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 on the new scatterplot, we need to understand the relationship between correlation and the direction of the slope.
The correlation coefficient measures the strength and direction of the linear relationship between two variables. It ranges from -1 to +1. Positive values indicate a positive linear relationship (as one variable increases, the other tends to increase), while negative values indicate a negative linear relationship (as one variable increases, the other tends to decrease).
In this case, the correlation between the two variables is -0.57. This implies a negative linear relationship, meaning that as one variable increases, the other tends to decrease.
Now, when we multiply each y-value by -1, it is essentially reflecting the scatterplot along the x-axis. This means that the direction of the slope will be reversed, and the scatterplot will slope in the opposite direction compared to the original.
Since the original scatterplot has a negative correlation and slopes down to the right, reflecting it along the x-axis will result in a scatterplot that slopes up to the right. Therefore, the correct option is "It slopes up to the right, and the correlation is -0.57."