**Title: Analyzing Movie Budgets and Gross Earnings****Introduction**In the study of financial performance in the film industry, one critical aspect is understanding the relationship between a movie's budget and its gross earnings. This analysis involves the application of statistical methods to predict financial outcomes based on historical data. Here, we explore how to use regression analysis to make such predictions.**Data Overview**The paired data below shows movie budget amounts (predictor variable, $x$) and the gross amounts that the movies earned.| Budget ($) in Millions | Gross ($) in Millions ||------------------------|-----------------------|| 38 | 118 || 25 | 18 || 115 | 100 || 69 | 60 || 70 | 128 || 49 | 121 || 125 | 109 || 67 | 107 || 10 | 65 || 65 | 111 || 123 | 206 || 22 | 41 || 8 | 25 || 151 | 285 || 11 | 43 |**Objective**The task is to find the best predicted gross amount for a movie with a $115 million budget using the provided data. This involves calculating the regression equation, with the budget as the predictor. A significance level of $\alpha = 0.05$ is used to determine statistical validity.**Steps to Solve:**1. **Calculate the Regression Equation**: The regression equation is typically represented as $ ŷ = b_0 + b_1x $, where $ ŷ $ is the predicted value, $ b_0 $ is the y-intercept, and $ b_1 $ is the slope of the line.2. **Determine Statistical Significance**: It is essential to verify that the correlation between variables is statistically significant using the Pearson correlation coefficient.3. **Make Predictions**: After establishing the equation, use it to predict the gross earnings for the given budget of $115 million.**Instructions for Using the Regression Tool:**- Click the given icon to view the critical values for verifying the correlation.- Input the calculated values in the edit fields provided and click 'Check Answer' to validate your solution.This exercise demonstrates the

In this case Budget (x) is the independent variable and Gross (y) is the dependent variable. Enter…

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 $115 million. Use a significance level of a = 0.05. Budget ($)in Millions Gross ($) in Millions 65 123 22 8 151 115 38 25 115 69 70 49 125 67 10 111 206 41 25 285 43 118 18 100 60 128 121 109 107 65 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.)

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 $115 million. Use a significance level of a = 0.05. Budget ($)in Millions Gross ($) in Millions 65 123 22 8 151 115 38 25 115 69 70 49 125 67 10 111 206 41 25 285 43 118 18 100 60 128 121 109 107 65 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.)

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

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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

**Title: Analyzing Movie Budgets and Gross Earnings**

**Introduction**

In the study of financial performance in the film industry, one critical aspect is understanding the relationship between a movie's budget and its gross earnings. This analysis involves the application of statistical methods to predict financial outcomes based on historical data. Here, we explore how to use regression analysis to make such predictions.

**Data Overview**

The paired data below shows movie budget amounts (predictor variable, $x$) and the gross amounts that the movies earned.

| Budget ($) in Millions | Gross ($) in Millions |
|------------------------|-----------------------|
| 38 | 118 |
| 25 | 18 |
| 115 | 100 |
| 69 | 60 |
| 70 | 128 |
| 49 | 121 |
| 125 | 109 |
| 67 | 107 |
| 10 | 65 |
| 65 | 111 |
| 123 | 206 |
| 22 | 41 |
| 8 | 25 |
| 151 | 285 |
| 11 | 43 |

**Objective**

The task is to find the best predicted gross amount for a movie with a $115 million budget using the provided data. This involves calculating the regression equation, with the budget as the predictor. A significance level of $\alpha = 0.05$ is used to determine statistical validity.

**Steps to Solve:**

1. **Calculate the Regression Equation**: The regression equation is typically represented as $ ŷ = b_0 + b_1x $, where $ ŷ $ is the predicted value, $ b_0 $ is the y-intercept, and $ b_1 $ is the slope of the line.

2. **Determine Statistical Significance**: It is essential to verify that the correlation between variables is statistically significant using the Pearson correlation coefficient.

3. **Make Predictions**: After establishing the equation, use it to predict the gross earnings for the given budget of $115 million.

**Instructions for Using the Regression Tool:**

- Click the given icon to view the critical values for verifying the correlation.
- Input the calculated values in the edit fields provided and click 'Check Answer' to validate your solution.

This exercise demonstrates the

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