models from Parts B$-5,$ B$-6,$ B$-7.$ Compare the performance of the OLS model against Ridge and LASSO models on the testing data.