ation of the regression line. onstant three decimal places as needed. Round the coefficie
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.
![**Transcription for Educational Use**
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**Finding the Regression Equation**
Use the lemon import and crash data provided, where lemon imports are measured in metric tons, and crash fatality rates are per 100,000 people. The goal is to find the best predicted crash fatality rate for a year with 525 metric tons of lemon imports. Assess if the prediction is worthwhile.
| Lemon Imports (Metric Tons) | Crash Fatality Rate (Per 100,000 People) |
|-----------------------------|-----------------------------------------|
| 235 | 16 |
| 264 | 15.7 |
| 360 | 15.5 |
| 485 | 15.4 |
| 540 | 15 |
**Task:**
Find the equation of the regression line.
\[ \hat{y} = [\text{constant}] + [\text{coefficient}]x \]
*(Round the constant to three decimal places as needed. Round the coefficient to six decimal places as needed.)*
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![**Regression Analysis for Television Viewership vs. Salaries**
The data show the number of viewers for television stars with certain salaries. We are tasked with finding the regression equation, letting salary be the independent (x) variable. Additionally, we aim to find the best predicted number of viewers for a television star with a salary of $13 million. We need to determine if the result is close to the actual number of viewers, 2.0 million, using a significance level of 0.05.
**Data Table:**
| Salary (millions of $) | Viewers (millions) |
|------------------------|--------------------|
| 105 | 3.1 |
| 9 | 5.8 |
| 3 | 4.4 |
| 9 | 4.2 |
| 14 | 4.4 |
| 9 | 2.5 |
| 7 | 4.7 |
| 7 | 9.3 |
**Instructions:**
- Click the icon to view the critical values of the Pearson correlation coefficient \( r \).
**Question:**
What is the regression equation?
**Equation Format:**
\[
\hat{y} = \text{(intercept)} + \text{(slope)} \times x
\]
*Note: Round to three decimal places as needed.*
The task is to calculate the slope and intercept of the regression line based on the given salary and viewers data, and then use that equation to estimate the number of viewers for a star with a $13 million salary. Finally, determine if this estimate is reasonably close to 2.0 million viewers.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F68a1b863-bec7-4997-8d33-dc81d338a946%2F806769aa-d593-4f23-8207-8b7ce351be32%2Fxa6rcys_processed.jpeg&w=3840&q=75)
[Note: Since you have asked multiple questions, we will solve the first question for you. If you want any specific question to be solved then please specify the question number or post only that question.]
Regression analysis is the process of estimation between the dependable variable and one or more independent variable.
Let, the regression line be -
y =
where, and
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