The following data resulted from an experiment to assess the potential of unburnt colliery spoil as a medium for plant growth. The variables are x=acid extractable cations and y=exchangeable acidity/total cation exchange capacity.

\begin{array}{l}\begin{array} { c c c c c c c c } \hline x & - 23 & - 5 & 16 & 26 & 30 & 38 & 52 \\\hline x & 1.50 & 1.46 & 1.32 & 1.17 & .96 & .78 & .77 \\\hline\end{array}\\\\\begin{array} { l l l l l l l } \hline x & 58 & 67 & 81 & 96 & 100 & 113 \\\hline x & .91 & .78 & .69 & .52 & .48 & .55 \\\hline\end{array}\end{array}

Standardizing the independent variable x to obtain

x ^ { t } = ( x - \bar { x } ) / s _ { x }

and fitting the regression function

y = \vec { \beta } _ { 0 } + \vec\beta _ { 1 } x ^ { t } + \vec { \beta } _ { 2 } ( x ^{t}) ^ { 2 }

yielded the accompanying computer output. $The following data resulted from an experiment to assess the potential of unburnt colliery spoil as a medium for plant growth. The variables are x=acid extractable cations and y=exchangeable acidity/total cation exchange capacity. \begin{array}{l} \begin{array} { c c c c c c c c } \hline x & - 23 & - 5 & 16 & 26 & 30 & 38 & 52 \\ \hline x & 1.50 & 1.46 & 1.32 & 1.17 & .96 & .78 & .77 \\ \hline \end{array}\\\\ \begin{array} { l l l l l l l } \hline x & 58 & 67 & 81 & 96 & 100 & 113 \\ \hline x & .91 & .78 & .69 & .52 & .48 & .55 \\ \hline \end{array} \end{array} Standardizing the independent variable x to obtain x ^ { t } = ( x - \bar { x } ) / s _ { x } and fitting the regression function y = \vec { \beta } _ { 0 } + \vec\beta _ { 1 } x ^ { t } + \vec { \beta } _ { 2 } ( x ^{t}) ^ { 2 } yielded the accompanying computer output. a. Estimate \mu _ { y ^ { 50 } } . b. Compute the value of the coefficient of multiple determination. c. What is the estimated regression function \hat { \beta } _ { 10 } + \hat { \beta } _ { 1 } x + \hat { \beta } _ { 2 } x ^ { 2 } using the unstandardized variable x? d. What is the estimated standard deviation of \hat { \beta } _ { 2 } computed in part ( c )? e. Carry out a test using the standardized estimates to decide whether the quadratic term should be retained in the model. Repeat using the unstandardized estimates. Do your conclusions differ?$
a. Estimate

\mu _ { y ^ { 50 } }

.
b. Compute the value of the coefficient of multiple determination.
c. What is the estimated regression function

\hat { \beta } _ { 10 } + \hat { \beta } _ { 1 } x + \hat { \beta } _ { 2 } x ^ { 2 }

using the unstandardized variable x?
d. What is the estimated standard deviation of

\hat { \beta } _ { 2 }

computed in part ( c )?
e. Carry out a test using the standardized estimates to decide whether the quadratic term should be retained in the model. Repeat using the unstandardized estimates. Do your conclusions differ?

A Function Relating Y to X Is ___________ If by Means

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