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.
10.3. 2
![### Geometric Sum Evaluation
Evaluate the following geometric sum:
\[ \frac{1}{2} + \frac{1}{10} + \frac{1}{50} + \frac{1}{250} + \cdots + \frac{1}{31,250} \]
\[ \frac{1}{2} + \frac{1}{10} + \frac{1}{50} + \frac{1}{250} + \cdots + \frac{1}{31,250} = \quad \boxed{\phantom{a}} \]
**Instructions:**
1. Simplify your answer.
2. Type an integer or a fraction.
**Note:**
- This problem is a geometric series, where each term after the first is the product of the previous term and a fixed number called the common ratio.
- Identify the first term \( a \) and the common ratio \( r \) of the series.
- Use the geometric series sum formula for a finite series:
\[ S_n = a \frac{1 - r^n}{1 - r} \]
where \( S_n \) is the sum of the first \( n \) terms, \( a \) is the first term, \( r \) is the common ratio, and \( n \) is the number of terms.
To approach this problem, recognize that each fraction's denominator is increasing by a factor of 5. Use the formula accordingly and simplify your expression to find the final sum.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc6e3f9a5-c787-4ffe-9681-b775b8e4c46b%2F72578ba7-73e5-4ca3-b6b6-ec5737dfa218%2Fdil5cmb.jpeg&w=3840&q=75)
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