Question

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A)Determine the correlation coefficient between production budget and box office (dependent variable . .) and interpret its meaning. Plot a scatterplot.
B)Find the least squares linear regression equation for production budget (independent variable) and box office (dependent variable ). Use the equation to estimate the box office for a movie with a $45 million production budget. Interpret the meaning of the slope and the y-intercept (be specific using the context provided here).

Production Number of

Year Picture Studio Box Office Noms Wins Release Budget run time % box office Theatres
($millions) ($million) (min) before nom
2018 Green Book Uni. 85.1 5 3 16-Nov 23 130 49.9 2648
2017 The Shape of Water FoxS 63.9 13 4 1-Dec 19.5 119 47.7 2341
2016 Moonlight A24 27.9 8 3 21-Oct 1.5 110 56.9 650
2015 Spotlight ORF 45.1 6 2 6-Nov 20 128 64 1227
2014 Birdman FoxS 42.3 9 4 17-Oct 18 119 62.8 1213
2013 12 Years a Slave FoxS 56.7 9 3 18-Oct 20 133 68.9 1474
2012 Argo WB 136.0 10 7 12-Oct 45 120 81.1 3247
2011 The Artist Wein 44.5 10 5 24-Nov 15 100 19.4 662
2010 The King's Speech Wein 135.5 12 4 25-Nov 15 118 57.9 1680
2009 The Hurt Locker Sum. 16.4 9 6 26-Jun 15 130 77.3 535
2008 Slumdog Millionaire FoxS 141.3 10 8 12-Nov 15 120 31.6 2943
2007 No Country for Old Men Mira. 74.3 8 4 9-Nov 14 122 65.8 2037
2006 The Departed WB 132.4 5 4 6-Oct 90 150 92 3017
2005 Crash Lions 54.6 6 3 6-May 6.5 100 97.8 1905
2004 Million Dollar Baby WB 100.5 7 4 15-Dec 30 137 8.5 2375
2003 The Lord of the Rings: The Return of the King NL 377.0 11 11 17-Dec 94 200 89.7 3703
2002 Chicago Mira. 170.7 13 6 27-Dec 45 107 37.8 2701
2001 A Beautiful Mind Uni. 170.7 8 4 21-Dec 58 136 66.6 2250
2000 Gladiator DW 187.7 12 5 5-May 103 155 99.4 3188
1999 American Beauty DW 130.1 8 5 15-Sep 15 122 57.4 1990
1998 Shakespeare in Love Mira. 100.3 13 7 11-Dec 25 123 36.4 2030
1997 Titanic Par. 600.8 14 11 19-Dec 200 194 56.4 3265
1996 The English Patient Mira. 78.7 12 9 15-Nov 27 162 53.8 1409
1995 Braveheart Par. 75.6 10 5 24-May 72 177 88.7 2037
1994 Forrest Gump Par. 329.7 13 6 6-Jul 55 141 91.2 2365
1993 Schindler's List Uni. 96.1 12 7 15-Dec 22 194 30.9 1389
1992 Unforgiven WB 101.2 9 4 7-Aug 18 131 74.4 2087
1991 The Silence of the Lambs Orion 130.7 7 5 14-Feb 19 118 100 1642
1990 Dances with Wolves Orion 184.2 12 7 9-Nov 22 183 56.6 1636
1989 Driving Miss Daisy WB 106.6 9 4 15-Dec 16 99 31.5 1668
1988 Rain Man MGM 172.8 8 4 16-Dec 25 133 56.1 1590
1987 The Last Emperor Col. 44.0 9 9 20-Nov 25 219 27.1 877
1986 Platoon Orion 138.5 8 4 19-Dec 6 120 28.4 1564
1985 Out of Africa Uni. 87.1 11 7 20-Dec 10 161 63.8 1102
1984 Amadeus Orion 51.6 11 8 21-Sep 8 158 49.9 802
1983 Terms of Endearment Par. 108.4 11 5 23-Nov 11 131 67.2 1259
1982 Gandhi Col. 52.8 11 8 10-Dec 22 188 22.5 825
1981 Chariots of Fire Col. 59.0 7 4 25-Sep 9 123 13.2 810
1980 Ordinary People Par. 54.8 7 4 19-Sep 7 124 100 1005
1979 Kramer Vs. Kramer Col. 106.3 10 5 19-Dec 8 105 45.7 898
1978 The Deer Hunter Uni. 49.0 9 5 8-Dec 7 183 87 902

Answer 1

A)Determine the correlation coefficient between production budget and box office (dependent variable . .) and interpret its meaning. Plot a scatter plot.

the correlation between production budget and box office=0.8057

B)Find the least squares linear regression equation for production budget (independent variable) and box office (dependent variable ). Use the equation to estimate the box office for a movie with a $45 million production budget. Interpret the meaning of the slope and the y-intercept (be specific using the context provided here).

700 600 R2 0.649 500 400 300 200 100 50 100 150 200 250 Production Budget(x)

the linear regression is given as box_office(y)=43.43+2.360*production_budget(x)

for production budget x=45, the box office budget y=43.43+2.360*45=149.63

here slope=2.360 means if we change the one unit of production budget then there will be change in box office budget =2.360 unit in same direction i.e. increase in production increase in box office and vice-versa.

here intercept=43.43 meaning when production budget is zero then box office will be 43.43, some time intercept does not have practical interpretation like here also. if there would not be production budget so no film/movie can be made, ultimately no box-office.