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
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The correct answer is: It slopes up to the right, and the correlation is +0.57.
When multiplying the y-values by -1, the direction or slope of the scatterplot remains the same, but the correlation coefficient changes sign. In this case, since the original correlation is -0.57, when the y-values are multiplied by -1, the correlation becomes +0.57.
To determine the effect of multiplying the y-values by -1 on the scatterplot, we need to understand the relationship between correlation and the direction of the scatterplot.
Correlation measures the strength and direction of the linear relationship between two variables. It ranges from -1 to +1, where a positive value indicates a positive linear relationship (as one variable increases, the other also tends to increase) and a negative value indicates a negative linear relationship (as one variable increases, the other tends to decrease).
In this case, with a correlation of -0.57, we know there is a negative linear relationship between the two variables. This means that as one variable increases, the other tends to decrease.
When we multiply the y-values by -1, we are essentially reflecting the scatterplot across the x-axis, which will flip its direction. In other words, if the original scatterplot sloped up to the right, it will now slope down to the right, and if it sloped down to the right, it will now slope up to the right.
Therefore, the correct answer is: It slopes down to the right, and the correlation is -0.57.