Module 3 Problem 1 (48 points): The electric power consumed by a chemical plant is thought to be related to average ambient temperature, number of days in the month, average product purity, and tons of product produced. You have one year of data, and the data is provided in the Moodle assignment (IE4362_JMP2_P1_MultReg.jmp). 1. First examine the dataset to determine which variables are meaningful and which might be correlated (and therefore unnecessary). Do this through 2 steps: a. (8) Examine the correlations between the input variables. Show the correlations table and discuss the relationship between each pair in terms of direction and strength. b. (12) Develop a scatterplot and simple linear regression model between power and each input variable. Discuss which variables appear to have a meaningful impact on power, and how you came to that conclusion. 2. Conduct a backward stepwise regression to find the best model of power consumption from the 4 input variables provided. a. (2) Based on the scatterplots and simple linear regressions developed in 1.b., which variable should be removed first? b. (5) Show the JMP output for the final model. c. (3) What is the overall significance of the model, and does it indicate a good fit for the data? d. (3) How much variance is explained by the model, and does it indicate a good fit for the data? e. (3) Which variables should be included in the final model, and why? f. (3) How much variance is NOT explained by the model? List a few potential causes for the unexplained variance. 3. (6) Write the final model equation and specify the ranges of each variable for which the model is valid. 4. (3) Evaluate the final model: Would you recommend that management use this model to predict power consumption? Give a yeso answer and reasoning.