The quarterly sales data (number of copies sold) for a college textbook over the past three years follow. Quarter Year 1 Year 2 Year 3 1 1,690 1,800 1,860 2 950 910 1,110 3 2,625 2,910 2,940 4 2,510 2,370 2,615 (a) Construct a time series plot. What type of pattern exists in the data? There appears be a downward linear trend but no seasonal pattern in the data.There appears to be a seasonal pattern in the data and perhaps a moderate upward linear trend. There appears be an upward linear trend but no seasonal pattern in the data.There appears to be a seasonal pattern in the data and perhaps a moderate downward linear trend. (b) Use a regression model with dummy variables as follows to develop an equation to account for seasonal effects in the data. (Round your numerical values to the nearest integer.) Qrt1 = 1 if quarter 1, 0 otherwise; Qrt2 = 1 if quarter 2, 0 otherwise; Qrt3 = 1 if quarter 3, 0 otherwise t = (c) Using the equation developed in part (b), compute the quarterly forecasts for year 4. (Round your answers to the nearest ten.) quarter 1 forecastquarter 2 forecastquarter 3 forecastquarter 4 forecast (d) Let t = 1 refer to the observation in Quarter 1 of Year 1; let t = 2 refer to the observation in Quarter 2 of Year 1; and t = 12 to refer to the observation in Quarter 4 of Year 3. Using the dummy variables defined in part (b) and also using t, develop an equation to account for seasonal effects and any linear trend in the time series. (Round your numerical values to the nearest integer.) t =

Calculus For The Life Sciences

2nd Edition

ISBN:9780321964038

Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Chapter7: Integration

Section7.CR: Chapter 7 Review

Problem 88CR

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The quarterly sales data (number of copies sold) for a college textbook over the past three years follow.

Quarter	Year 1	Year 2	Year 3
1	1,690	1,800	1,860
2	950	910	1,110
3	2,625	2,910	2,940
4	2,510	2,370	2,615

(a)

Construct a time series plot.

What type of pattern exists in the data?

There appears be a downward linear trend but no seasonal pattern in the data.There appears to be a seasonal pattern in the data and perhaps a moderate upward linear trend. There appears be an upward linear trend but no seasonal pattern in the data.There appears to be a seasonal pattern in the data and perhaps a moderate downward linear trend.

(b)

Use a regression model with dummy variables as follows to develop an equation to account for seasonal effects in the data. (Round your numerical values to the nearest integer.)

Qrt1 = 1 if quarter 1, 0 otherwise; Qrt2 = 1 if quarter 2, 0 otherwise; Qrt3 = 1 if quarter 3, 0 otherwise

_t =

(c)

Using the equation developed in part (b), compute the quarterly forecasts for year 4. (Round your answers to the nearest ten.)

quarter 1 forecastquarter 2 forecastquarter 3 forecastquarter 4 forecast

(d)

Let

t = 1

refer to the observation in Quarter 1 of Year 1; let

t = 2

refer to the observation in Quarter 2 of Year 1;

and

t = 12

to refer to the observation in Quarter 4 of Year 3. Using the dummy variables defined in part (b) and also using t, develop an equation to account for seasonal effects and any linear trend in the time series. (Round your numerical values to the nearest integer.)

_t =

Based upon the seasonal effects in the data and linear trend, compute the quarterly forecasts for year 4. (Round your answers to the nearest ten.)

quarter 1 forecastquarter 2 forecastquarter 3 forecastquarter 4 forecast

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