Find the Least-Squares Regression Line and Use the Line to Make

question 175

Multiple Choice

Find the Least-Squares Regression Line and Use the Line to Make Predictions
-In order for a company's employees to work in a foreign office, they must take a test in the language of the country where they plan to work. The data below shows the relationship between the number of years that employees have studied a particular language and the grades they received on the proficiency exam. Find the equation of the regression line for the given data.
$\begin{array}{l|c|c|c|c|c|c|c|c|c|}\text { Number of years, } \mathrm{x} & 3 & 4 & 4 & 5 & 3 & 6 & 2 & 7 & 3 \\\hline \text { Grades on test, } \mathrm{y} & 61 & 68 & 75 & 82 & 73 & 90 & 58 & 93 & 72\end{array}$

• A) \(\hat {y} = 6.91 x + 46.26\)
• B) \(\hat { y } = 6.91 \mathrm { x } - 46.26\)
• C) \(\hat {y} = 46.26 x - 6.91\)
• D) \(\hat { y } = 46.26 x + 6.91\)

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Definitions:

Cause in Fact

A legal principle that establishes an event as the direct cause of an injury, required for proving negligence.

Res Ipsa Loquitur

A doctrine in tort law that infers negligence from the very nature of an accident or injury, in the absence of direct evidence on how any defendant behaved.

Causation

The relationship between cause and effect, where one event (the cause) directly leads to the occurrence of another event (the effect).

Duty of Care

A legal obligation imposed on individuals or organizations to adhere to a standard of reasonable care while performing acts that could foreseeably harm others.