The owner of Showtime Movie Theaters, Inc., used multiple regression analysis to predict gross revenue (y) as a function of television advertising (x 1) and newspaper advertising (x 2). The estimated regression equation was Weekly Gross Revenue ($1000s) Televison Advertising ($1000s) Newspaper Advertising ($1000s) 97 6 1.5 91 3 2 95 5 2.5 93 3.5 2.5 96 4 4.3 94 4.5 2.3 95 3.5 4.2 95 4 3.5 ŷ = 82.5 + 2.01 x 1 + 1.26 x 2 The computer solution provided SST = 24 and SSR = 22.876. Compute R 2 and R a 2 (to 3 decimals). R 2 R a 2 When television advertising was the only independent variable, R 2 = 0.551 and R a 2 = 0.476. Are the multiple regression analysis results preferable?
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.
The owner of Showtime Movie Theaters, Inc., used multiple
| Weekly Gross Revenue ($1000s) | Televison Advertising ($1000s) | Newspaper Advertising ($1000s) |
| 97 | 6 | 1.5 |
| 91 | 3 | 2 |
| 95 | 5 | 2.5 |
| 93 | 3.5 | 2.5 |
| 96 | 4 | 4.3 |
| 94 | 4.5 | 2.3 |
| 95 | 3.5 | 4.2 |
| 95 | 4 | 3.5 |
ŷ = 82.5 + 2.01 x 1 + 1.26 x 2
The computer solution provided SST = 24 and SSR = 22.876.
- Compute R 2 and R a 2 (to 3 decimals).
R 2 R a 2 - When television advertising was the only independent variable, R 2 = 0.551 and R a 2 = 0.476. Are the multiple regression analysis results preferable?
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