If the correlation coefficient is -0.54, what is the sign of the slope of the regression line?
- As the correlation coefficient decreases from 0.86 to 0.81, do the points of the scatter plot move toward the regression line, or away from it
It goes from upper left to lower right, so what would the sign be?
There is more variability as the correlation coefficient decreases, so away.
To determine the sign of the slope of the regression line, you can use the correlation coefficient.
If the correlation coefficient (r) is negative, the slope of the regression line will also be negative. This means that as the independent variable increases, the dependent variable will decrease. So, in this case, the sign of the slope of the regression line would be negative.
Regarding the movement of the points of the scatter plot, the correlation coefficient is a measure of the strength and direction of the linear relationship between two variables.
As the correlation coefficient decreases from 0.86 to 0.81, the points of the scatter plot do not necessarily move toward or away from the regression line. The change in the correlation coefficient does not directly indicate whether the points move closer or farther from the regression line. It only reflects a change in the strength of the linear relationship between the variables.
To determine the sign of the slope of the regression line, we need to examine the sign of the correlation coefficient. The correlation coefficient measures the strength and direction of the linear relationship between two variables. It can take values between -1 and +1.
If the correlation coefficient is positive, it means that as one variable increases, the other variable tends to increase as well. In this case, the slope of the regression line will be positive.
On the other hand, if the correlation coefficient is negative, it means that as one variable increases, the other variable tends to decrease. In this case, the slope of the regression line will be negative.
Since the given correlation coefficient is -0.54, which is negative, the sign of the slope of the regression line will also be negative.
As for the second question, when the correlation coefficient decreases from 0.86 to 0.81, it means that the strength of the linear relationship between the two variables is decreasing. The points of the scatter plot do not necessarily move toward or away from the regression line solely based on the change in correlation coefficient.
The movement of points toward or away from the regression line depends on other factors, such as the spread or dispersion of the data points. A lower correlation coefficient does not necessarily indicate whether the points move closer to or further from the regression line. It merely suggests a weaker linear relationship between the variables. Therefore, without additional information about the scatter plot and the data, we cannot determine if the points move toward or away from the regression line.