Movie companies need to predict the gross receipts of individual movies after a
ID: 3327565 • Letter: M
Question
Movie companies need to predict the gross receipts of individual movies after a movie has debuted. The accompanying results are the first weekend gross, the national gross, and the worldwide gross (in millions of dollars) of six movies. Complete parts (a) through (d) below.
a.Compute the covariance between first weekend gross and national gross, first weekend gross and worldwide gross, and national gross and worldwide gross.
Compute the covariance between first weekend gross and national gross.
cov(X,Y)=
(Round to four decimal places as needed.)
Compute the covariance between first weekend gross and worldwide gross.
cov(X,Y)=
(Round to four decimal places as needed.)
Compute the covariance between national gross and worldwide gross.
cov(X,Y)=
(Round to four decimal places as needed.)
b. Compute the coefficient of correlation between first weekend gross and national gross, first weekend gross and worldwide gross, and national gross and worldwide gross.
Compute the coefficient of correlation between first weekend gross and national gross.
r=
(Round to four decimal places as needed.)
Compute the coefficient of correlation between first weekend gross and worldwide gross.
r=
(Round to four decimal places as needed.)
Compute the coefficient of correlation between national gross and worldwide gross.
r=
(Round to four decimal places as needed.)
c. Which is more valuable in expressing the relationship between first weekend gross, national gross, and wordwide gross, the covariance or the coefficient of correlation? Explain.
A.The correlation coefficient is more valuable for expressing the relationship between first weekend gross, national gross, and worldwide gross because it can prove that there is a causation effect between first weekend gross, national gross, and worldwide gross.
B.The correlation coefficient is more valuable for expressing the relationship between first weekend gross, national gross, and worldwide gross because it does not depend on the units used to measure first weekend gross, national gross, and worldwide gross.
C.The covariance is more valuable for expressing the relationship between first weekend gross, national gross, and worldwide gross because it measures the relative strength between first weekend gross, national gross, and worldwide gross.
d. Based on (a) and (b), what conclusions can be reached about the relationship between first weekend gross, national gross, and worldwide gross?
A.There is a strong negative linear relationship between first weekend gross and both national gross and worldwide gross. There is a strong positive linear relationship between national gross and worldwide gross.
B.There is a weak positive linear relationship between first weekend gross and both national gross and worldwide gross. There is a strong negative linear relationship between national gross and worldwide gross.
C.There is a weak negative linear relationship between first weekend gross and both national gross and worldwide gross. There is a strong positive linear relationship between national gross and worldwide gross.
Title
First Weekend
National Gross
Worldwide Gross
Movie A
90.047
317.295
976.889
Movie B
88.466
261.795
878.428
Movie C
93.331
249.6652
795.687
Movie D
102.529
290.922
896.363
Movie E
77.016
292.508
938.899
Movie F
77.502
301.387
934.156
Title
First Weekend
National Gross
Worldwide Gross
Movie A
90.047
317.295
976.889
Movie B
88.466
261.795
878.428
Movie C
93.331
249.6652
795.687
Movie D
102.529
290.922
896.363
Movie E
77.016
292.508
938.899
Movie F
77.502
301.387
934.156
Explanation / Answer
Here we need to use two excel function "=covar(set1, set2)" and ="correl(set1, set2)".
(a)
The covariance between first weekend gross and national gross is,
cov(X,Y)= -50.3440
The covariance between first weekend gross and worldwide gross is,
cov(X,Y)= -208.4107
The covariance between national gross and worldwide gross is,
cov(X,Y)=1247.9431
(b)
The coefficient of correlation between first weekend gross and national gross.
r = -0.2456
The coefficient of correlation between first weekend gross and worldwide gross.
r = -0.4071
The coefficient of correlation between national gross and worldwide gross.
r = 0.9405
(c)
Answer:
B.The correlation coefficient is more valuable for expressing the relationship between first weekend gross, national gross, and worldwide gross because it does not depend on the units used to measure first weekend gross, national gross, and worldwide gross.
(d)
Answer:
C.There is a weak negative linear relationship between first weekend gross and both national gross and worldwide gross. There is a strong positive linear relationship between national gross and worldwide gross.
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