Problem $3-7($Algo$)$

Freight car loadings over an $18-$week period at a busy port are as follows:

$\backslash$table$[[$Week$,$Number$],[1,400],[2,415],[3,430],[4,415],[5,430],[6,435],[7,465],[8,495],[9,525],[10,510],[11,540],[12,570],[13,575],[14,580],[15,610],[16,625],[17,640],[18,655]]$

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a$.$ Determine a linear trend line for expected freight car loadings.

Note: Round your intermediate calculations and final answers to $2$ decimal places.

hat$(Y)=$

$$

$+$

$$

b$.$ Use the above trend equation to predict expected loadings for Weeks $20$ & $21.$ Note: Round your final answers to $2$ decimal places.

The forecasted demand for Week $20$ is

and for Week $21$ is

c$.$ The manager intends to install new equipment when the volume exceeds $980$ loadings per week. Assuming the current trend continues, in which week $($at the earliest$)$ should the loading volume reach that level?

Note: Use the rounded answers, as required, from any previous part of this problem. Do not round any other intermediate calculations. Round your final answer to $2$ decimal places.

It should reach $980$ loadings in Week