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.
![**Understanding Graphs of Linear Equations**
**Graph Analysis:**
In this section, we will look at a graph of a linear equation and walk you through identifying its key features.
The graph provided shows a coordinate plane with:
1. **X-axis**: Horizontal line numbered from -5 to 5.
2. **Y-axis**: Vertical line numbered from -5 to 5.
3. A linear line that cuts through these axes.
**Key Features of the Graph:**
- The line passes through point (0, -2.5) on the Y-axis and gradually rises up as it moves to the right, indicating a positive slope.
- The line crosses the Y-axis at (0, -2.5), which gives the y-intercept of the line.
- The line also crosses the X-axis at (2.5, 0), which gives the x-intercept of the line.
**Equation of the Line:**
To find the equation of the line, we follow these steps:
1. Identify the slope (m). The rise over run between the intercepts (y-intercept and x-intercept) gives m.
2. Identify the y-intercept (b), which is where the line crosses the Y-axis.
Using the intercept form, the general formula for the equation of the line is:
\[ y = mx + b \]
**Determining the Equation:**
- Since the line seems to go upward with an inclination to the right, it has a positive slope.
- The slope (m) can be approximated through rise over run calculation using the intercepts (2.5, 0) and (0, -2.5).
- The y-intercept (b) is -2.5.
Hence, the graphed line equation appears in the form:
\[ y = mx - 2.5 \]
Where m represents the slope of the line.
**Summary:**
This graph depicts the linear equation in standard form highlighting fundamental concepts such as slope and intercepts. Understanding these components helps in constructing linear equations accurately.
**Equation:**
```shell
Equation: y = mx - 2.5
```
This instructional breakdown ensures students grasp how to interpret and translate graphs into linear equations effectively.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F9a621c50-9c57-48ac-8b66-70c4aca2a5cb%2F0c2f6aaf-ce06-4f29-aa53-0bb559c148d6%2Fkxij21g_processed.jpeg&w=3840&q=75)
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