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 scatterplot and correlation, let's first understand what the correlation coefficient represents.
The correlation coefficient measures the strength and direction of the linear relationship between two variables. It ranges from -1 to +1. A positive value indicates a positive slope (increase in one variable leads to an increase in the other), while a negative value indicates a negative slope (increase in one variable leads to a decrease in the other).
In this case, the correlation coefficient between the two variables is -0.57. This negative value suggests a negative slope, meaning as one variable increases, the other tends to decrease, and vice versa.
When we multiply each of the y-values by -1, it effectively reverses the direction of the relationship. The positive values become negative, and the negative values become positive.
Therefore, the new scatterplot will slope up to the right, opposite to the original scatterplot, since the relationship has been reversed. However, the correlation coefficient remains the same at -0.57 because the strength and direction of the relationship are still the same, just reversed.
Considering the given options:
- It slopes up to the right, and the correlation is -0.57 : This is the correct answer. The slope of the new scatterplot is positive, and the correlation remains -0.57.
- It slopes up to the right, and the correlation is +0.57: This option is incorrect because the correlation coefficient should remain negative.
- It slopes down to the right, and the correlation is -0.57: This option is incorrect because the correlation remains the same.
- It slopes down to the right, and the correlation is +0.57: This option is incorrect because the correlation coefficient should remain negative.
- None of the above is true: This option is incorrect because the first option is true.
In summary, when each of the y-values is multiplied by -1, the new scatterplot will slope up to the right, and the correlation will remain -0.57.