A statistical program is recommended. A certain company 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 $10 million over the past 10 years. But increased competition has slowed their growth rate in the past few years. The annual revenue, in millions of dollars, for the previous 10 years is shown. Year Revenue 1 8.63 2 10.94 3 12.88 4 14.11 5 16.21 6 17.11 7 18.47 8 18.35 9 18.40 10 18.33 (a) Construct a time series plot. A time series plot contains a series of 10 points connected by line segments. The horizontal axis ranges from 0 to 11 and is labeled: Year. The vertical axis ranges from 0 to 20 and is labeled: Revenue ($ millions). The first point is at approximately (1, 18). The rest are plotted from left to right at regular increments of 1 year in a nearly horizontal direction until the fourth point. Afterwards, they are plotted in a downward, diagonal direction until the last point at approximately (10, 9). Consecutive points are close together with little scatter. A time series plot contains a series of 10 points connected by line segments. The horizontal axis ranges from 0 to 11 and is labeled: Year. The vertical axis ranges from 0 to 20 and is labeled: Revenue ($ millions). The first point is at approximately (1, 16). The rest are plotted from left to right at regular increments of 1 year in a nearly horizontal direction until the fourth point. Afterwards, they are plotted in a downward, diagonal direction until the last point at approximately (10, 7). Consecutive points are close together with little scatter. A time series plot contains a series of 10 points connected by line segments. The horizontal axis ranges from 0 to 11 and is labeled: Year. The vertical axis ranges from 0 to 20 and is labeled: Revenue ($ millions). The first point is at approximately (1, 7). The rest are plotted from left to right at regular increments of 1 year in an upward, diagonal direction until the seventh point. Afterwards, they are plotted in a nearly horizontal direction until the last point at approximately (10, 16). Consecutive points are close together with little scatter. A time series plot contains a series of 10 points connected by line segments. The horizontal axis ranges from 0 to 11 and is labeled: Year. The vertical axis ranges from 0 to 20 and is labeled: Revenue ($ millions). The first point is at approximately (1, 9). The rest are plotted from left to right at regular increments of 1 year in an upward, diagonal direction until the seventh point. Afterwards, they are plotted in a nearly horizontal direction until the last point at approximately (10, 18). Consecutive points are close together with little scatter. Comment on the appropriateness of a linear trend. The time series plot shows that a linear trend is most appropriate.The time series plot shows that a curvilinear trend may be more appropriate. The time series plot shows that neither a linear nor a curvilinear trend is appropriate. (b) Using Minitab or Excel, develop a quadratic trend equation that can be used to forecast revenue (in millions of dollars). (Round your numerical values to three decimal places.) Tt = (c) Using the trend equation developed in part (b), forecast revenue (in millions of dollars) in year 11. (Round your answer to two decimal places.) $ million

A statistical program is recommended. A certain company 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 $10 million over the past 10 years. But increased competition has slowed their growth rate in the past few years. The annual revenue, in millions of dollars, for the previous 10 years is shown. Year Revenue 1 8.63 2 10.94 3 12.88 4 14.11 5 16.21 6 17.11 7 18.47 8 18.35 9 18.40 10 18.33 (a) Construct a time series plot. A time series plot contains a series of 10 points connected by line segments. The horizontal axis ranges from 0 to 11 and is labeled: Year. The vertical axis ranges from 0 to 20 and is labeled: Revenue ($ millions). The first point is at approximately (1, 18). The rest are plotted from left to right at regular increments of 1 year in a nearly horizontal direction until the fourth point. Afterwards, they are plotted in a downward, diagonal direction until the last point at approximately (10, 9). Consecutive points are close together with little scatter. A time series plot contains a series of 10 points connected by line segments. The horizontal axis ranges from 0 to 11 and is labeled: Year. The vertical axis ranges from 0 to 20 and is labeled: Revenue ($ millions). The first point is at approximately (1, 16). The rest are plotted from left to right at regular increments of 1 year in a nearly horizontal direction until the fourth point. Afterwards, they are plotted in a downward, diagonal direction until the last point at approximately (10, 7). Consecutive points are close together with little scatter. A time series plot contains a series of 10 points connected by line segments. The horizontal axis ranges from 0 to 11 and is labeled: Year. The vertical axis ranges from 0 to 20 and is labeled: Revenue ($ millions). The first point is at approximately (1, 7). The rest are plotted from left to right at regular increments of 1 year in an upward, diagonal direction until the seventh point. Afterwards, they are plotted in a nearly horizontal direction until the last point at approximately (10, 16). Consecutive points are close together with little scatter. A time series plot contains a series of 10 points connected by line segments. The horizontal axis ranges from 0 to 11 and is labeled: Year. The vertical axis ranges from 0 to 20 and is labeled: Revenue ($ millions). The first point is at approximately (1, 9). The rest are plotted from left to right at regular increments of 1 year in an upward, diagonal direction until the seventh point. Afterwards, they are plotted in a nearly horizontal direction until the last point at approximately (10, 18). Consecutive points are close together with little scatter. Comment on the appropriateness of a linear trend. The time series plot shows that a linear trend is most appropriate.The time series plot shows that a curvilinear trend may be more appropriate. The time series plot shows that neither a linear nor a curvilinear trend is appropriate. (b) Using Minitab or Excel, develop a quadratic trend equation that can be used to forecast revenue (in millions of dollars). (Round your numerical values to three decimal places.) Tt = (c) Using the trend equation developed in part (b), forecast revenue (in millions of dollars) in year 11. (Round your answer to two decimal places.) $ million

