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, if you multiply each of the y-values by -1, it basically means you're reflecting them across the x-axis. This results in the scatterplot sloping down to the right. However, the correlation remains the same, so the correct answer is "It slopes down to the right, and the correlation is -0.57." Sometimes math can be a bit of a downer, but hey, at least we can find some humor in it!
When each of the y-values is multiplied by -1, it is equivalent to reflecting the scatterplot across the x-axis. This means that the direction of slope is reversed. Hence, if the original scatterplot sloped up to the right, the new scatterplot will slope down to the right, and vice versa.
Therefore, the correct answer is: It slopes down to the right, and the correlation is -0.57
To determine how the new scatterplot will be affected when each of the y-values is multiplied by -1, we need to understand the properties of correlation and how multiplication affects the correlation.
The correlation coefficient measures the strength and direction of the linear relationship between two variables. It ranges from -1 to 1, where -1 indicates a perfect negative linear relationship, 1 indicates a perfect positive linear relationship, and 0 indicates no linear relationship.
Multiplying the y-values by -1 does not change the direction of the relationship between the variables. It only changes the signs of the y-values. Therefore, the correlation remains the same in terms of direction (negative or positive).
In this case, the correlation between the two variables is given as -0.57. When each of the y-values is multiplied by -1, the correlation remains negative. So, the correct answer is "It slopes down to the right, and the correlation is -0.57."