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Predicting Room Rate from Hotel Star Rating

APSTAT-D3$IDJ

A popular travel website rates hotels using a star system. The worst hotels may receive $0$ stars or $1$ star and the most luxurious hotels are rated a maximum of $5$ stars. Nicky needs to book a hotel room in a large metropolitan area in order to attend a friend's wedding.

She decided to see if there was a relationship between the number of stars in a hotel's rating and the lowest price for staying at a hotel the night of her friend's wedding. From a random sample of data gathered on the travel website, she developed the following LSRL.

$$\hat { y } =27.54+50.27x$$

...where $x$ is the hotel's star rating and $\hat{y}$ is the predicted lowest price (in dollars) for booking a room at the hotel.

If Nicky wants to stay at a $4$ star hotel, what is the lowest price she would expect to pay for her room?

A

$\$50.27$

B

$\$182.35$

C

$\$201.08$

D

$\$228.62$

E

$\$311.24$