At a hydrocarbon processing$$ factory, process control involves periodic analysis of samples for a certain process quality parameter. The analytic procedure currently used is costly and time consuming. A faster and more economical alternative procedure has been proposed.$$ However, the numbers for the quality parameter given by the alternative procedure are somewhat different from those given by the current$$ procedure, not because of any inherent errors but because of changes in the nature of the chemical analysis.

Management believes that if the numbers from the new procedure can be used to forecast reliably the corresponding numbers from the current$$ procedure, switching to the new procedure would be reasonable and cost effective. The following data were obtained for the quality parameter by analyzing samples using both$$ procedures:

$$

Current$($Y$)$

Proposed$($X$)$

Current$($Y$)$

Proposed$($X$)$

$2\mathrm{.}62\mathrm{.}6$

$3\mathrm{.}03\mathrm{.}0$

$3\mathrm{.}13\mathrm{.}1$

$3\mathrm{.}13\mathrm{.}1$

$3\mathrm{.}73\mathrm{.}7$

$3\mathrm{.}83\mathrm{.}8$

$2\mathrm{.}52\mathrm{.}5$

$3\mathrm{.}03\mathrm{.}0$

$2\mathrm{.}92\mathrm{.}9$

$3\mathrm{.}33\mathrm{.}3$

$3\mathrm{.}33\mathrm{.}3$

$3\mathrm{.}63\mathrm{.}6$

$3\mathrm{.}63\mathrm{.}6$

$4\mathrm{.}04\mathrm{.}0$

$3\mathrm{.}43\mathrm{.}4$

$4\mathrm{.}04\mathrm{.}0$

$3\mathrm{.}73\mathrm{.}7$

$3\mathrm{.}53\mathrm{.}5$

$2\mathrm{.}12\mathrm{.}1$

$2\mathrm{.}62\mathrm{.}6$

$2\mathrm{.}72\mathrm{.}7$

$3\mathrm{.}63\mathrm{.}6$

$2\mathrm{.}62\mathrm{.}6$

$3\mathrm{.}03\mathrm{.}0$

$2\mathrm{.}22\mathrm{.}2$

$3\mathrm{.}73\mathrm{.}7$

$2\mathrm{.}92\mathrm{.}9$

$2\mathrm{.}92\mathrm{.}9$

Part $2$

a$.$ Use linear regression to find a relation to forecast$$ Y$,$ which is the quality parameter from the current$$ procedure, using the values from the proposed$$ procedure, X$.$

The forecasting model is given by the equation Yequals$=$enter your response hereplus$+$enter your response hereX. $($Enter your responses rounded to three decimal$$ places