**Understanding Opening Weekend Box Office Revenue**Opening weekend box office revenue is an important source of income to the movie industry and a crucial preliminary indicator of the long-run profitability of a motion picture. Below are visual representations of the relationship between the Opening Weekend Revenue and the World Gross Revenue for 136 Hollywood movies in 2011 using simple linear regression:### Graph Descriptions#### Scatter Plot (Left Graph)- **Title:** World Gross Revenue vs. Opening Weekend Revenue- **X-axis:** Opening Weekend Revenue (millions of dollars), ranging from 0 to 170.- **Y-axis:** World Gross Revenue (millions of dollars), ranging from 0 to 1200.- **Details:** This scatter plot displays the World Gross Revenue data points plotted against the Opening Weekend Revenue. - The majority of data points are located towards the lower range of the Opening Weekend Revenue. - A positive linear trend is apparent, indicated by a line.#### Residual Plot (Right Graph)- **Title:** Residuals vs. Opening Weekend Revenue- **X-axis:** Opening Weekend Revenue (millions of dollars), ranging from 0 to 170.- **Y-axis:** Residual (millions of dollars), ranging from -400 to 400.- **Details:** This residual plot displays the residuals from the linear regression model plotted against the Opening Weekend Revenue. - Residuals are scattered around zero. - The variability of residuals increases with higher Opening Weekend Revenue.### Key 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 In examining the residual plot, it can be observed that the variability of residuals does not remain constant across the range of the Opening Weekend Revenue, indicating a violation of the constant variability assumption.

Option ii is correct ii) constant variability

Opening weekend box office revenue is an important source of income to the movie industry and crucial preliminary indicator of long-run profitability of a motion picture. Here are a scatter plot and e residual plot for predicting the World Gross Revenue from the Opening-Weekend Revenues for 136 ollywood 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) rom 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 World Gross Revenue (millions of dollars) 008 1200 000 Residual (millions of dollars) 200 400

Opening weekend box office revenue is an important source of income to the movie industry and crucial preliminary indicator of long-run profitability of a motion picture. Here are a scatter plot and e residual plot for predicting the World Gross Revenue from the Opening-Weekend Revenues for 136 ollywood 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) rom 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 World Gross Revenue (millions of dollars) 008 1200 000 Residual (millions of dollars) 200 400

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Concept explainers

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.

Question

**Understanding Opening Weekend Box Office Revenue**

Opening weekend box office revenue is an important source of income to the movie industry and a crucial preliminary indicator of the long-run profitability of a motion picture. Below are visual representations of the relationship between the Opening Weekend Revenue and the World Gross Revenue for 136 Hollywood movies in 2011 using simple linear regression:

### Graph Descriptions

#### Scatter Plot (Left Graph)
- **Title:** World Gross Revenue vs. Opening Weekend Revenue
- **X-axis:** Opening Weekend Revenue (millions of dollars), ranging from 0 to 170.
- **Y-axis:** World Gross Revenue (millions of dollars), ranging from 0 to 1200.
- **Details:** This scatter plot displays the World Gross Revenue data points plotted against the Opening Weekend Revenue.
- The majority of data points are located towards the lower range of the Opening Weekend Revenue.
- A positive linear trend is apparent, indicated by a line.

#### Residual Plot (Right Graph)
- **Title:** Residuals vs. Opening Weekend Revenue
- **X-axis:** Opening Weekend Revenue (millions of dollars), ranging from 0 to 170.
- **Y-axis:** Residual (millions of dollars), ranging from -400 to 400.
- **Details:** This residual plot displays the residuals from the linear regression model plotted against the Opening Weekend Revenue.
- Residuals are scattered around zero.
- The variability of residuals increases with higher Opening Weekend Revenue.

### Key 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

In examining the residual plot, it can be observed that the variability of residuals does not remain constant across the range of the Opening Weekend Revenue, indicating a violation of the constant variability assumption.

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