Operations

Solutions to Exercises

1. There have been a steady increasing number of consumers using smart phones in United States since 2009. Suppose that the sales of smart phones in Union County, NJ, between January 2011 and August 2011 are as those presented in the table below.

a). Suppose that the trend will continue for that next year. Construct a simple regression model to predict the sales in Union County for the first quarter of 2012.

Step 1. Enter the given data into Excel.

Step 2. Select Data-Data Analysis-Regression.

Step 3. Input Y Range as $B$3:$B$11, and Input X Range as $A$3:$A$11.

Step 4. Click OK to see the result as shown below.

Note that the result at Cell B32 corresponds to slope of month, and the result at Cell B31 corresponds to the intercept, i.e., the model is Y=23.881*X+195.216 where Y represents sales and X represents months.

Step 5. The first quarter of 2012 corresponds to Months 13, 14, and 15. We want to predict the sales for these months, so let X=13, 14, and 15 respectively, and use the regression model to calculate Y.

X=13, Y=23.881*13+195.216=505.738;

X=14, Y=23.881*14+195.216=529.619;

X=15, Y=23.881*15+195.216=553.5

Final solution: 01/2012: 505.738

02/2012: 529.619

03/2012: 553.5

b). Let ==0.2, S0=391, and G0=b. Predict the sales of the first quarter of 2012 using the Holt’s trend model.

Assume that t=0 refers to August 2011, and thus t=5 refers to January 2012, t=6 refers to February 2012, and t=7 refers to March 2012.

According to the multi-step ahead forecasting formula, we have

2. The following data is published online. Predict the cash dividend of year 2011, 2012, 2013, and 2014 using simple regression model.

Step 1. Enter the first and third columns of the given data into Excel.

Step 2. Select Data-Data Analysis-Regression.

Step 3. Input Y Range as $B$3:$B$14, and Input X Range as $A$3:$A$14.

Step 4. Click OK to see the result as...