Suppose the correlation between two variables is -0.57. If each of the y-values is multiplied by -1, which of the following is true about the new scatterplot?
It slopes up to the right, and the correlation is -0.57
It slopes up to the right, and the correlation is +0.57
It slopes down to the right, and the correlation is -0.57
It slopes down to the right, and the correlation is +0.57
None of the above is true
Well, well, well. It seems we have a correlation dilemma here. If each y-value is multiplied by -1, the scatterplot will actually slope down to the right because the direction of the relationship will be reversed. However, the correlation will still be -0.57 because multiplying all the y-values by -1 doesn't change the strength or direction of the relationship between the two variables. So the answer is: It slopes down to the right, and the correlation is -0.57.
To determine the effects of multiplying the y-values by -1 on the new scatterplot, we need to understand the concept of correlation and the relationship between variables.
Correlation measures the strength and direction of the linear relationship between two variables. The correlation coefficient can range from -1 to +1. A positive correlation indicates that as one variable increases, the other also tends to increase. A negative correlation indicates that as one variable increases, the other tends to decrease. The magnitude of the correlation coefficient indicates the strength of the relationship, with values closer to -1 or +1 suggesting a stronger correlation.
Given that the correlation between the two variables is -0.57, we know that there is a negative relationship between the variables. This means that as one variable increases, the other tends to decrease.
When each of the y-values is multiplied by -1, it essentially reflects the scatterplot over the x-axis. This transformation reflects the points on the scatterplot but does not change their individual relationships or the overall relationship between the variables.
Therefore, the slope of the new scatterplot will still be the same as the original scatterplot. In this case, the slope is not provided, so we cannot determine whether it slopes up or down to the right.
However, we can conclude that the new scatterplot will also have a negative correlation, -0.57. Multiplying the y-values by -1 does not change the direction of the relationship.
Therefore, the correct answer is: None of the above is true.