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 β₃?

Question

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 β₃?

Quizplus · Accepted Answer

The null hypothesis should be that β₃= 0 (meaning that the number of miles from the beach does not significantly affect the price of the house), and the alternative hypothesis should be that β₃< 0 (meaning that the number of miles from the beach has a negative effect on the price of the house). This is because a lower number of miles from the beach is likely to be seen as more desirable, and therefore have a positive effect on the price, while a higher number of miles from the beach is likely to be seen as less desirable, and therefore have a negative effect on the price.