When solving provide explanation for each step and clearly state the meaning of abbreviated formulae such as what MAD stands for.

$1.$ The number of fishing rods selling each day is given below. Perform analyses of the time

series to determine which model should be used for forecasting. $(10$ points$)$

a$.3$ day moving average analysis

b$.4$ day moving average analysis

c$.3$ day weighted moving average analysis with weights w$1=0\mathrm{.}2,$ w$2=0\mathrm{.}3$ and w$3=0\mathrm{.}5$ with

w$1$ on the oldest data

d$.$ exponential smoothing analysis with a $=0\mathrm{.}3.$

e$.$ Which model provides a better fit of the data?

f$.$ Forecast day $13$ sales of fishing rods using the model chosen in part $($e$).$

Day Rods sold

$160$

$270$

$3110$

$480$

$570$

$685$

$7115$

$8105$

$965$

$1075$

$1195$

$1285$