An Avid Football Fan Was in the Process of Examining $$y = \beta _ { 0 } + \beta _ { 1 } x + \beta _ { 2 } x ^ { 2 } + \varepsilon$$

question 55

Essay

An avid football fan was in the process of examining the factors that determine the success or failure of football teams. He noticed that teams with many rookies and teams with many veterans seem to do quite poorly. To further analyse his beliefs, he took a random sample of 20 teams and proposed a second-order model with one independent variable. The selected model is: $$y = \beta _ { 0 } + \beta _ { 1 } x + \beta _ { 2 } x ^ { 2 } + \varepsilon$$ .
where
y = winning team's percentage.
x = average years of professional experience.
The computer output is shown below:
THE REGRESSION EQUATION IS: $y =$ $32.6 + 5.96 x - 0.48 x ^ { 2 }$ $$\begin{array} { | c | r r r | } \hline \text { Predictor } & \text { Coef } & \text { SyDev } & \text { T } \\\hline \text { Constant } & 32.6 & 19.3 & 1.689 \\x & 5.96 & 2.41 & 2.473 \\x ^ { 2 } & - 0.48 & 0.22 & - 2.182 \\\hline\end{array}$$ S = 16.1 R-Sq = 43.9%.
ANALYSIS OF VARIANCE $$\begin{array} { | l | c c c c | } \hline \text { Source of Variation } & d f & \text { SS } & M S & F \\\hline \text { Regression } & 2 & 3452 & 1726 & 6.663 \\\text { Error } & 17 & 4404 & 259.059 & \\\hline \text { Total } & 19 & 7856 & & \\\hline\end{array}$$ Test to determine at the 10% significance level whether the $x ^ { 2 }$ term should be retained.

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Definitions:

Organizational Culture

The shared values, beliefs, attitudes, and practices that characterize an organization and influence its members' behavior.

Team Work

A collaborative effort of a group to achieve a common goal or to complete a task in the most effective and efficient way.

Incremental Increases

Gradual enhancements or raises in salary or benefits over time.

Economic Value

The worth of a good or service determined by the market forces of demand and supply, or the utility it provides to individuals or society.