-2 7. 4 21 1 3 15 10 -2 3. -0.885 -0.778 -0.994 -0.671
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.
Calculate the linear
![The image presents a problem statement that asks the reader to calculate the linear correlation between two variables, \(x\) and \(y\). The data for the variables is organized in a tabular format:
\[
\begin{array}{|c|c|c|c|c|c|c|c|}
\hline
x & -2 & 0 & 7 & \frac{4}{3} & 2 & 3 & 5 & 6 \\
\hline
y & \frac{1}{15} & 10 & -2 & \frac{1}{3} & \frac{1}{7} & \frac{1}{8} & 5 & 0 & -1 \\
\hline
\end{array}
\]
Below the table, there are multiple-choice options for the correlation coefficient:
- \(-0.885\)
- \(-0.778\)
- \(-0.994\)
- \(-0.671\)
The task involves determining which of these options correctly represents the linear correlation between the two sets of data. To solve this, one would typically compute the Pearson correlation coefficient using the given data.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd89b30fe-c8d7-4dd6-9457-cfcf042cb064%2F211dbb11-8a8b-4c9a-ae6d-f1384edcadf9%2Fdbjepu_processed.jpeg&w=3840&q=75)
Number of counts (n) = 9
| x | y | x2 | y2 | xy | |
| -2 | 15 | 4 | 225 | -30 | |
| 0 | 10 | 0 | 100 | 0 | |
| 7 | -2 | 49 | 4 | -14 | |
| 4 | 3 | 16 | 9 | 12 | |
| 2 | 7 | 4 | 49 | 14 | |
| 1 | 8 | 1 | 64 | 8 | |
| 3 | 5 | 9 | 25 | 15 | |
| 5 | 0 | 25 | 0 | 0 | |
| 6 | -1 | 36 | 1 | -6 | |
| Sum: | 26 | 45 | 144 | 477 | -1 |
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