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Opening weekend box office revenue is an important source of income to the movie industry and a crucial preliminary indicator of long-run profitability of a motion picture. Here are a scatter plot and the residual plot for predicting the World Gross Revenue from the Opening-Weekend Revenues for 136 Hollywood movies in 2011 using simple linear regression. 50 100 150 50 100 150 Opening Weekend Revenue (millions of dollars) Opening Weekend Revenue (millions of dollars) From the two plots above, which assumption of a simple linear model is most clearly violated? (i) linearity (ii) constant variability (iii) normal residuals (iv) independence

Opening weekend box office revenue is an important source of income to the movie industry and a crucial preliminary indicator of long-run profitability of a motion picture. Here are a scatter plot and the residual plot for predicting the World Gross Revenue from the Opening-Weekend Revenues for 136 Hollywood movies in 2011 using simple linear regression. 50 100 150 50 100 150 Opening Weekend Revenue (millions of dollars) Opening Weekend Revenue (millions of dollars) From the two plots above, which assumption of a simple linear model is most clearly violated? (i) linearity (ii) constant variability (iii) normal residuals (iv) independence

Algebra and Trigonometry (MindTap Course List)
Algebra and Trigonometry (MindTap Course List)
4th Edition
ISBN:9781305071742
Author:James Stewart, Lothar Redlin, Saleem Watson
Publisher:James Stewart, Lothar Redlin, Saleem Watson
Chapter1: Equations And Graphs
Section1.FOM: Focus On Modeling: Fitting Lines To Data
Problem 12P: Demand for Candy Bars In this problem you will determine a linear demand equation that describes the...
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## Analysis of Opening Weekend Box Office Revenue and World Gross Revenue Opening weekend box office revenue is a critical source of income for the movie industry and serves as a crucial preliminary indicator of the long-term profitability of a motion picture. Below is an analysis that involves a scatter plot and a residual plot for predicting the World Gross Revenue from the Opening-Weekend Revenues for 136 Hollywood movies in 2011 using simple linear regression. ### Graph Descriptions 1. **Scatter Plot: World Gross Revenue vs. Opening Weekend Revenue** - **X-Axis (Horizontal):** Opening Weekend Revenue (in millions of dollars) - **Y-Axis (Vertical):** World Gross Revenue (in millions of dollars) - **Description:** This scatter plot displays the relationship between Opening Weekend Revenue and World Gross Revenue. Generally, it shows an upward trend, indicating that movies with higher opening weekend revenues tend to have higher world gross revenues. 2. **Residual Plot: Residuals vs. Opening Weekend Revenue** - **X-Axis (Horizontal):** Opening Weekend Revenue (in millions of dollars) - **Y-Axis (Vertical):** Residual (in millions of dollars) - **Description:** This residual plot examines the residuals from the linear regression model, plotting them against the Opening Weekend Revenue. - **Observation:** There is a noticeable pattern in the residual plot, which can indicate potential issues with the assumptions of the linear regression model. ### Discussion The residual plot shows a clear funnel shape, or spread in variability, as the Opening Weekend Revenue increases. This suggests that as the Opening Weekend Revenue increases, the variability in the residuals also increases. ### Question From the two plots above, which assumption of a simple linear model is most clearly violated? (i) Linearity (ii) Constant variability (iii) Normal residuals (iv) Independence Based on the residual plot, the assumption most clearly violated is: - **(ii) Constant variability** ### Conclusion The analysis reveals that the assumption of constant variability is violated, suggesting that the linear regression model may not be the best fit for this data. Other models or transformations might be necessary to address the heteroscedasticity observed in the residuals.
