You are given the following scatterplot, with Variable A on the Y-Axis and Variable B on the X-Axis:

If the axes are then swapped, such that Variable B is now on the Y-Axis, and Variable A is now on the X-Axis, what could you say about the change in the value of Pearson’s correlation coefficient (r)?

Question

You are given the following scatterplot, with Variable A on the Y-Axis and Variable B on the X-Axis:

If the axes are then swapped, such that Variable B is now on the Y-Axis, and Variable A is now on the X-Axis, what could you say about the change in the value of Pearson’s correlation coefficient (r)?

BlackTom AI · Accepted Answer

When thinking about Pearson’s correlation coefficient, it measures the strength and direction of the linear relationship between two variables. 
Option 1: The sign would change from negative to positive. This would require the direction of the linear association to flip, but swapping axes does not flip the actual relationship between the variables; it merely re-labels which variable is on which axis. Therefore this is not correct. 
Option 2: The sign would change from positive to negative. Similar to option 1, swapping axes does not invert the underlying association; the direction of the relationship remains the same when you interchange X and Y. So this is also not correct. 
Option 3: There would be no change in the value of Pearson’s r. This is the correct idea: r(X,Y) equals r(Y,X), since correlation depends on the covariance and standard deviations in a symmetric way. Swapping axes does not alter the magnitude or sign of the correlation. 
Option 4: Pearson’s r would remain negative in sign, although its value would change slightly. In a scatterplot that originally has a certain sign (positive or negative), swapping axes does not change that sign or the magnitude; r stays the same. Thus this statement is inaccurate. 
Overall, the key concept is the symmetry r(X,Y) = r(Y,X); axis labels do not affect the computed correlation.

类似问题

Which of the following values best represents the Pearson correlation for the data in the following scatterplot?

A researcher is interested in examining the relationship between the number of bears in an area (Y) and its human population (X). The scatterplot of the data is reproduced below. This scatterplot would suggest that the correlation (Pearson’s r) for this distribution would be:

Which of the following values best represents the Pearson correlation for the data in the following scatterplot?

Which of the following values best represents the Pearson correlation for the data in the following scatterplot?

A researcher is interested in examining the relationship between the number of bears in an area (Y) and its human population (X). The scatterplot of the data is reproduced below. This scatterplot would suggest that the correlation (Pearson’s r) for this distribution would be:

A Pearson correlation of 0.25 indicates that a graph of the data would show:

This is the formula for [ Select ] Pearson’s r correlation z-test for an individual score between-subjects t-test pooled variance .

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