TABLE 15-7
a Chemist Employed by a Pharmaceutical Firm Has

question 57

True/False

TABLE 15-7
A chemist employed by a pharmaceutical firm has developed a muscle relaxant. She took a sample of 14 people suffering from extreme muscle constriction. She gave each a vial containing a dose (X) of the drug and recorded the time to relief (Y) measured in seconds for each. She fit a "centered" curvilinear model to this data. The results obtained by Microsoft Excel follow, where the dose (X) given has been "centered."
SUMMARY OUTPUT
$$\begin{array}{l}\begin{array} { l r } \begin{array} { l } \end{array} \\\hline\text { Regression Statistics }\\\hline \text { Multiple R } & 0.747 \\\text { RSquare } & 0.558 \\\text { Adjusted R Square } & 0.478 \\\text { Standard Error } & 863.1 \\\text { Observations } & 14 \\\hline\end{array}\\\text { ANOVA }\\\\\begin{array} { l r r r l l } \hline & d f & { \text { SS } } & \text { MS } & F & \text { Significance } F \\\hline \text { Regression } & 2 & 10344797 & 5172399 & 6.94 & 0.0110 \\\text { Residual } & 11 & 8193929 & 744903 & & \\\text { Total } & 13 & 18538726 & & & \\\hline\end{array}\\\\\begin{array} { l c c c c } \hline & \text { Coeff } & \text { Std Error } & t \text { Stut } & p \text {-value } \\\hline \text { Intercept } & 1283.0 & 352.0 & 3.65 & 0.0040 \\\text { CenDose } & 25.228 & 8.631 & 2.92 & 0.0140 \\\text { CenDoseSq } & 0.8604 & 0.3722 & 2.31 & 0.0410 \\\hline\end{array}\end{array}$$
-Referring to Table 15-7, suppose the chemist decides to use an F test to determine if there is a significant curvilinear relationship between time and dose. If she chooses to use a level of significance of 0.01 she would decide that there is a significant curvilinear relationship.

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Definitions:

Cost Function

A mathematical formula that calculates the total cost of producing a given quantity of output, factoring in fixed and variable costs.

Profit-Maximizing Output

The level of production at which a firm achieves the highest profit, where marginal cost equals marginal revenue.

Competitive Firm

A company that operates in a market where it must accept the prevailing prices set by the market through supply and demand.

Variable Factors

Inputs or resources whose usage level can be altered in the short run to influence the level of output produced.