Consider the following time series data.

Given Table

t yt

$15$

$210$

$38$

$413$

$516$

$618$

$720$

$821$

$925$

$1025$

$1129$

$1230$

$1330$

$1433$

$1535$

$1639$

$1740$

$1842$

$1945$

$2046$

$2148$

$2249$

$2353$

$2456$

$2559$

$($a$)$

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

The time series plot shows a nonlinear trend.

The time series plot shows a horizontal pattern.

The time series plot shows a downward linear trend.

The time series plot shows an upward linear trend.

The time series plot shows a seasonal pattern.

$($b$)$

Use simple linear regression analysis to find the estimated parameters for the line that minimizes MSE for this time series. $($Round your answers to two decimal places.$)$

b$0=$

b$1=$

$($c$)$

What is the forecast for

t $=26?$

$($Round your answer to two decimal places.$)$