Question

"Real Estate Rent, Vacancy Rates Don't Always Tell The Story" reported in a local paper in January 2005 that "At first glance, office space in the city's market seems to violate the law of supply and demand, which says that the greater the supply of something relative to demand, the lower its price should be."

(a) If the so-called law of supply and demand were to hold, what kind of correlation should we expect from the regression of rental rate on vacancy rate?

closer to 0

closer to −1     

closer to +1

(b) Use this output to assess the size of the P-value.

Pearson correlation of VacancyRate and RentalRate = 0.107 T=+0.36

P-value is small

P-value is not small     

(c) Choose the most accurate of the following conclusions about the population of rental areas.

Rental rates decrease as vacancy rates rise for the sample, and there is evidence that this is the case for the population as well.

Rental rates do not decrease as vacancy rates rise for the sample, nor is there evidence of a relationship in the population.     

Rental rates do not decrease as vacancy rates rise for the sample, but there is evidence of some relationship in the population.

Rental rates do decrease as vacancy rates rise for the sample, but there is no evidence that this is the case for the population.

(d) Based on your answer to (c), is the article's title appropriate?

Yes

No     

(e) Would the P-value have been small if we had carried out the test with a one-sided alternative β₁ < 0?

Yes

No     

(f) Refer to this scatterplot of the data. A regression of rental rate (in dollars per square foot) on vacancy rate reports two unusual observations: one that has a great deal of influence on the line but a residual that is not particularly large, and another with a large residual but no undue influence on the line. Which one of these corresponds to the area with vacancy rate 0.52 and rental rate $21.85 per square foot?

the one that has a great deal of influence on the line but a residual that is not particularly large

the one with a large residual but no undue influence on the line  

Answer 1

(A) closer to -1 because if vacancyrate increases, the rental rate decreases, hence, negative correlation.

(B) P-value is not small

(C) Rental rates do not decrease as vacancy rates rise for the sample, but there is evidence of some relationship in the population. ( because Pearson correlation of VacancyRate and RentalRate = 0.107 )

(D)Yes, because Rental rates do not decrease as vacancy rates rise for the sample, but there is evidence of some relationship in the population.