Slove by hand $.$production planning and inventory $.$Problem #$3$:

Shoreline Park in Mountain View, California, has kept close tabs on the number of patrons using the park since its opening in January $1993.$ For the first six months of $2013,$ the following figures were recorded:

$\backslash$table$[[$Month$,$Number of Patrons,Month,Number of Patrons$],[$January$,133,$April,$640],[$February$,183,$May,$1,876],[$March$,285,$June,$2,550]]$

a$.$ Draw a graph of these six data points. Assume that January $=$ period $1,$ February $=$ period $2,$ and so on$.$ Using a ruler, "eyeball" the best straight$-$line fit of the data. Estimate the slope and intercept from your graph.

b$.$ Compute the exact values of the intercept a and the slope $b$ from the regression equations.

c$.$ What are the forecasts obtained for July through December $2013$ from the regression equation determined in part $(b)?$