₁₀ Suppose That X₁ Is Measured with Error $\beta$ ₀

question 18

Multiple Choice

_10. Suppose that X₁ is measured with error.
Y_i = $\beta$ ₀ + $\beta$ ₁X_1i + $\varepsilon$ _i
X_i = X*_1i + $\varepsilon$ _i
Which of the following is most accurate?

• A) The estimate of \(\beta\)₁hat will be larger than it should be.
• B) The estimate of \(\beta\)₁hat will be smaller than it should be.
• C) \(\beta\)₁hat will be biased toward zero.
• D) We know \(\beta\)₁hat will be biased, but do not know which direction.

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Definitions:

Immediate

Pertaining to something occurring or done without delay.

Heteronomous

Subject to external rules or laws rather than being independent in one's ethics or morality.

Autonomous

The capacity to make an informed, uncoerced decision independently.

Moral Development

The growth of an individual's understanding of right and wrong, including the formation of ethical and moral beliefs throughout life.