#$1.$ The Fastgro Fertilizer Company distributes fertilizer to various lawn and garden shops. The company must base its quarterly production schedule on a forecast of how many tons of fertilizer will be demanded from it$.$ The company has gathered this data for the past $3$ years.

a$)$ Compute the $3-$term $(3-$quarter$)$ moving average and the absolute value of the error, for $2016$ Q$4$ to $2019$ Q$1.$

b$)$ Compute the $5-$term $(5-$quarter$)$ moving average and the absolute value of the error for $2017$ Q$2$ to $2019$ Q$1.$

c$)$ Compute the linear trend line using a regression model for $2016$ Q$1$ to $2019$ Q$1.$ Also compute the absolute value of the error.

d$)$ Compare the forecasts developed in parts a$),$ b$),$ and c$)$ using MAD. Which method appears to be the most accurate? Do any of the methods exhibit any bias $($consistently higher or lower than the actual values$)?$ Show your answers in the spaces below the table.

e$)$ Graph the quarter on the $x$ axis and the demand on the $y$ axis and include the graph below. Can you identify any cycles or seasonal patterns? $($Highlight the two datasets, click Insert, then select Scatterplot with lines.$)$