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					   A company that has distribution rights to home video sales of previously released movies           Observation Gross     Videos
   would like to be able to estimate the number of units that it can expect to sell. Data are                 1       1.1     57.18
   available for 30 movies that indicate the box office gross (in millions of dollars) and the number         2      1.13     26.17
   of units sold (in thousands) of home videos.                                                               3      1.18     92.79
                                                                                                              4      1.25      61.6
a)                                                                                                            5      1.44      46.5
                       Predicting Home Video Sales w/ Box                                                     6      1.53     85.06
                                         Office Gross                                                         7      1.53    103.52
                                                            y = 4.333x + 76.535                               8      1.69     30.88
                                                                   2
                                                                 R = 0.728                                    9      1.74     49.29
              400                                                                                            10      1.77     24.14
      Video sales (thousands)




              350                                                                                            11      2.42    115.31
              300                                                                                            12      5.34     87.04
              250                                                                                            13       5.7    128.45
                                                                                                             14      6.43    126.64
              200
                                                                                                             15      8.59    107.28
              150                                                                                            16      9.36     190.8
              100                                                                                            17      9.89    121.57
                50                                                                                           18     12.66     183.3
                 0                                                                                           19     15.35    204.72
                    0         10         20       30      40         50       60                             20     17.55    112.47
                                                                                                             21     17.91    162.95
                                 Box office gross (millions of $)                                            22     18.25     109.2
                                                                                                             23     23.13    280.79
                                                                                                             24     27.62    229.51
b)                                                                                                           25     37.09    277.68
The results of fitting a line with the least-squares method are visible above, in the right-hand             26     40.73    226.73
corner of the scatter diagram.                                                                               27     45.55    365.14
                                                                                                             28     46.62    218.64
c)                                                                                                           29      54.7    286.31
If S=Video Sales and B=box office gross, then the regression equation would be: S  .5  .33B
                                                                                           76 4              30     58.51    254.58

d)
The intercept term, 76.5, tells us that predicted sales of a movie that made nothing at the box office
would be 76,535 units.
The slope coefficient, 4.333, says that every one-million dollar increase in box office gross raises
our prediction of video sales by 4,333.

e)
To predict video sales for a movie with a box office gross of $20 million, we "plug" $20 million into
the regression equation:
           76.5+4.33*20=               163.2
Thus, we'd expect the video to sell 163,200 units.

f)
Other factors that might affect video sales:
Quality of reviews in books of video reviews, e.g. that by Leonard Maltin.
Genre, perhaps children's movies do better than adult titles, given that children watch the same video many times.
Popular actor or actress in leading role; maybe movies with high-profile leads have "longer legs."

				
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posted:4/22/2014
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