The Fresh Detergent Case Enterprise Industries produces Fresh, a brand of liquid detergent. In order to more effectively manage its inventory, the company would like to better predict demand for Fresh. To develop a prediction model, the company has gathered data concerning demand for Fresh over the last 33 sales periods. Each sales period is defined as one month. The variables are as follows: Demand = Y = demand for a large size bottle of Fresh (in 100,000) Price = the price of Fresh as offered by Ent. Industries AIP = the average industry price ADV = Ent. Industries Advertising Expenditure (in $100,000) to Promote Fresh in the sales period. DIFF = AIP - Price = the "price difference" in the sales period 1- Make time series scatter plots of all five variables (five graphs). Insert linear trend line, equation, and R-squared. Observe graphs and provide interpretation of results. 2- Construct scatter plots of Demand vs. DIFF and Demand vs. ADV, Demand vs. AIP, and Demand vs. Price. Insert linear fitted line, equation, and R-squared. Observe graphs and provide interpretation. Note that Demand is always on the Y axis. 3- Obtain the correlation matrix for all six variables and rank the variables based on absolute correlation with Demand. Explain your findings in plain language. 4- Use simple linear regression to perform trend analysis on demand values. Is trend analysis suitable for this data? Explain the Excel Regression output (trend equation, r, R-Squared, goodness of model). 5- Perform simple linear regression analysis with ADV as the independent variable to predict demand. Write the equation and explain the Excel Regression output. 6- Repeat part (6) with DIFF as the independent variable. 7- Construct multiple linear regression model with Period, AIP, DIFF, and ADV as independent variables. Formulate the equation and explain the output. Rank variables based on their degree of contribution to the model. Observe significant F, R-squared, and p-values and explain. 8- Perform multiple linear regression analysis with Period, DIFF, and ADV as independent variables. Formulate the equation. Which variable is the most significant predictor of demand? Rank the independent variables based on their degree of contribution to the model. Observe significant F, R-squared, and p-values and explain. 10- Use the model obtained in parts 9 and make forecasts for the following months. Period Price AIP ADV May 2023 $6.50 $6.25 $11.9 June 2023 $6.75 $6.30 $12.5 July 2023 $6.90 $6.75 $12.9 11- Provide a brief conclusion based on above analysis