Construct the Indicated Prediction Interval for an Individual Y $\hat { y } = 73.012 + 0.8859 x$

question 36

Multiple Choice

Construct the indicated prediction interval for an individual y.
-The regression equation for the given paired data is $\hat { y } = 73.012 + 0.8859 x$ and the standard error of estimate is $\mathrm { s_e } = 2.78807 .$ Find the $95 \%$ prediction interval of $\mathrm { y }$ for $\mathrm { x } = 37$ .
$\begin{array}{r|rrrrrr}\mathrm{x} & 25 & 26 & 36 & 36 & 40 & 48 \\\hline \mathrm{y} & 95 & 95 & 102 & 109 & 110 & 114\end{array}$

• A) \(73.0 < \mathrm { y } < 114.2\)
• B) \(97.4 < \mathrm { y } < 114.2\)
• C) \(73.0 < y < 105.8\)
• D) \(97.4 < \mathrm { y } < 10.8\)

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Definitions:

Homogeneous Products

Goods that are identical in quality and cannot be distinguished from one another by consumers, often found in perfectly competitive markets.

Differentiated Products

Goods or services that are distinct from those offered by competitors, making them non-identical and typically appealing to different consumer preferences.

Contestable Market

A market where entry and exit are costless enough that companies face potential competition, leading to competitive pricing and behavior as if the market were competitive, even if it’s dominated by a few firms.

Market Entry

The strategy or process by which a company enters a new market.