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 each of the y-values by -1, you need to understand the relationship between correlation and slope. The correlation coefficient measures the strength and direction of a linear relationship between two variables. The slope of a scatterplot indicates the direction and steepness of the relationship between the variables.
In a scatterplot, a positive slope means that as one variable increases, the other variable also tends to increase. A negative slope means that as one variable increases, the other variable tends to decrease.
Given that the correlation between the two variables is -0.57, it indicates a negative linear relationship. Thus, the scatterplot initially slopes down to the right.
Multiplying each of the y-values by -1 will invert the direction of the scatterplot. Consequently, the scatterplot will now slope up to the right since the y-values are now decreasing as the x-values increase.
Therefore, the correct answer is: It slopes up to the right, and the correlation is -0.57.