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 = - 71.92x + 50.13 and the r = - 0.191. What proportion of the variation in y can be explained by the variation in the values of x? p2 = Report answer as a percentage accurate to one decimal place.
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.
![**Understanding Linear Regression: An Example**
In a recent statistical analysis using a popular statistics software package, a scatter plot was generated along with a regression equation and a correlation coefficient to explore the relationship between two variables, \( x \) and \( y \).
The regression equation obtained from the data is:
\[ y = -71.92x + 50.13 \]
Additionally, the correlation coefficient, \( r \), is given as:
\[ r = -0.191 \]
### Question
What proportion of the variation in \( y \) can be explained by the variation in the values of \( x \)?
To solve this, we need to calculate \( r^2 \), which represents the proportion of the variance in the dependent variable ( \( y \) ) that is predictable from the independent variable ( \( x \) ). The formula is:
\[ r^2 = (-0.191)^2 \]
After calculating \( r^2 \), convert it to a percentage and report it accurate to one decimal place.
**Answer:**
\[ r^2 = 0.0365 \]
As a percentage: **3.7%**
Therefore, 3.7% of the variation in \( y \) can be explained by the variation in the values of \( x \).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa218d9b0-33cd-49fb-8966-615774819802%2F590054d4-f2aa-4774-ad6e-3178e70a17bf%2F4rgb8yp_processed.png&w=3840&q=75)
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