You generate a scatter plot using Excel. You then have Excel plot the trend line and report the equation and the r2 value. The regression equation is reported as y = 96.35z + 77.69 and the r2 = 0.36. What is the correlation coefficient for this data set?
You generate a scatter plot using Excel. You then have Excel plot the trend line and report the equation and the r2 value. The regression equation is reported as y = 96.35z + 77.69 and the r2 = 0.36. What is the correlation coefficient for this data set?
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![### Linear Regression and Correlation Coefficient
When performing a linear regression analysis, you typically generate a scatter plot using software like Excel. The next step is to plot the trend line and find the corresponding regression equation and \( r^2 \) value.
In this example, Excel reports the regression equation as:
\[ y = 96.35x + 77.69 \]
Additionally, it provides the \( r^2 \) value:
\[ r^2 = 0.36 \]
To understand the strength and direction of the linear relationship between the variables, we need to calculate the correlation coefficient, denoted as \( r \).
**Question: What is the correlation coefficient for this data set?**
You can calculate the correlation coefficient by taking the square root of \( r^2 \). Since \( r^2 = 0.36 \), we compute \( r \) as follows:
\[ r = \sqrt{0.36} \]
Since \( r \) can be either positive or negative depending on the direction of the relationship:
\[ r = \pm 0.6 \]
So, the correlation coefficient for this data set can be \( +0.6 \) or \( -0.6 \), indicating a moderate positive or negative linear relationship, respectively. The actual sign of \( r \) would depend on the nature of the data and the slope of the regression line. Given that the slope of the regression equation \( 96.35 \) is positive, \( r \) would be \( +0.6 \).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fae9dff02-6614-4387-a434-63ee01638e81%2F8535d76a-4c2c-4f5a-86a1-45efdf946257%2Fa9e6w8b_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Linear Regression and Correlation Coefficient
When performing a linear regression analysis, you typically generate a scatter plot using software like Excel. The next step is to plot the trend line and find the corresponding regression equation and \( r^2 \) value.
In this example, Excel reports the regression equation as:
\[ y = 96.35x + 77.69 \]
Additionally, it provides the \( r^2 \) value:
\[ r^2 = 0.36 \]
To understand the strength and direction of the linear relationship between the variables, we need to calculate the correlation coefficient, denoted as \( r \).
**Question: What is the correlation coefficient for this data set?**
You can calculate the correlation coefficient by taking the square root of \( r^2 \). Since \( r^2 = 0.36 \), we compute \( r \) as follows:
\[ r = \sqrt{0.36} \]
Since \( r \) can be either positive or negative depending on the direction of the relationship:
\[ r = \pm 0.6 \]
So, the correlation coefficient for this data set can be \( +0.6 \) or \( -0.6 \), indicating a moderate positive or negative linear relationship, respectively. The actual sign of \( r \) would depend on the nature of the data and the slope of the regression line. Given that the slope of the regression equation \( 96.35 \) is positive, \( r \) would be \( +0.6 \).
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