Current$($Y$)$

Proposed$($X$)$

Current$($Y$)$

Proposed$($X$)$

$3\mathrm{.}1$

$3\mathrm{.}0$

$3\mathrm{.}1$

$3\mathrm{.}1$

$3\mathrm{.}4$

$3\mathrm{.}8$

$2\mathrm{.}9$

$2\mathrm{.}8$

$3\mathrm{.}3$

$3\mathrm{.}5$

$3\mathrm{.}3$

$3\mathrm{.}6$

$3\mathrm{.}6$

$4\mathrm{.}0$

$3\mathrm{.}0$

$4\mathrm{.}0$

$3\mathrm{.}5$

$3\mathrm{.}5$

$2\mathrm{.}1$

$2\mathrm{.}6$

$2\mathrm{.}7$

$3\mathrm{.}6$

$2\mathrm{.}7$

$3\mathrm{.}2$

$3\mathrm{.}3$

$3\mathrm{.}5$

$2\mathrm{.}4$

$2\mathrm{.}7$

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.$)$

Part $3$

b$.$ Is there a strong relationship between Y and$$ X$?$ Explain.

The correlation$$ coefficient, r$,$ is

$$

enter your response here. $($Enter your response rounded to three decimal$$ places.$)$

Part $4$

The coefficient of$$ determination, r squared$,$ is

$$

enter your response here. $($Enter your response rounded to three decimal$$ places.$)$

Part $5$

The standard error of estimate is

$$

enter your response here. $($Enter your response rounded to three decimal$$ places.$)$

Part $6$

The increases in X mostly result in

$$

in Y$.$ Also,

$$

enter your response here$\%$ of the variation in Y is explained by X$.$ The obtained value of the standard error of$$ estimate, in$$ turn, measures how closely the data on the dependent variable cluster around the

$$

mean

regression line

$.($Enter your response rounded to one decimal$$ place.$)$