The Equation of the Regression Line for the Paired Data $\hat { y } = 6.1829 + 4.3394 \mathrm { x }$

question 6

Multiple Choice

The equation of the regression line for the paired data below is $\hat { y } = 6.1829 + 4.3394 \mathrm { x }$ and the standard error of estimate is $\mathrm { se } _ { \mathrm { e } } = 1.6419$ . Find the $99 \%$ prediction interval of $\mathrm { y }$ for $\mathrm { x } = 12$ .
$\begin{array}{r|rrrrrrr}\mathrm{x} & 9 & 7 & 2 & 3 & 4 & 22 & 17 \\\hline \mathrm{y} & 43 & 35 & 16 & 21 & 23 & 102 & 81\end{array}$

• A) \(56.4 < y < 68.5\)
• B) \(53.6 < y < 71.3\)
• C) \(59.9 < y < 64.9\)
• D) \(51.1 < y < 65.4\)

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Definitions:

Descriptive Study

A research method focused on observing, describing, and documenting aspects of a situation as it naturally occurs, without intervention by the researcher.

Random Sample

A sample of participants that fairly represents the population because each member of the population had an equal chance of being included.

Convenience Sample

A sampling technique where participants are selected based on their easy accessibility and proximity to the researcher.

Experiment

A scientific procedure undertaken to make a discovery, test a hypothesis, or demonstrate a known fact by controlling and varying variables.