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, the movie, and x, = total book sales prior to movie release. All units are in millions of dollars. first-year box office receipts of the movie, x, total production costs of the movie, x3 = total promotional costs of %D X2 8.5 12.9 Хз X4 85.1 5.1 4.7 106.3 5.8 8.8 50.2 5.2 2.1 15.1 130.6 10.7 8.4 12.2 54.8 3.1 2.9 10.6 30.3 3.5 1.2 3.5 79.4 9.2 3.7 9.7 91.0 9.0 7.6 5.9 135.4 15.1 7.7 20.8 7.9 89.3 10.2 4.5
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.
(d) Write out the regression equation. (Use 2 decimal places.)
| x1 = | + x2 | + x3 | + x4 |
If x2 (production costs) and x4 (book sales) were held fixed but x3 (promotional costs) were increased by 0.7 million dollars, what would you expect for the corresponding change in x1 (box office receipts)? (Use 2 decimal places.)
(e) Test each coefficient in the regression equation to determine if it is zero or not zero. Use level of significance 5%. (Use 2 decimal places for t and 3 decimal places for the P-value.)
| t | P-value | |
| β2 | ||
| β3 | ||
| β4 |
(f) Find a 90% confidence interval for each coefficient. (Use 2 decimal places.)
| lower limit | upper limit | |
| β2 | ||
| β3 | ||
| β4 |
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