Suppose you are interested in studying the relationship between the number of visitors a museum gets and the revenue of their gift shop. You take a sample of 27 different days and record the number of visitors and the revenue of the gift shop in dollars. Also suppose on the 27 days you sampled, the number of visitors ranged from 100 people to 600 people. You get the following regression line: ŷ 5.6x-419, where ŷ is the revenue in dollars and a is the number of visitors. We also get that r≈.57. (a) Give the value of the slope of this regression line. Interpret this value in the context of the situation. (b) Is there enough evidence for a correlation? Why or why not? (c) What does our model predict the revenue will be on a day where the museum gets 1000 visitors? Would you trust this prediction? Why or why not? (d) Suppose that the first day we visited the museum it had 220 visitors and made a revenue of 780 dollars. Calculate the residual for this data point. Make sure to include units. (e) According to our model how many visitors does the museum need to get for the gift shop to make 2000 dollars in revenue?
Suppose you are interested in studying the relationship between the number of visitors a museum gets and the revenue of their gift shop. You take a sample of 27 different days and record the number of visitors and the revenue of the gift shop in dollars. Also suppose on the 27 days you sampled, the number of visitors ranged from 100 people to 600 people. You get the following regression line: ŷ 5.6x-419, where ŷ is the revenue in dollars and a is the number of visitors. We also get that r≈.57. (a) Give the value of the slope of this regression line. Interpret this value in the context of the situation. (b) Is there enough evidence for a correlation? Why or why not? (c) What does our model predict the revenue will be on a day where the museum gets 1000 visitors? Would you trust this prediction? Why or why not? (d) Suppose that the first day we visited the museum it had 220 visitors and made a revenue of 780 dollars. Calculate the residual for this data point. Make sure to include units. (e) According to our model how many visitors does the museum need to get for the gift shop to make 2000 dollars in revenue?
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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EC1
Transcribed Image Text:Suppose you are interested in studying the relationship between the number of visitors a museum
gets and the revenue of their gift shop. You take a sample of 27 different days and record the
number of visitors and the revenue of the gift shop in dollars.
Also suppose on the 27 days you sampled, the number of visitors ranged from 100 people to 600
people.
You get the following regression line:
ŷ 5.6x419, where û is the revenue in dollars and a is the number of visitors.
We also get that r≈.57.
(a) Give the value of the slope of this regression line. Interpret this value in the context of the
situation.
(b) Is there enough evidence for a correlation? Why or why not?
(c) What does our model predict the revenue will be on a day where the museum gets 1000 visitors?
Would you trust this prediction? Why or why not?
(d) Suppose that the first day we visited the museum it had 220 visitors and made a revenue
of 780 dollars. Calculate the residual for this data point. Make sure to include units.
(e) According to our model how many visitors does the museum need to get for the gift shop
to make 2000 dollars in revenue?
Look back at Question 3. Suppose there was a day where the gift shop had not received one of its
stock shipments and lots of its merchandise was out of stock. Would we expect that day to have a
positive or negative residual? Why?
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