Use Technology to Find a Logistic Regression Curve $y = \frac { N } { 1 + A b ^ { - x } }$

question 37

Multiple Choice

Use technology to find a logistic regression curve $y = \frac { N } { 1 + A b ^ { - x } }$ approximating the given data. (Round b to three significant digits and A and N to two significant digits.) $$\begin{array} { | l | l | l | l | l | l | l | } \hline x & 0 & 20 & 40 & 60 & 80 & 100 \\\hline y & 2.2 & 3.8 & 5.0 & 6.1 & 6.8 & 6.9 \\\hline\end{array}$$

• A) \(y = \frac { 7.2 } { 1 + 2.2 \left( 1.04 ^ { - x } \right) }\)
• B) \(y = \frac { 7.2 } { 4.4 \left( 1.04 ^ { - x } \right) }\)
• C) \(y = \frac { 5.2 } { 1 + 2.2 \left( 1.04 ^ { - x } \right) }\)
• D) \(y = \frac { 5.2 } { 1 + 4.4 \left( 2.08 ^ { - x } \right) }\)
• E) \(y = \frac { 7.2 } { 1 + 2.2 \left( 2.08 ^ { - x } \right) }\)

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Definitions:

Few Firms

A market structure characterized by a small number of companies dominating the industry, often leading to oligopolistic competition.

Optimal Strategy

A method or plan chosen to bring about a desired future, such as achievement of a goal or solution to a problem, where the choice is made to maximize effectiveness or efficiency.

Oligopolists

Firms that are part of an oligopoly, possessing significant market power which allows them to influence the market's prices, output, and overall conditions.

Unique Product

A good or service that is distinct from others in the market due to its unique features, design, or branding.