a. Develop an estimated regression equation with the amount of television advertising as the independent variable (to 1 decimal). Revenue = TVAdv b. Develop an estimated regression equation with both television advertising and newspaper advertising as the independent variables (to 2 decimals). Revenue = TVAdv + NVAdv c. Is the estimated regression equation coefficient for television advertising expenditures the same in part (a) and in part (b)? - Select your answer - Interpret the coefficient in each case.
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.
a. Develop an estimated regression equation with the amount of television advertising as the independent variable (to 1 decimal).
![The owner of Showtime Movie Theaters, Inc., would like to predict weekly gross revenue as a function of advertising expenditures. Historical data for a sample of eight weeks follow:
| Weekly Gross Revenue ($1,000s) | Television Advertising ($1,000s) | Newspaper Advertising ($1,000s) |
|-----------------------------------|------------------------------------|------------------------------------|
| 104 | 5.0 | 1.5 |
| 90 | 2.0 | 2.0 |
| 95 | 4.0 | 1.5 |
| 92 | 2.5 | 2.5 |
| 100 | 3.0 | 3.3 |
| 94 | 3.5 | 2.3 |
| 95 | 4.2 | 4.2 |
| 96 | 3.0 | 2.5 |
**Questions:**
a. Develop an estimated regression equation with the amount of television advertising as the independent variable (to 1 decimal).
\[ \text{Revenue} = \_\_\_\_ + \_\_\_\_ \times \text{TVAdv} \]
b. Develop an estimated regression equation with both television advertising and newspaper advertising as the independent variables (to 2 decimals).
\[ \text{Revenue} = \_\_\_\_ + \_\_\_\_ \times \text{TVAdv} + \_\_\_\_ \times \text{NVAdv} \]
c. Is the estimated regression equation coefficient for television advertising expenditures the same in part (a) and in part (b)?
- Select your answer -
**Interpret the coefficient in each case:**
- In - Select your answer -, the coefficient is an estimate of the change in revenue due to a one-unit change in television advertising expenditures.
- In - Select your answer -, the coefficient is an estimate of the change in revenue due to a one-unit change in television advertising expenditures with the amount of newspaper advertising held constant.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ffc8e2d68-695c-49ad-a9b1-8d66f1d1c9ea%2F5a20191a-da13-4015-8382-fff71ef6c5fc%2Fyfem62_processed.jpeg&w=3840&q=75)
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