Consider the following time series data.

$\backslash$table$[[$Quarter$,$Year $1,$Year $2,$Year $3],[1,5,7,8],[2,1,2,5],[3,2,4,5],[4,6,8,9]]$

$($a$)$ Construct a time series plot. What type of pattern exists in the data?

The time series plot shows a horizontal pattern and no seasonal pattern in the data.

The time series plot shows a linear trend and a seasonal pattern in the data.

The time series plot shows a linear trend and no seasonal pattern in the data.

The time series plot shows a horizontal pattern, but there is also a seasonal pattern in the data.

$x_1=1$ if quarter $1,0$ otherwise; $x_2=1$ if quarter $2,0$ otherwise; $x_3=1$ if quarter $3,0$ otherwise

hat$(y{)}_t=$

$($c$)$ Compute the quarterly forecasts for the next year based on the model you developed in part $($b$).($Round your answers to two decimal places.$)$

quarter $1$ forecast

quarter $2$ forecast

quarter $3$ forecast

quarter $4$ forecast

hat$(y{)}_t=$

$($e$)$ Compute the quarterly forecasts for the next year based on the model you developed in part $($d$).($Round your answers to two decimal places.$)$

quarter $1$ forecast

quarter $2$ forecast

quarter $3$ forecast

quarter $4$ forecast