Find the least squares linear regression equation for run time and production bu

Question

  Find the least squares linear regression equation for run time and production budget. Interpret the meaning of the slope and the y-intercept.

Source: boxofficemojo.com Winner of Best Picture Oscar Production Number of Year Picture Studio Box Office Noms Wins Release Budget run time % box office Theatres ($millions) ($million) (min) before nom 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

Explanation / Answer

Using MS-Excel data add-in:

We run the multiple linear regression as follows:

Interpretation:

1. All the independent variables are significant at 5% level

2. If all the independent variables are 0, the production budget will go negative

3. Interpretation of slopes:

Run time: One minute increase in run time increases the production budget by $0.285 mn (keeping other factors constant)

Box office: One million $ increase in box office increases the production budget by $0.188 mn (keeping other factors constant)

Number of theatre: unit increases in number of theatres increase production budget by $0.014 mn

All the variables are significant at 5% level

$1mn increase in production budget increaes the run time by 0.59 minutes

If there is no production budget the picture's expected run time will be 150 min

Regression equation for Production budget Regression Statistics Multiple R 0.871259 R Square 0.759093 Adjusted R Square 0.737836 Standard Error 19.22097 Observations 38 ANOVA df SS MS F Significance F Regression 3 39579.93 13193.31 35.71109 1.3E-10 Residual 34 12561.16 369.4457 Total 37 52141.09 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Intercept -56.0461 16.87211 -3.32182 0.002146 -90.3344 -21.7579 run time (min) 0.285219 0.107428 2.654967 0.011981 0.066898 0.503539 Box Office ($millions) 0.18841 0.04216 4.46891 8.29E-05 0.10273 0.27409 Number of Theatres 0.013943 0.005252 2.654935 0.011982 0.00327 0.024617

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