15) Construct a scatter-plot, find the value of the linear correlation coefficient r, find the critical
value of r from Table A-6 by using  = 0.05, and determine whether there is a linear correlation
between the two variables. Listed below are the budgets (in millions of dollars) for randomly
selected movies. Does there appear to be a linear correlation between the money spent making
the movie and the amount that it recovered in theaters? Apart from the budge amount, identify
one other important factor that is likely to affect the amount that a movie earns.
Budget
Gross
62
65
90
64
50
48
35
57
200
601
100
146
90
47
 The scatter-plot looks like this (produced in Excel):
Gross
Correlation Movie Budget and Gross
Income
700
600
500
400
300
200
100
0
0
50
100
150
200
250
Budget
 The scatter-plot looks like this (produced in SPSS):
Correlation Between Movie Budget and Gross Income
600
Gross
400
200
0
0
50
100
Budget
150
200
 To calculate r, use the following terms:
 x  62  90  50  35  200  100  90  627
 y  65  64  48  57  601  146  47  1028
 xy  62  65  90  64  50  48  35  57  200  601  100 146  90  47 
4030  5760  2400  1995  120200  14600  4230  153215
 x 2  62 2  90 2  50 2  352  200 2  100 2  90 2 
3844  8100  2500  1225  40000  10000  8100  73769
 y 2  65 2  64 2  48 2  57 2  6012  146 2  47 2 
4225  4096  2304  3249  361201  21316  2209  398600
n xy   x  y 
7153215  627 1028
r


2
2
2
2
773769   627   7398600  1028
n x 2    x   n y 2    y 
1072502  644556
427949

516383  393129  2790200  1056784
123254  1733416
427949

 0.925848877117  0.926
462223.382862

427949
351.075490  1316.592671
 To calculate r, SPSS produced the following output:
Correlations
Budget
Budget
Gross
Pearson Correlation
Sig. (2-tailed)
N
Pearson Correlation
Sig. (2-tailed)
N
1
7
.926**
.003
7
**. Correlation is s ignificant at the 0.01 level
(2-tailed).
Gross
.926**
.003
7
1
7
 The critical value for  = 0.05 and n = 7 is: ±0.754
 Due to the fact that 0.926 exceeds the critical value of 0.754, we can conclude that
there IS a linear relationship between the budget and the gross income for movies.
 Other factors that might contribute to the success of a movie (in terms of income)
could include: the type of movie, the season that it is released, the audience, the
ratings, etc.