The Following Data Resulted from an Experiment to Assess the Potential

question 26

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?

---

Definitions:

Embezzled Funds

Money that is dishonestly taken from an employer or organization by someone in a position of trust, typically for personal use.

Unqualified Opinion

An auditor's report that the financial statements of an entity present fairly its affairs in all material respects according to the applicable financial reporting framework.

CPA

Certified Public Accountant, a professional designation given to accountants who pass a licensing examination in accounting.

GAAP

Generally Accepted Accounting Principles, a collection of commonly-followed accounting rules and standards for financial reporting in the United States.