Listed below are paired data consisting of movie budget amounts and the amounts that the movies grossed. Find the regression equation, letting the budget be the predictor (x) variable. Find the best predicted amount that a movie will gross if its budget is $120 million. Use a significance level of a = 0.05. Budget ($)in Millions Gross ($) in Millions 40 20 118 67 71 48 119 62 8 64 128 18 11 147 4 0 115 21 112 67 120 119 93 102 51 114 219 34 11 287 43 Click the icon to view the critical values of the Pearson correlation coefficient r. The regression equation is y =+x. (Round to one decimal place as needed.)
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 text presents a statistical exercise involving paired data of movie budgets and their corresponding gross earnings. The task is to find the regression equation, using the budget (x) as the predictor variable. The goal is to estimate the predicted gross earnings for a film with a $120 million budget, using a significance level of α = 0.05.
The dataset includes the following values:
- **Budget ($) in Millions:** 40, 20, 118, 67, 71, 48, 119, 62, 8, 64, 128, 18, 11, 147
- **Gross ($) in Millions:** 115, 21, 112, 67, 120, 119, 93, 102, 51, 114, 219, 34, 11, 287, 43
Instructions to view the critical values of the Pearson correlation coefficient are included, as well as a placeholder for the regression equation:
\[
\hat{y} = \text{[ ]} + \text{[ ]}x
\]
Users are reminded to round to one decimal place as needed.
No graphs or diagrams are present in this image.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F913862dd-ac5f-4038-847e-173683e2f265%2Fcc886711-a28d-4f67-a252-96512e8962bc%2F2elemb7_processed.jpeg&w=3840&q=75)
Trending now
This is a popular solution!
Step by step
Solved in 2 steps with 1 images
