The data show the chest size and weight of several bears. Find the regression equation, letting chest size be the independent (x) variable. Then find the best predicted weight of a bear with a chest size of 48 inches. Is the result close to the actual weight of 528 pounds? Use a significance level of 0.05. Chest size (inches) Weight (pounds) 36 56 50 39 49 42 296 570 501 353 487 385 What is the regression equation? 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.
what is the best predicted weight for a bear with 48 inches, and what is the regression equation
![## Analyzing the Relationship Between Chest Size and Weight of Bears
The data below exhibits the chest size and weight of several bears. We'll determine the regression equation, considering the chest size as the independent variable (x). The goal is to predict the weight of a bear with a chest size of 48 inches and verify whether the predicted weight is close to the actual weight of 528 pounds. A significance level of 0.05 will be utilized for this analysis.
### Data Table
| Chest Size (inches) | 36 | 56 | 50 | 39 | 49 | 42 |
|---------------------|-----|-----|-----|-----|-----|-----|
| Weight (pounds) | 296 | 570 | 501 | 353 | 487 | 385 |
### Steps to Determine the Regression Equation
1. **Identify the variables:**
- Independent variable (x): Chest size (inches)
- Dependent variable (y): Weight (pounds)
2. **Find the regression equation:**
- The regression equation is in the form: \( \hat{y} = \beta_0 + \beta_1 x \)
- To find the values of \( \beta_0 \) (y-intercept) and \( \beta_1 \) (slope), apply the least squares method.
3. **Determine the best predicted weight for a chest size of 48 inches:**
- Substitute \( x = 48 \) into the regression equation.
4. **Compare the predicted weight with the actual weight of 528 pounds.**
### Graphs and Diagram (not provided in the image)
- **Scatter Plot:**
- Chest size (inches) on the x-axis.
- Weight (pounds) on the y-axis.
- Each bear's weight corresponding to its chest size is plotted as a point.
- **Regression Line:**
- A line that best fits the scatter plot points, indicating the trend between chest size and weight.
### Regression Equation
\[ \hat{y} = [\text{Intercept}] + [\text{Slope}] \times x \]
(Requested to round the values to one decimal place.)
### Note:
This data analysis exercise seeks to provide an understanding of how to use linear regression to predict outcomes based on historical data. The calculation of the regression](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F1bbe1ef9-cacf-48b7-b15f-bf536b5508cd%2Fc76dd147-366a-4367-8a08-9f05e1e75a80%2Fgup67hf.jpeg&w=3840&q=75)
Trending now
This is a popular solution!
Step by step
Solved in 3 steps with 3 images
