Que 1:

The following data shows the selling price of three-month-old calves at a livestock auction for a period of 22 weeks.

Week	Price	Week	Price
1	176	12	172
2	172	13	174
3	174	14	177
4	177	15	180
5	173	16	178
6	171	17	176
7	172	18	179
8	173	19	175
9	174	20	176
10	173	21	174
11	171	22	175

a. Prepare a line graph of these data. Do the data appear to be stationary or non stationary?

b. Compute the two-period (k = 2) and four-period (k = 4) moving average predictions for the data set. i. Compute the MSE for each of the two moving averages. Which appears to provide a better fit for this data set? ii. Compute forecasts for weeks 23 and 24 using the two-period and four period moving average techniques.

c. Use Excel Solver to determine the weights for a four-period weighted moving average on the data set that minimizes the MSE.

i. What are the optimal values for the weights?

ii. What are the forecasts for weeks 23 and 24 using the four-period weighted moving average technique?

d. Create an exponential smoothing model that minimizes the MSE for the data set. Use Excel Solver to estimate the optimal value of a. i. What is the optimal value of a? ii. What are the forecasts for weeks 23 and 24 using the exponential smoothing technique?

e. Which method appears to provide the best fit for this data set? Explain.

Que 2

The following data shows actual average prices of existing single-family homes in the U.S. for 1989-2001.

Year	Average Price($1000)
1989	114.4
1990	115.3
1991	124.7
1992	126.6
1993	129.3
1994	133.5
1995	135.8
1996	141.8
1997	150.5
1998	159.1
1999	168.3
2000	176.2
2001	185.3

a. Prepare a line graph for these data. Do the data seem to be stationary or nonstationary?

b. Fit a linear trend model to the data. What is the estimated regression equation?

c. Interpret the R2 value for your model.

d. Prepare a line graph comparing the linear trend predictions against the original data. e. What are the forecasts for 2002 and 2003 using the linear trend model?

f. Fit a quadratic trend model to the data. What is the estimated regression equation? g. Compare the adjusted R2 value for the quadratic model in part

(f) to that of the linear trend model in part (b). What is implied by this comparison?

h. Prepare a line graph comparing the quadratic trend predictions against the original data.

i. What are the forecasts for 2002 and 2003 using the quadratic trend model?

j. If you had to choose between the linear and quadratic trend models, which one would you use? Why?

k. If you had chosen either a moving average or an exponential smoothing technique instead of a trend model, what implications would it have on your forecasts?