The Following Data Resulted from an Experiment to Assess the Potential

Essay

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?