The data below consist of the closing price of the common stock of the American Telephone and Telegraph Corporation on 10 recent trading days.
Time(t)
Price
Time(t)
Price
1
$24.10
6
$22.73
2
23.80
7
22.60
3
23.39
8
21.76
4
22.90
9
22.14
5
22.10
10
21.69
Using a five-period moving average, forecast the price of the stock for period 10.
What is the error of the forecast in #1-a?
Using a five-period moving average, forecast the price of the stock for period 11.
A product is manufactured in distinct batches of various sizes. The cost accountant wished to obtain an equation to use for estimating the cost of a batch. He obtained data on a number of batches, consisting of the size of the batch, measured in number of pieces, and the total cost of the batch, consisting of the setup cost and the variable costs of labor, material, etc. The total cost is stated in thousands of dollars.
Which is the dependent variable? The independent variable?
Draw the scatterplot of this data. Does a straight line look like a reasonable fit?
Obtain the x2, xy, and y2 columns.
What is the value of the slope?
What is the interpretation of the slope?
Size of Batch
Cost of Batch
20
$1.4
30
3.4
40
4.1
50
3.8
70
6.7
80
6.6
100
7.8
120
10.4
150
11.7
650
$55.9
What is the value of the y intercept?
What is the interpretation of the y intercept?
Estimate the cost of a batch of 125 pieces.
What is the value of the coefficient of correlation? Does it appear to indicate a high degree of association between the size of the batch and the cost?
What is the value of r2?
The president of the Rich and Greene College of Business Administration wishes to forecast the enrollment for next fall. The enrollment is measured in Full Time Equivalents (FTE), which represent the number of full-time students, which is equivalent to the existing mixture of full-time and part-time students. Data representing the fall enrollment for the past ten years is given below:
time(t)
Enrollment
1
907
2
981
3
1014
4
1015
5
1050
6
1071
7
1123
8
1118
9
1175
10
1216
Draw a scatterplot. Does the data appear to contain a linear trend?
Obtain the t, y, and ty columns.
What is the value of the slope?
What is the interpretation of the slope?
What is the value of the y intercept?
What is the interpretation of the y intercept?
Forecast the enrollment for next fall.
The table below contains data on the monthly amount, in millions of dollars, which was spent by "leading national advertisers" for advertising apparel and accessories in magazines, in four recent years.
Year
Month
1
2
3
4
January
$6.7
$7.9
$ 8.8
$ 7.4
February
6.2
8.4
10.3
17.4
March
12.1
15.1
20.4
26.1
April
14.4
15.9
17.3
26.6
May
11.1
11.8
15.7
17.0
June
7.4
5.5
9.0
10.4
July
6.4
7.6
8.9
7.9
August
12.9
13.0
20.0
24.7
September
21.1
23.2
32.6
35.6
October
15.4
17.2
24.2
24.8
November
16.5
16.7
22.0
22.2
December
11.6
11.9
16.9
19.8
Source: Survey of Current Business, U.S. Department of Commerce, Washington, D.C., various dates.
Use this data to obtain a set of 12 monthly seasonal indexes.
Obtain the set of 37 12-month moving averages. The first value will fall between June and July of Year 1, and the last value will fall between June and July of Year 4.
Obtain the set of 36 centered 12 -month moving averages. The first value will fall in July of Year 1, and the last value in June of Year 4.
Obtain the 36 ratios of the observed values to the centered moving averages. Group them by months.
Find the mean of the ratios for each month.
Adjust the means to add to 12. These are the monthly seasonal indexes.
Describe the seasonal pattern in magazine advertising for apparel and accessories which is revealed by the monthly seasonal indexes.
This problem utilizes the data in Problem #4 to make forecasts using the naive methods in your textbook.
Use the actual value in the previous period to forecast the amount which will be spent on advertising apparel and accessories for year 5.
Use the actual value in the same month of the previous year to forecast the amount which will be spent on advertising apparel and accessories for January of year 5.
Use the data for year 1 in Problem #4 for this problem. Calculate the single-factor exponential smoothing forecasts for advertising for the last 11 months of Year 1. Use the first actual value as the starting forecast, and α = 0.20.
Construct the worksheet for single-factor smoothing and obtain the forecasts for the months of February through December.
Draw the graph of the actual values and the forecasted values.
Use your work in Problem #6 in this problem, which involves the mean squared error (MSE), the mean absolute deviation (MAD), and the tracking signal. Use the tracking signal to estimate when a change occurs in the rate of spending on advertising apparel and accessories.
Obtain the actual column, the forecasted column, and the error column for single-factor smoothing of the data for year 1 in Problem #4. (The actual column will have 12 entries, and the forecasted column will have 11 entries.)
Obtain squared error column.
Obtain the MSE for year 1.
Obtain the absolute error column.
Obtain the MAD for year 1.
Beginning with the absolute error of 0.50 for February of year 1, obtain updated estimates of MAD for the months of February through December. Use α = .20.
Obtain the tracking signal column.
Plot the tracking signals on a control chart with limits of ±4.
What conclusion can be drawn from the tracking signal?
Use your work in Problem #6 to obtain the MAPE.
What is the column?
What is the column?
Obtain the MAPE.
Solve problem #7-a, on an EXCEL spreadsheet.
Obtain the cumulative (A - F) column on the same spreadsheet.
Obtain the |A-F| column.
Obtain the cumulative |A - F| column.
Obtain the MAD column.
Obtain the tracking signal column.
Did you get the same answers?
Use the data for Year I in Problem 4 for this problem. Calculate the trend-adjusted exponential smoothing forecasts for advertising for the last 8 months of Year 1. Use α = β = .20 and use the first four actual values to obtain the starting values.
What is the starting estimate of the trend, T4?
What is the initial forecast, TAF5?
Construct the worksheet for trend-adjusted smoothing and obtain the forecasts for the months of May through December.
Draw the graph of the actual values and the forecasted values.
