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.

---

Definitions:

Working Capital

The disparity between an enterprise's existing assets and current debts, demonstrating its short-term financial status and operational performance.

Discount Rate

In discounted cash flow analysis, the interest rate that is used to evaluate the present value of anticipated cash flows.

Net Present Value

Net Present Value (NPV) is a financial metric that calculates the total value today of a series of future cash flows, adjusting for the time value of money.

Capital Budgeting

The process of planning and managing a company's long-term investments in major projects or assets.