Revenues of popular movies. The Internet Movie Database

(www.imdb.com) monitors the gross revenues of all major motion pictures. The table on p. 791 gives both the domestic (United States and Canada) and international gross revenues for a sample of 22 popular movies.

a. Write a first-order model for international gross revenues y as a function of domestic gross revenues x.

b. Write a second-order model for international gross revenues y as a function of domestic gross revenues x.

c. Construct a scatterplot of these data. Which of the models appears to be a better choice for explaining variation in international gross revenues?

d. Fit the model of part b to the data and investigate its usefulness. Is there evidence of a curvilinear relationship between international and domestic gross revenues?
Test, using a = .05.

e. On the basis of your analysis in part

d, which of the two models better explains the variation in international gross revenues?

Movie (Year) Domestic Gross ($ millions) International Gross ($ millions)
Avatar (2009) 760.5 2,021.0 Titanic (1997) 600.8 1,234.6 The Dark Knight (2008) 533.3 464.0 Pirates of the Caribbean (2006) 423.0 642.9 E.T. (1982) 434.9 321.8 Spider Man (2002) 403.7 417.9 Frozen (2013) 400.7 867.1 The Hunger Games (2012) 408.0 283.2 Jurassic Park (1993) 356.8 563.0 Lion King (1994) 328.4 455.0 Harry Potter Sorcerer’s Stone (2001) 317.6 651.1 Inception (2010) 291.4 468.2 Sixth Sense (1999) 293.5 368.0 The Hangover (2009) 277.3 201.6 Jaws (1975) 260.0 210.6 Ghost (1990) 217.6 300.0 Saving Private Ryan (1998) 216.1 263.2 Gladiator (2000) 187.7 258.3 Dances with Wolves (1990) 184.2 240.0 The Exorcist (1973) 204.6 153.0 My Big Fat Greek Wedding (2002) 241.4 115.1 Rocky IV (1985) 127.9 172.6