Attracted by the possible returns from a portfolio of movies, hedge funds have invested in the movie industry by financially backing individual films and/or studios. The hedge fund Star Ventures is currently conducting some research involving movies involving Adam Sandler, an American actor, screenwriter, and film producer. As a first step, Star Ventures would like to cluster Adam Sandler movies based on their gross box office returns and movie critic ratings. Using the data in the file Sandler, apply k-means clustering with k = 3 to characterize three different types of Adam Sandler movies. Base the clusters on the variables Rating and Box. Rating corresponds to movie ratings provided by critics (a higher score represents a movie receiving better reviews). Box represents the gross box office earnings in 2015 dollars. Normalize the values of the input variables to adjust for the different magnitudes of the variables.

In the Data tab of the Rattle GUI - R window, uncheck the box next to Partition. For the Rating and Box variables, select the Input button. Select the Ignore button for the other variables and then click Execute button. In the Transform tab, in the Type: row, select Rescale and in the Normalize: row, select Recenter. Select the Rating and Box variables and then click the Execute button. In the Cluster tab, in the Type: row, select KMeans, de-select the box next to Iterate Clusters. Enter 3 in the Clusters: box, enter 42 in the Seed: box, and enter 1000 in the Runs: box. De-select the box next to Re-Scale. Then, click the Execute button. To generate various statistics on the clusters, on the Cluster tab, click Stats.

Click on the datafile logo to reference the data.

	Report the characteristics of each cluster including a count of movies, the average rating of movies, and the average box office earnings of movies in each cluster. How would you describe the movies in each cluster?
	Enter your answers for cluster sizes and correspoding data as they appear in JMP Pro output. Round your answers for Rating and Box Office (M$) to the nearest tenth.