Theater revenue, x (in millions of dollars) Rental revenue, y (in millions of dollars)   xy 61.2 10.5   642.6 25.6 6.7   171.52 44.5 7.0   311.5 25.3 8.6   217.58 21.5 5.1   109.65 28.4 3.0   85.2 65.8 9.2   605.36 29.9 5.5   164.45 14.3 1.6   22.88 26.5 11.6   307.4 12.7 9.6   121.92 61.3 15.5   950.15 6.5 2.6   16.9 48.9 16.0   782.4 36.4 11.8   429.52        y 2 4 6 8 10 12 14 16 18 x 10 20 30 40 50 60 70 0                                    Figure 1       Answer the following. Carry your intermediate computations to at least four decimal places, and round your answer as specified below.   What is the value of the sample correlation coefficient for these data? Round your answer to at least three decimal places.

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A movie studio wishes to determine the relationship between the revenue from rental of DVDs and videotapes of comedies and the revenue generated from the theatrical release of such movies. The studio has the following bivariate data from a sample of fifteen comedies released over the past five years. These data give the revenue 
x
 from theatrical release (in millions of dollars) and the revenue 
y
 from DVD and videotape rentals (in millions of dollars) for each of the fifteen movies. The data are displayed in the Figure 1 scatter plot. Also given are the products of the values for theater revenue and values for rental revenue for each of the fifteen movies. (These products, written in the column labelled "
xy
," may aid in calculations.)

 

Theater revenue, x
(in millions of dollars)
Rental revenue, y
(in millions of dollars)
  xy
61.2 10.5   642.6
25.6 6.7   171.52
44.5 7.0   311.5
25.3 8.6   217.58
21.5 5.1   109.65
28.4 3.0   85.2
65.8 9.2   605.36
29.9 5.5   164.45
14.3 1.6   22.88
26.5 11.6   307.4
12.7 9.6   121.92
61.3 15.5   950.15
6.5 2.6   16.9
48.9 16.0   782.4
36.4 11.8   429.52
      
y
2
4
6
8
10
12
14
16
18
x
10
20
30
40
50
60
70
0
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 Figure 1
 

 

 

Answer the following. Carry your intermediate computations to at least four decimal places, and round your answer as specified below.

 

What is the value of the sample correlation coefficient for these data? Round your answer to at least three decimal places.
 
 
 
 
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