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Giovanni Food Products produces and sells frozen pizzas to public schools throughout the eastern United States. Using a very aggressive marketing strategy they have been able to increase their annual revenue by approximately $10 million over the past 10 years. But increased competition has slowed their growth rate in the past few years. The annual revenue, in millions of dollars, for the previous 10 years is contained in the Excel Online file below. Construct a spreadsheet to answer the following questions.
Year Revenue
1 8.53
2 10.84
3 12.98
4 14.11
5 16.31
6 17.21
7 18.37
8 18.45
9 18.40
10 18.43
a. Construct a time series plot. Comment on the appropriateness of a linear trend.
b. Using Minitab or Excel, develop a quadratic trend equation that can be used to forecast revenue.
c. Using the trend equation developed in part (b), forecast revenue in year 11.

Sagot :

Answer:

a-1. See part a-1 of the attached excel file for the time series plot.

a-2. The linear trend is not appropriate

b. The quadratic trend equation is y = -0.1618x^2 + 2.889x + 5.7022

c. Revenue in year 11 is 17.90.

Step-by-step explanation:

a-1. Construct a time series plot. Comment on the appropriateness of a linear trend.

Note: See part a-1 of the attached excel file for the time series plot.

a-2. Comment on the appropriateness of a linear trend.

Note: See part a-2 of the attached excel file for the time series plot with a linear trend.

From the time series plot with a linear trend, it can be seen that the movements of the time series plot and the linear trend are not the same. This implies that the linear trend is not appropriate

b. Using Minitab or Excel, develop a quadratic trend equation that can be used to forecast revenue.

Note: See part b of the attached excel file for the quadratic equation trend.

From the quadratic equation trend, we obtained the following quadratic trend equation that can be used to forecast revenue:

y = -0.1618x^2 + 2.889x + 5.7022 ……………. (1)

Where;

y = Revenue

x = Year

c. Using the trend equation developed in part (b), forecast revenue in year 11.

Substituting x = 11 into equation (1), we have:

y = (-0.1618 * 11^2) + (2.889 * 11) + 5.7022 = 17.90

Therefore, revenue in year 11 is 17.90.

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