### Perform simple linear regression analysis with adv

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Use regression to perform trend analysis on the de-seasonalized demand values. Is trend analysis suitable for this data? Find MAD and MSE and explain the Excel Regression

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

2- Make time series scatter plots of all five variables (five graphs). Observe graphs and provide interpretation.

3- Construct scatter plots of Demand vs. DIFF and Demand vs. ADV, Demand vs. AIP, and Demand vs. Price.  Observe the graphs and provide interpretation.

4- Obtain the correlation matrix for all six variables and list the variables that have strong correlation with each other.  High correlation is r > 0.50.

5- Use 3-month and 6-month moving averages to predict the demand for October 2015. Find MAD and MSE for both forecasts and identify the preferred one based on each calculation.

6- Use Exponential smoothing forecasts with alpha of 0.1, 0.2,  ..., 0.9 to predict October 2015 demand.  Identify which alpha results in the lowest MAD and lowest MSE.

7- Find the monthly seasonal indices for the demand values using SA method.  Find the de-seasonalized demand values by dividing monthly demand by seasonal indices.

8- Use regression to perform trend analysis on the de-seasonalized demand values. Is trend analysis suitable for this data? Find MAD and MSE and explain the Excel Regression output.

9- Find the seasonally adjusted trend forecasts for October through December 2015.

10- Perform simple linear regression analysis with ADV as the independent variable to predict demand. Find MAD and MSE and explain the Excel Regression output.

11- Repeat part (10) with DIFF as the independent variable.

12- Construct four variable regression model with Period, AIP, DIFF, and ADV as independent variables. Find MAD and MSE 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.

13- Perform multiple linear regression analysis with Period, DIFF, and ADV as independent variables.  Find MAD and MSE. 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.

14- Use the model obtained in parts 13 and make forecasts for the following months.  Make sure to seasonalize final forecast.

Oct.  2015                      \$4.10               \$4.65               \$10.2

Nov. 2015                      \$4.25               \$4.70               \$10.4

Dec.  2015                      \$4.60               \$4.95               \$10.5

15- Provide a complete case analysis report.

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