$1.$ Find the value of t for Quarter $42019.$

$2.$ Find the predicted Amazon sales in Quarter $4$ of $2019$ based on trend and seasonality.

$3.$ Find the predicted Amazon sales in Quarter $1$ of $2020$ based on trend and seasonality.

$4.$ Find the residual for the Amazon sales in Quarter $4$ of $2019($nd the residual based on the model

accounting for trend and seasonality$).$

$5.$ Find the predicted residual in Quarter $1$ of $2020$ using the AR$(1)$ model.

Use at least $4$ decimal places with all your calculations.

$6.$ What is the updated forecast for the Amazon Sales in Quarter $1$ of $2020$ based on trend, seasonality and the residual forecast?

Use at least $4$ decimal places with all your calculations.

$7.$ On page $2$ of the homework output is the time series plot for this amazon dataset. We have also estimated $3$ different models. One model accounts for the quadratic trend, another models only the seasonality and the $3$rd model incorporates both the seasonality and the quadratic trend. For each of these models we created residual plots. These residual plots are given in plots A$,$ B and C but in no particular order.

$($a$)$ Which residual plot $($Plot A$,$ Plot B or Plot C$)$ was produced from the model accounting only for the trend? Think about how a residual is calculated before considering your answer.

$($b$)$ Which residual plot $($Plot A$,$ Plot B or Plot C$)$ was produced from the model accounting only for the seasonality? Think about how a residual is calculated before considering your answer.