Method: Use R script to solve the following problem

Dataset: https://raw.githubusercontent.com/AliUofC/Data601/refs/heads/main/water.csv

Problem 1. (From Exercise 1) The amount of water used by the production facilities of a plant varies. Observations on water usage and other, possibility related, variables were collected for 250 months. The data are given in water.csv file. The explanatory variables are TEMP= average monthly temperature (degree celsius) PROD=amount of production (in hundreds of cubic) DAYS=number of operationing day in the month (days) HOUR=number of hours shut down for maintenance (hours) The response variable is USAGE=monthly water usage (gallons/minute) a. b. om Fit the model containing all four independent variables. What is the estimated multiple regression equation? Test the hypothesis for the full model i.e the test of overall significance. Use significance level 0.05. Ensure that you include the hypotheses, p-value, and conclusion. . Would you suggest the model in part b for predictive purposes? Which model or set of models would you suggest for predictive purposes? Hint: Use Individual Coefficients Test (t-test) to find the best model. Make sure you provide your hypotheses, p-value(s), and final model.) _ Use Partial F' test to confirm that the independent variable (removed from part c) should be out of the model at significance level 0.05. Ensure that you include the hypotheses, p-value, and conclusion. . Obtain a 95% confidence interval of regression coefficient for TEMP from the model in part c. Give an interpretation. Use the method of Model Fit to calculate Reaj and RSE to compare the full model in part a and the model in part c. Which model or set of models would you suggest for predictive purpose'? For the final model, give an interpretation of Ria and RSE. . Build an interaction model to fit the multiple regression model from the model in part f. From the output, which model would you recommend jor predictive purposes? Be sure to explain your process