Use the data provided in the Excel spreadsheet Module 4 Dataset - Insurance Expenses.xlsx (file above) to execute the following activities:

1. In the Excel sheet Matrix Algebra Regression, calculate the least squares coefficients using Excel matrix algebra functions. Make sure to show all sub-matrices in your calculations. Note work done outside Excel is not acceptable.
2. In the Excel sheet Excel Regression, execute a regression using the Excel regression function (using linest is not acceptable). Note that Excel automatically includes a constant in the regression as a default.
3. Use Generative AI (BARD or ChatGPT) to access R code to run a regression using the Insurance Expense dataset. Execute the regression in R. Provide a copy of the R code executed as well as the raw output/results.
4. Compare the results across different regression methods to ensure consistency across coefficient values and write up a brief explanation of what the regression results reveal about the relation among the variables.