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

question 22

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: $y =$ $32.6 + 5.96 x - 0.48 x ^ { 2 }$ $$\begin{array} { | c | r c r | } \hline \text { Predictor } & \text { Coef } & S 2 D e v & T \\\hline \text { Constant } & 32.6 & 19.3 & 1.689 \\x & 5.96 & 2.41 & 2.473 \\x ^ { 2 } & - 0.48 & 0.22 & - 2.182 \\\hline\end{array}$$ S = 16.1 R-Sq = 43.9%.
ANALYSIS OF VARIANCE $$\begin{array} { | l | c c c c | } \hline \text { Source of Variation } & d f & \text { SS } & \text { MS } & F \\\hline \text { Regression } & 2 & 3452 & 1726 & 6.663 \\\text { Error } & 17 & 4404 & 259.059 & \\\hline \text { Total } & 19 & 7856 & & \\\hline\end{array}$$ What is the coefficient of determination? Explain what this statistic tells you about the model.

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Definitions:

Impairment

A decrease in the recoverable amount of an asset to below its carrying amount on the balance sheet, resulting in a charge to the company's earnings.

Cash-Generating Units

The smallest identifiable group of assets that generates cash inflows independently of other assets or groups of assets.

Business Combination

A transaction or event in which a buyer obtains control of one or more businesses.

Goodwill

An intangible asset reflecting the premium paid over the fair market value of assets during an acquisition, attributed to the company's brand, customer relations, and reputation.