5. For the following scores, Y 4. 1 4 5 a. Sketch a scatter plot and estimate the Pearson correlation. b. Compute the Pearson correlation. onon
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 Statement
5. For the following scores:
| X | Y |
|---|---|
| 4 | 0 |
| 1 | 5 |
| 1 | 0 |
| 4 | 5 |
a. Sketch a scatter plot and estimate the Pearson correlation.
b. Compute the Pearson correlation.
### Explanation
The table lists paired values of variables X and Y. You need to perform two tasks:
1. **Sketch a Scatter Plot**:
- Plot the points (4, 0), (1, 5), (1, 0), and (4, 5) on a Cartesian plane.
- Visually estimate the Pearson correlation by observing the trend in the distribution of points.
2. **Compute Pearson Correlation**:
- Use the formula for Pearson correlation to calculate the exact value:
\[
r = \frac{{n(\Sigma xy) - (\Sigma x)(\Sigma y)}}{{\sqrt{[n \Sigma x^2 - (\Sigma x)^2][n \Sigma y^2 - (\Sigma y)^2]}}}
\]
- Where n is the number of pairs, \( \Sigma xy \) is the sum of the products of paired scores, \( \Sigma x \) and \( \Sigma y \) are the sums of X and Y scores respectively, \( \Sigma x^2 \) and \( \Sigma y^2 \) are the sums of the squares of X and Y scores.
This exercise helps in understanding relationships between two variables through correlation and visual representation.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F27d815e0-a80e-4266-9598-4da2405c7cae%2F068ada4f-9153-4663-8aaf-0f7fbc29d41f%2F95udogr_processed.jpeg&w=3840&q=75)
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