A movie studio wishes to determine the relationship between the revenue from rental of DVDS and videotapes of comedies and the revenue generated from the theatrical release of such movies. The studio has the following bivariate data from a sample of fifteen comedies released over the past five years. These data give the revenue x from theatrical release (in millions of dollars) and the revenue y from DVD and videotape rentals (in millions of dollars) for each of the fifteen movies. The data are displayed in the Figure 1 scatter plot. Also given is the product of the theater revenue and the rental revenue for each of the fifteen movies. (These products, written in the column labelled "xy", may aid in calculations.) Theater Rental revenue, y (in millions of dollars) revenue, x ху (in millions of dollars) 14.1 2.6 36.66 25.8 . 6.7 172.86 7.0 2.6 18.2 27.7 11.7 324.09 31.4 5.3 166.42 49.3 14.9 734.57 36.2 12.5 452.5 20.5 4.7 96.35 65.9 9.3 612.87 60.2 15.7 945.14 25.7 8.9 228.73 Theater revenue 61.8 9.9 611.82 (in millions of dollars) 27.2 2.7 73.44 Figure 1 13.6 9.7 131.92 44.5 7.1 315.95 Rental revenue (in millions of dollars)

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A movie studio wishes to determine the relationship between the revenue from rental of DVDs and videotapes of comedies and the revenue generated from the theatrical release of such movies. The studio has the following bivariate data from a sample of fifteen comedies released over the past five years. These data give the revenue \( x \) from theatrical release (in millions of dollars) and the revenue \( y \) from DVD and videotape rentals (in millions of dollars) for each of the fifteen movies. The data are displayed in the Figure 1 scatter plot. Also given is the product of the theater revenue and rental revenue for each of the fifteen movies. (These products, written in the column labeled "xy", may aid in calculations.)

| **Theater revenue, \( x \)** | **Rental revenue, \( y \)** | **\( xy \)**  |
|------------------------------|-----------------------------|---------------|
| 14.1                         | 2.6                         | 36.66         |
| 25.8                         | 6.7                         | 172.86        |
| 7.0                          | 2.6                         | 18.2          |
| 27.7                         | 11.7                        | 324.09        |
| 31.4                         | 5.3                         | 166.42        |
| 49.3                         | 14.9                        | 734.57        |
| 36.2                         | 12.5                        | 452.5         |
| 20.5                         | 4.7                         | 96.35         |
| 65.9                         | 9.3                         | 612.87        |
| 60.2                         | 15.7                        | 945.14        |
| 13.9                         | 8.9                         | 123.71        |
| 22.5                         | 8.9                         | 228.73        |
| 61.8                         | 9.9                         | 611.82        |
| 27.2                         | 2.7                         | 73.44         |
| 44.5                         | 7.1                         | 315.95        |

### Figure 1: Scatter Plot Explanation
- **X-Axis:** Represents theater revenue in millions of dollars.
- **Y-Axis:** Represents rental revenue
Transcribed Image Text:A movie studio wishes to determine the relationship between the revenue from rental of DVDs and videotapes of comedies and the revenue generated from the theatrical release of such movies. The studio has the following bivariate data from a sample of fifteen comedies released over the past five years. These data give the revenue \( x \) from theatrical release (in millions of dollars) and the revenue \( y \) from DVD and videotape rentals (in millions of dollars) for each of the fifteen movies. The data are displayed in the Figure 1 scatter plot. Also given is the product of the theater revenue and rental revenue for each of the fifteen movies. (These products, written in the column labeled "xy", may aid in calculations.) | **Theater revenue, \( x \)** | **Rental revenue, \( y \)** | **\( xy \)** | |------------------------------|-----------------------------|---------------| | 14.1 | 2.6 | 36.66 | | 25.8 | 6.7 | 172.86 | | 7.0 | 2.6 | 18.2 | | 27.7 | 11.7 | 324.09 | | 31.4 | 5.3 | 166.42 | | 49.3 | 14.9 | 734.57 | | 36.2 | 12.5 | 452.5 | | 20.5 | 4.7 | 96.35 | | 65.9 | 9.3 | 612.87 | | 60.2 | 15.7 | 945.14 | | 13.9 | 8.9 | 123.71 | | 22.5 | 8.9 | 228.73 | | 61.8 | 9.9 | 611.82 | | 27.2 | 2.7 | 73.44 | | 44.5 | 7.1 | 315.95 | ### Figure 1: Scatter Plot Explanation - **X-Axis:** Represents theater revenue in millions of dollars. - **Y-Axis:** Represents rental revenue
**Data Table:**

| Theater Revenue (in millions of dollars) | Rental Revenue (in millions of dollars) | Total Revenue (in millions of dollars) |
|------------------------------------------|----------------------------------------|---------------------------------------|
| 49.3                                     | 14.9                                   | 734.57                                |
| 36.2                                     | 12.5                                   | 452.5                                 |
| 20.5                                     | 4.7                                    | 96.35                                 |
| 65.9                                     | 9.3                                    | 612.87                                |
| 60.2                                     | 15.7                                   | 945.14                                |
| 25.7                                     | 8.9                                    | 228.73                                |
| 61.8                                     | 9.9                                    | 611.82                                |
| 27.2                                     | 2.7                                    | 73.44                                 |
| 13.6                                     | 9.7                                    | 131.92                                |
| 44.5                                     | 7.1                                    | 315.95                                |

**Graph Description:**

- The graph plots rental revenue (in millions of dollars) on the y-axis against theater revenue (in millions of dollars) on the x-axis.
- Each data point is represented by an 'x'.
- The spread of points suggests a relationship between theater and rental revenues.

**Question:**

What is the slope of the least-squares regression line for these data? Carry your intermediate computations to at least four decimal places and round your answer to at least two decimal places. (If necessary, consult a list of formulas.)

**Actions:**

- Buttons available for sending data to a calculator or Excel.
- Input box provided for the answer.
Transcribed Image Text:**Data Table:** | Theater Revenue (in millions of dollars) | Rental Revenue (in millions of dollars) | Total Revenue (in millions of dollars) | |------------------------------------------|----------------------------------------|---------------------------------------| | 49.3 | 14.9 | 734.57 | | 36.2 | 12.5 | 452.5 | | 20.5 | 4.7 | 96.35 | | 65.9 | 9.3 | 612.87 | | 60.2 | 15.7 | 945.14 | | 25.7 | 8.9 | 228.73 | | 61.8 | 9.9 | 611.82 | | 27.2 | 2.7 | 73.44 | | 13.6 | 9.7 | 131.92 | | 44.5 | 7.1 | 315.95 | **Graph Description:** - The graph plots rental revenue (in millions of dollars) on the y-axis against theater revenue (in millions of dollars) on the x-axis. - Each data point is represented by an 'x'. - The spread of points suggests a relationship between theater and rental revenues. **Question:** What is the slope of the least-squares regression line for these data? Carry your intermediate computations to at least four decimal places and round your answer to at least two decimal places. (If necessary, consult a list of formulas.) **Actions:** - Buttons available for sending data to a calculator or Excel. - Input box provided for the answer.
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