Using your favorite statistics software package, you generate a scatter plot with a regression equation and correlation coefficient. The regression equation is reported as y = - 51.77x + 40.56 and the r = - 0.9. What percentage of the variation in y can be explained by the variation in the values of x? * (Report exact answer, and do not enter the % sign) Submit Question
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.
![Using your favorite statistics software package, you generate a scatter plot with a regression equation and correlation coefficient. The regression equation is reported as
\[ y = -51.77x + 40.56 \]
and the correlation coefficient \( r = -0.9 \).
What percentage of the variation in \( y \) can be explained by the variation in the values of \( x \)?
\[ r^2 = \_\_\_\_ \] % (Report exact answer, and do not enter the % sign)
[Submit Question]
**Explanation:**
In this problem, you're asked to find the coefficient of determination (\( r^2 \)), which tells you what percentage of the variation in the dependent variable \( y \) is explained by the independent variable \( x \). Given that the correlation coefficient \( (r) \) is \(-0.9\), calculate \( r^2 \) as follows:
\[ r^2 = (-0.9)^2 = 0.81 \]
Thus, 81% of the variation in \( y \) is explained by the variation in \( x \). Enter the value of \( r^2 \) in the provided space without the percentage sign, as instructed.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F8aff6ed6-30e2-4d58-a5d3-1b768148d1ba%2F018c1b6e-76bb-437a-8c77-b4387e5f8bbb%2Fh7k96yj_processed.jpeg&w=3840&q=75)
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