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

question 36

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 $$\begin{array} { | l | c c c c | } \hline \text { Source of Variation } & d f & \text { SS } & \text { MS } & F \\\hline \text { Regression } & 2 & 3452 & 1726 & 6.663 \\\text { Error } & 17 & 4404 & 259.059 & \\\hline \text { Total } & 19 & 7856 & & \\\hline\end{array}$$ Test to determine at the 10% significance level if the linear term should be retained.

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Definitions:

Trial Close

A soft questioning technique used by salespeople during the sales process to gauge a prospect's readiness to buy.

Sales Presentation

A pitch or demonstration given to potential buyers highlighting the benefits and features of a product or service.

Approach Phase

The initial stage in the sales process where the salesperson first contacts the potential customer, aiming to establish rapport and understand customer needs.

Building Rapport

The process of establishing a connection or trust with someone, essential in sales to facilitate open communication and understanding.