Linear Algebra: A Modern Introduction

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ISBN:9781285463247

Author:David Poole

Publisher:David Poole

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Section4.6: Applications And The Perron-frobenius Theorem

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A statistical program is recommended.

A certain company 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 shown.

Year	Revenue
1	8.63
2	10.94
3	12.88
4	14.11
5	16.21
6	17.11
7	18.47
8	18.35
9	18.40
10	18.33

(a)

Construct a time series plot.

A time series plot contains a series of 10 points connected by line segments. The horizontal axis ranges from 0 to 11 and is labeled: Year. The vertical axis ranges from 0 to 20 and is labeled: Revenue ($ millions). The first point is at approximately (1, 18). The rest are plotted from left to right at regular increments of 1 year in a nearly horizontal direction until the fourth point. Afterwards, they are plotted in a downward, diagonal direction until the last point at approximately (10, 9). Consecutive points are close together with little scatter.

A time series plot contains a series of 10 points connected by line segments. The horizontal axis ranges from 0 to 11 and is labeled: Year. The vertical axis ranges from 0 to 20 and is labeled: Revenue ($ millions). The first point is at approximately (1, 16). The rest are plotted from left to right at regular increments of 1 year in a nearly horizontal direction until the fourth point. Afterwards, they are plotted in a downward, diagonal direction until the last point at approximately (10, 7). Consecutive points are close together with little scatter.

A time series plot contains a series of 10 points connected by line segments. The horizontal axis ranges from 0 to 11 and is labeled: Year. The vertical axis ranges from 0 to 20 and is labeled: Revenue ($ millions). The first point is at approximately (1, 7). The rest are plotted from left to right at regular increments of 1 year in an upward, diagonal direction until the seventh point. Afterwards, they are plotted in a nearly horizontal direction until the last point at approximately (10, 16). Consecutive points are close together with little scatter.

A time series plot contains a series of 10 points connected by line segments. The horizontal axis ranges from 0 to 11 and is labeled: Year. The vertical axis ranges from 0 to 20 and is labeled: Revenue ($ millions). The first point is at approximately (1, 9). The rest are plotted from left to right at regular increments of 1 year in an upward, diagonal direction until the seventh point. Afterwards, they are plotted in a nearly horizontal direction until the last point at approximately (10, 18). Consecutive points are close together with little scatter.

Comment on the appropriateness of a linear trend.

The time series plot shows that a linear trend is most appropriate.The time series plot shows that a curvilinear trend may be more appropriate. The time series plot shows that neither a linear nor a curvilinear trend is appropriate.

(b)

Using Minitab or Excel, develop a quadratic trend equation that can be used to forecast revenue (in millions of dollars). (Round your numerical values to three decimal places.)

T_t =

(c)

Using the trend equation developed in part (b), forecast revenue (in millions of dollars) in year 11. (Round your answer to two decimal places.)

$ million

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