Question

Match these values of r with the accompanying scatterplots: 0.995, 0.769, -1, 0.404, and -0.404. 

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Answer 1

Scatterplot 1, r = -1

Scatterplot 2, r = -0.404

Scatterplot 3, r = 0.404

Scatterplot 4, r = 0.995

Scatterplot 5, r = 0.769

Reason: 'r' represents the co-efficient of correlation between the two variables plotted in the graph. This value varies from -1 to 1. The co-efficient of correlation actually represents how both the variables are related. If both the variables take same values all the time, then value of r is 1. If both the variables take are completely inversely proportional, then value of r is -1. Value of r is 0 when one variable is independent of other. Therefore, when r = 1, the scatterplot line makes 45⁰ with the X-axis in anti-clockwise direction and when r = -1, the scatterplot line makes 135⁰ with the X-axis in anti-clockwise direction. For the remaining values of r, it is in between these two angles. Based on these observations, the above matching is provided.