A statistical program is recommended.Consider the following time series.

t	1	2	3	4	5	6	7
Yt	83	61	45	36	30	30	34

(a)Construct a time series plot.

A time series plot contains a series of 7 points connected by line segments. The horizontal axis ranges from 0 to 8 and is labeled: Time Period (t). The vertical axis ranges from 0 to 90 and is labeled: Time Series Value. The points are plotted from left to right at regular increments of 1 period starting at period 1 and are between 20 to 75 on the vertical axis. Initially, the points are plotted in a downward, diagonal direction that becomes less steep moving from left to right. However, the last 2 points appear to be plotted in an upward, diagonal direction instead.

A time series plot contains a series of 7 points connected by line segments. The horizontal axis ranges from 0 to 8 and is labeled: Time Period (t). The vertical axis ranges from 0 to 90 and is labeled: Time Series Value. The points are plotted from left to right in a fairly consistent downward, diagonal direction at regular increments of 1 period starting at period 1. The points are between 30 to 85 on the vertical axis.

A time series plot contains a series of 7 points connected by line segments. The horizontal axis ranges from 0 to 8 and is labeled: Time Period (t). The vertical axis ranges from 0 to 90 and is labeled: Time Series Value. The points are plotted from left to right at regular increments of 1 period starting at period 1 and are between 30 to 85 on the vertical axis. Initially, the points are plotted in a downward, diagonal direction that becomes less steep moving from left to right. However, the last 2 points appear to be plotted in an upward, diagonal direction instead.

A time series plot contains a series of 7 points connected by line segments. The horizontal axis ranges from 0 to 8 and is labeled: Time Period (t). The vertical axis ranges from 0 to 90 and is labeled: Time Series Value. The points are plotted from left to right at regular increments of 1 period starting at period 1 and are between 30 to 85 on the vertical axis. The first 2 points are plotted in a downward, diagonal direction. However, the rest of the points are plotted in an upward, diagonal direction that becomes steeper moving from left to right.

What type of pattern exists in the data?

The time series plot exhibits a horizontal pattern.The time series plot exhibits a curvilinear trend. The time series plot exhibits a seasonal pattern.The time series plot exhibits a linear trend.

(b)Using statistical software, develop the quadratic trend equation for the time series. (Round your numerical values to two decimal places.)T_t=

(c)What is the forecast for

t= 8?

(Round your answer to one decimal place.)