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
To determine the effect of multiplying the y-values by -1, let's first understand the correlation coefficient. The correlation coefficient, denoted as r, measures the strength and direction of the linear relationship between two variables. It ranges from -1 to +1.
In this case, the correlation coefficient is -0.57. The negative sign indicates a negative linear relationship, meaning that as one variable increases, the other variable tends to decrease. The magnitude of the correlation coefficient, 0.57, indicates a moderate strength of the relationship.
Now, when each of the y-values is multiplied by -1, it essentially reflects the scatterplot over the x-axis. This reflection does not change the direction of the relationship but only its visual representation.
Since the correlation coefficient only measures the direction and strength of the relationship, it remains the same after reflecting the scatterplot. Therefore, the correct answer is:
None of the above is true.