A motion picture industry analyst is studying movies based on epic novels. The following data were obtained for 10 Hollywood movies made in the past five years. Each movie was based on an epic novel. For these data, x, = first-ycar box office receipts of the movie, x, = total production costs of the movie, x3 = total promotional costs of the movie, and x4 - total book sales prior to movie release. All units are in millions of dollars. 85.1 х X2 8.5 12.9 5.2 10.7 3.1 3.5 9.2 9.0 5.1 5.8 2.1 8.4 2.9 1.2 3.7 7.6 7.7 4.7 8.8 106.3 15.1 130.6 54.8 30.3 79.4 12.2 10.6 3.5 9.7 5.9 91.0 135.4 15.1 20.8 89.3 10.2 4.5 7.9
Correlation
Correlation defines a relationship between two independent variables. It tells the degree to which variables move in relation to each other. When two sets of data are related to each other, there is a correlation between them.
Linear Correlation
A correlation is used to determine the relationships between numerical and categorical variables. In other words, it is an indicator of how things are connected to one another. The correlation analysis is the study of how variables are related.
Regression Analysis
Regression analysis is a statistical method in which it estimates the relationship between a dependent variable and one or more independent variable. In simple terms dependent variable is called as outcome variable and independent variable is called as predictors. Regression analysis is one of the methods to find the trends in data. The independent variable used in Regression analysis is named Predictor variable. It offers data of an associated dependent variable regarding a particular outcome.
(b) For each pair of variables, generate the
| r | r2 | |
| x1, x2 | ||
| x1, x3 | ||
| x1, x4 | ||
| x2, x3 | ||
| x2, x4 | ||
| x3, x4 |
What percent of the variation in box office receipts can be attributed to the corresponding variation in production costs? (Use 1 decimal place.)
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