Sundar Balakrishnan$,$ the general manager of Precision Engineering Corporation $($PEC$),$ thinks that his$$ firm's engineering services contracted to highway construction firms are directly related to the volume of highway construction business contracted with companies in his geographic area. He wonders if this is really$$ so$,$ and if it$$ is$,$ can this information help him plan his operations better by forecasting the quantity of his engineering services required by construction firms in each quarter of the$$ year? The following table presents the sales of his services and total amounts of contracts for highway construction over the past $8$ quarters.

$$

Quarter

$1$

$2$

$3$

$4$

$5$

$6$

$7$

$8$

Sales of PEC Services$($in $$$ thousands$)$

$9$

$11$

$15$

$8$

$12$

$12$

$13$

$15$

Contracts Released$($in $$$ thousands$)$

$150$

$175$

$197$

$175$

$185$

$196$

$205$

$223$

Part $2$

$$a$)$ Using the given$$ data, the$$ least$-$squares regression equation for predicting the level of demand of PEC$\text{'}$s services$$ is: $($Round your responses to two decimal$$ places.$)$

ModifyingAbove y with caretequals

$$

enter your response hereplus

$$

enter your response here$$x$,$

where ModifyingAbove y with caretequalsDependent Variable and xequalsIndependent Variable.

Part $3$

$$b$)$ The coefficient of correlationLOADING... for the$$ least$-$squares regression modelequals

$$

enter your response here. $($Round your response to two decimal$$ places.$)$

Part $4$

For the$$ least$-$squares model, the standard error of the estimateLOADING...equals$$$

$$

enter your response here thousand. $($Round your response to two decimal$$ places.$)$