Transcribed Image Text:## Analysis of Opening Weekend Box Office Revenue and World Gross Revenue Opening weekend box office revenue is a critical source of income for the movie industry and serves as a crucial preliminary indicator of the long-term profitability of a motion picture. Below is an analysis that involves a scatter plot and a residual plot for predicting the World Gross Revenue from the Opening-Weekend Revenues for 136 Hollywood movies in 2011 using simple linear regression. ### Graph Descriptions 1. **Scatter Plot: World Gross Revenue vs. Opening Weekend Revenue** - **X-Axis (Horizontal):** Opening Weekend Revenue (in millions of dollars) - **Y-Axis (Vertical):** World Gross Revenue (in millions of dollars) - **Description:** This scatter plot displays the relationship between Opening Weekend Revenue and World Gross Revenue. Generally, it shows an upward trend, indicating that movies with higher opening weekend revenues tend to have higher world gross revenues. 2. **Residual Plot: Residuals vs. Opening Weekend Revenue** - **X-Axis (Horizontal):** Opening Weekend Revenue (in millions of dollars) - **Y-Axis (Vertical):** Residual (in millions of dollars) - **Description:** This residual plot examines the residuals from the linear regression model, plotting them against the Opening Weekend Revenue. - **Observation:** There is a noticeable pattern in the residual plot, which can indicate potential issues with the assumptions of the linear regression model. ### Discussion The residual plot shows a clear funnel shape, or spread in variability, as the Opening Weekend Revenue increases. This suggests that as the Opening Weekend Revenue increases, the variability in the residuals also increases. ### Question From the two plots above, which assumption of a simple linear model is most clearly violated? (i) Linearity (ii) Constant variability (iii) Normal residuals (iv) Independence Based on the residual plot, the assumption most clearly violated is: - **(ii) Constant variability** ### Conclusion The analysis reveals that the assumption of constant variability is violated, suggesting that the linear regression model may not be the best fit for this data. Other models or transformations might be necessary to address the heteroscedasticity observed in the residuals.
**Problem Statement** Continue the previous problem. Which statement is TRUE for the two plots above? 1. The average of the residuals is exactly 0. 2. The residuals are positively correlated with the Opening Weekend Revenue because the magnitude of residuals tends to increase as the Opening Weekend Revenue increases. 3. The point with an arrow pointed to on the top right corner of the scatter plot is an influential point. 4. The point with an arrow pointed to on the top right corner of the scatter plot is a point with the greatest residual in magnitude. **Explanation for Visual Aids** - **Scatter Plot Diagram**: Assume there are two scatter plots provided above the text. The exact diagrams are not shown, but a scatter plot graphically depicts the relationship between two variables with points plotted in a Cartesian grid. Each point represents an observation in the dataset. - **Residuals**: These are the differences between observed values and the predicted values in a regression analysis. The residual plot helps to visualize any patterns and the goodness of fit in a regression model. Residuals are shown in a separate residual plot. - **Influential Point**: Refers to a data point that significantly affects the interpretation of the data regression analysis. Such points are indicated using arrows. - **Magnitude of Residual**: This refers to the absolute value of the residuals. A point with the greatest residual in magnitude shows the maximum deviation from the expected predicted line in the dataset. These components are integral to understanding the provided text and validating the true statement regarding the plots. Note: Since the actual plots are not visible in the provided image, make sure to check the plots visually to verify which statement holds true.
Transcribed Image Text:**Problem Statement** Continue the previous problem. Which statement is TRUE for the two plots above? 1. The average of the residuals is exactly 0. 2. The residuals are positively correlated with the Opening Weekend Revenue because the magnitude of residuals tends to increase as the Opening Weekend Revenue increases. 3. The point with an arrow pointed to on the top right corner of the scatter plot is an influential point. 4. The point with an arrow pointed to on the top right corner of the scatter plot is a point with the greatest residual in magnitude. **Explanation for Visual Aids** - **Scatter Plot Diagram**: Assume there are two scatter plots provided above the text. The exact diagrams are not shown, but a scatter plot graphically depicts the relationship between two variables with points plotted in a Cartesian grid. Each point represents an observation in the dataset. - **Residuals**: These are the differences between observed values and the predicted values in a regression analysis. The residual plot helps to visualize any patterns and the goodness of fit in a regression model. Residuals are shown in a separate residual plot. - **Influential Point**: Refers to a data point that significantly affects the interpretation of the data regression analysis. Such points are indicated using arrows. - **Magnitude of Residual**: This refers to the absolute value of the residuals. A point with the greatest residual in magnitude shows the maximum deviation from the expected predicted line in the dataset. These components are integral to understanding the provided text and validating the true statement regarding the plots. Note: Since the actual plots are not visible in the provided image, make sure to check the plots visually to verify which statement holds true.
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