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.
![### Problem: Solve for \( x \). Round to the nearest tenth of a degree, if necessary.
#### Description:
In this problem, you are provided with a right triangle \( \triangle HFG \). The following dimensions and angle are given:
- \( HG = 5.3 \)
- \( HF = 8.5 \)
- Angle \( HFG = 90^\circ \)
- \( \angle x \) is the angle opposite the side \( HG \) and adjacent to side \( HF \).
The task is to find the value of angle \( x \) in degrees and round it to the nearest tenth if necessary.
#### Diagram:
The triangle is labeled with points H, G, and F such that:
- \( H \) is at the top-left, forming angle \( x^\circ \).
- \( G \) is at the top-right, forming a right angle with H and F.
- \( F \) is at the bottom, forming the hypotenuse with \( H \).
The diagram of the triangle is as follows:
```
H x°
|\
| \
5.3 \
| \
| \
| \
| \
8.5 \
|________________\
F G
```
#### Steps to Solve for \( x \):
1. **Identify the Trigonometric Function:**
Since angle \( x \) is opposite side \( HG \) and adjacent to side \( HF \), you can use the tangent function:
\[
\tan(x) = \frac{\text{opposite}}{\text{adjacent}} = \frac{HG}{HF}
\]
2. **Calculate the Tangent:**
Substitute the given values:
\[
\tan(x) = \frac{5.3}{8.5}
\]
3. **Compute the Value:**
\[
\tan(x) \approx 0.6235
\]
4. **Find the Angle:**
Use the inverse tangent (arctan) function to find the angle \( x \):
\[
x = \tan^{-1}(0.6235)
\]
Using a calculator:
\[
x \approx 32.1^\circ
\]
#### Solution:
The angle \( x \) is approximately \( 32.1^\circ \).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F0f7ba434-4bd9-4cca-80d0-ba9774d8e657%2F1dc7331e-0551-42f9-a6a2-384177352158%2Fgm3eeq_processed.jpeg&w=3840&q=75)
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