Computation: Grocery Retailer

Info

This repo served as a submission for an assignment for the class Statistical Learning at Illinois Institute of Technology in Spring 2024. Below you can find the problem statement.

Assignment

A large, national grocery retailer tracks productivity and costs of its facilities closely. Data were obtained from a single distribution center for a one-year period. Each data point for each variable represents one week of activity. The variables included are the number of cases shipped ($X_1$), the indirect costs of the total labor hours as a percentage ($X_2$), a qualitative predictor called holiday that is coded 1 if the week has a holiday and 0 otherwise ($X_3$), and the total labor hours ($Y$). (Data file: Grocery.txt). The columns from left to right are $Y,X_1,X_2,X_3$.

1. Fit the linear model $$Y = \beta_0 + \beta_1X_1 + \beta_2X_2 + \beta_3X_3 + \epsilon.$$ Show the table of the fitted model: coefficient estimation, their standard deviation, z-score, and p-values. Show the estimation $\hat{\sigma}^2$.

2. Use both best subset ($C_p$, forward stepwise, backward stepwise) to find a smaller model with the best fits. Show the results of the fits as in (a).

3. Use F-test to check whether the model returns from (b) significantly different ($\alpha=0.05$) from the complete model in (a).