THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION

question 2

Multiple Choice

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION:
A real estate broker is interested in identifying the factors that determine the price of a house.She wants to run the following regression: Y = β₀ + β₁X₁ + β₂X₂ + β₃X₃ + ε where Y = price of the house in $1,000s,X₁ = number of bedrooms,X₂ = square footage of living space,and X₃ = number of miles from the beach.Taking a sample of 30 houses,the broker runs a multiple regression and gets the following results:
= 123.2 + 4.59x₁ + 0.125x₂ - 6.04x₃,
= 103.2,
= 2.13,
= 0.062,
= 4.17,R² = 0.47,and
= 0.45 (adjusted) .
-What should the null and alternative hypotheses be for β₂?

• A)H₀ : β₂ = 0, H₁ : β₂ > 0
• B)H₀ : β₂ ≠ 0, H₁ : β₂ = 0
• C)H₀ : β₂ > 0, H₁ : β₂ < 0
• D)H₀ : β₂ = 0, H₁ : β₂ ≠ 0

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Definitions:

Alternative Hypothesis

A hypothesis that contradicts the null hypothesis, asserting there is a significant difference or effect.

Type I Error

The mistaken dismissal of a correct null hypothesis, often referred to as a "false positive."

Null Hypothesis

A statement or premise in statistics that implies no significant effect or relationship between variables, serving as a default position until evidence suggests otherwise.

Alternative Hypothesis

The hypothesis that contradicts the null hypothesis, typically proposing a new effect, difference, or relationship.