Question

Question 1

The travel agency Paradise Retreats has developed a model to predict the price per night of holiday apartment rentals in the coast of Croatia:

?=550+11?1−5?2

?: price of the apartment per night (in kunas)

?1: area of the apartment (in square meters)

?2: distance to the beach (in km)

According to Paradise Retreats’ model:

How much more expensive (in kunas) will be the rental of a 60 square-meter apartment on the beachfront compared with a 60 square-meter apartment 10 km from the beach?

Introduce your answer as a positive number.

How much will the price per night decrease when the area of the apartment decreases by 20 square meters?

Introduce your answer as a positive number.

----------------------------------------------------------------

Question 2

The summary output of Paradise Retreats' model in Excel is in the tables below:

Regression Statistics
Multiple R	0.764437898
R Square	0.5843653
Adjusted R Square	0.555700838
Standard Error	315.8931794
Observations	60

	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%
Intercept	550	317.1379944	0.110883586	0.912472524	-613.4546286	683.785425
x1	11	7.187801286	1.304664049	0.202266328	-5.323038326	24.07837018
x2	5	9.990263453	3.509123492	0.001488311	14.62468522	55.48945112

According to the tables, which of the following statements about this regression model are true?

A) This regression model explains less than 60% of the variation of the price per night.

B) The area of the apartment is not significant at a confidence level of 95%.

C) The area of the apartment is not significant at a confidence level of 99%.

D) The area of the apartment is significant at a confidence level of 99%.

E) The distance to the beach is not significant at a confidence level of 99%.

F) None of the above.

----------------------------------------------------------------

Question 3

Paradise Retreats offer a wide range of options for an unforgettable holiday in Croatia. Their portfolio includes apartments on the coast and cabins in the mountains. On average, their customers book many more apartments than cabins every month. Paradise Retreats analyzed some historical data, did a chi-squared test and confirmed that the number of apartments booked every month follows a normal distribution with an average of 23 and a standard deviation of 7.

What is the probability that more than 29 apartments are booked through Paradise Retreats in a month?

Write your answer not as a percentage, but as a decimal number with 4 decimal places (e.g. if the probability is 87.56%, write 0.8756 in the answer box).

What is the probability that less than 21 apartments are booked through Paradise Retreats in a month?

Write your answer not as a percentage, but as a decimal number with 4 decimal places (e.g. if the probability is 87.56%, write 0.8756 in the answer box).

----------------------------------------------------------------

Question 4

The number of mountain cabins that are booked through Paradise Retreats every month follows a Poisson distribution with a mean of 4. At Paradise Retreats, they are considering to reduce the number of cabins included in their portfolio.

What is the probability that at least one cabin is booked through Paradise Retreats in any given month?

Write your answer not as a percentage, but as a decimal number with 4 decimal places (e.g. if the probability is 87.56%, write 0.8756 in the answer box).

If Paradise Retreats only has 3 cabins available for rent, what is the probability of not meeting the demand for cabins during a given month?

Write your answer not as a percentage, but as a decimal number with 4 decimal places (e.g. if the probability is 87.56%, write 0.8756 in the answer box).

Answer 1