Exam 16: Time-Series Forecasting and Index Numbers

TABLE 16-6 The number of cases of merlot wine sold by a Paso Robles winery in an 8-year period follows 1991 270 1992 356 1993 398 1994 456 1995 358 1996 500 1997 410 1998 376 -Referring to Table 16-6, exponential smoothing with a weight or smoothing constant of 0.2 will be used to forecast wine sales. The forecast for 1999 is ______ .

TABLE 16-10 The manager of a marketing consulting firm has been examining his company's yearly profits. He believes that these profits have been showing a quadratic trend since 1980. He uses Microsoft Excel to obtain the partial output below. The dependent variable is profit (in thousands of dollars), while the independent variables are coded years and squared of coded years, where 1980 is coded as 0, 1981 is coded as 1, etc. SUMMARY OUTPUT Regression Statistics Multiple R 0.998 RSquare 0.996 Adjusted R Square 0.996 Standard Error 4.996 Observations 17 Coefficients Intercept 35.5 Coded Year 0.45 Year Squared 1.00 -Referring to Table 16-10, the forecast for profits in 2005 is_____ .

When a time series appears to be increasing at an increasing rate, such that percentage difference from observation to observation is constant, the appropriate model to fit is the

If a time series does not exhibit a long-term trend, the method of exponential smoothing may be used to obtain short-term predictions about the future.

TABLE 16-2 The monthly advertising expenditures of a department store chain (in $1,000,000s) were collected over the last decade. The last 14 months of this time series follows: Month Expenditures (\ ) 1 1.4 2 1.8 3 1.6 4 1.5 5 1.8 6 1.7 7 1.9 8 2.2 9 1.9 10 1.9 11 2.1 12 2.4 13 2.8 14 3.1 -Referring to Table 16-2, set up a scatter diagram (i.e., time-series plot) with months on the horizontal X-axis.

TABLE 16-6 $\text { The number of cases of merlot wine sold by a Paso Robles winery in an 8-year period follows. }$ 1991 270 1992 356 1993 398 1994 456 1995 358 1996 500 1997 410 1998 376 -Referring to Table 16-6, a centered 5-year moving average is to be constructed for the wine sales. The moving average for 1996 is_____ .

The principle of parsimony indicates that the simplest model that gets the job done adequately should be used.

TABLE 16-5 A contractor developed a multiplicative time-series model to forecast the number of contracts in future quarters, using quarterly data on number of contracts during the 3-year period from 1996 to 1998. The following is the resulting regression equation: ln Y^{^} = 3.37 + 0.117 X - 0.083 Q₁ + 1.28 Q₂ + 0.617 Q₃ where Y^{^} is the estimated number of contracts in a quarter X is the coded quarterly value with X = 0 in the first quarter of 1996. Q₁ is a dummy variable equal to 1 in the first quarter of a year and 0 otherwise. Q₂ is a dummy variable equal to 1 in the second quarter of a year and 0 otherwise. Q₃ is a dummy variable equal to 1 in the third quarter of a year and 0 otherwise. -Referring to Table 16-5, using the regression equation, which of the following values is the best forecast for the number of contracts in the third quarter of 1999?

Which of the following statements about the method of exponential smoothing is not true?

TABLE 16-9 The executive vice-president of a drug manufacturing firm believes that the demand for the firm's most popular drug has been evidencing an exponential trend since 1985. She uses Microsoft Excel to obtain the partial output below. The dependent variable is the log base 10 of the demand for the drug, while the independent variable is years, where 1985 is coded as 0, 1986 is coded as 1, etc. SUMMARY OUTPUT Regression Statistics Multiple R 0.996 R Square 0.992 Adjusted R Square 0.991 Standard Error 0.02831 Observations 12 Coefficients Intercept 1.44 Coded Year 0.068 -Referring to Table 16-9, the forecast for the demand in 1999 is_____ .

TABLE 16-14 Given below are the average prices for three types of energy products in the United States from 1992 to 1995. Year Electricity N atural Gas Fuel Oil 1992 43.205 25.893 0.892 1993 16.959 28.749 0.969 1994 47.202 28.933 1.034 1995 48.874 29.872 0.913 1996 48.693 28.384 0.983 -Referring to Table 16-14, what is the Laspeyres price index for the group of three energy items in 1994 for a family that consumed 15 units of electricity, 24 units of natural gas and 200 units of fuel oil in 1992 using 1992 as the base year?

TABLE 16-8 The president of a chain of department stores believes that her stores' total sales have been showing a linear trend since 1980. She uses Microsoft Excel to obtain the partial output below. The dependent variable is sales (in millions of dollars), while the independent variable is coded years, where 1980 is coded as 0, 1981 is coded as 1, etc. $\text { SUMMARY OUTPUT }$ Regression Statistics Multiple R 0.604 RSquare 0.365 Adjusted R Square 0.316 Standard Error 4.800 Obervations 17 Coefficients Intercept 31.2 Coded Year 0.78 -Referring to Table 16-8, the fitted trend value (in millions of dollars) for 1980 is______ .

A simple price index tracks the price of a group of commodities at a given period of time to the price paid for that group of commodities at a particular point of time in the past.