Here is a bivariate data set. y 53.4 78.8 59.5 54.6 56.7 70 56.1 65 58.7 46.9 52.2 86.7 66 48.5 71.6 45.4 Use technology to find the correlation coefficient and report it accurate to three decimal places.
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.
![**Bivariate Data Set Analysis**
Below is a bivariate data set displayed in a table, where each pair of values represents corresponding data points for the variables x and y:
| x | y |
|-----|-------|
| 53.4 | 78.8 |
| 59.5 | 54.6 |
| 56.7 | 70 |
| 56.1 | 65 |
| 58.7 | 46.9 |
| 52.2 | 86.7 |
| 66 | 48.5 |
| 71.6 | 45.4 |
**Task:**
Use technology to calculate the correlation coefficient for this data set. Ensure the result is accurate to three decimal places.
**Instructions:**
1. Input the values into statistical software or a calculator that computes correlation coefficients.
2. Record the correlation coefficient in the provided space.
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**Note:** The correlation coefficient is a measure that determines the degree to which two variables' movements are associated. It ranges from -1 to 1, where 1 indicates a perfect positive linear relationship, -1 indicates a perfect negative linear relationship, and 0 indicates no linear relationship.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F938610b7-ae22-4121-80e0-e09aca732ea7%2F0edd4fc3-6a81-48c2-83e0-76ca3ce54aec%2Fyupt7qn_processed.png&w=3840&q=75)
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