Question

Matching Here are several scatterplots. The calculated correlations are -0.923, -0.487, 0.006, and 0.777.
Which is which?

Answer 1

The scatter plots gives the graph of the two variables from which one can depict the relationship between the two variables.
The correlation is a measure which tells mathematically the kind of relationship the two variables has. It can be a direct, inverse, or no relationship.
The scatter plot (a) depicts that initially, as the value of one variable increases, the value of other variable also increases and then the pattern is changed, now as the value of one variable increases, the value of other variable also decreases.
But it can be seen that there is significant dip in the values of the variable when the other variables' value increases. Hence, overall it must have negative correlation but a moderate negative correlation.
Therefore, it must have correlation of -0.487.
The scatter plot (b) depicts that overall as the value of one variable increases, the value of other variable also increases. It can be seen that there is significant rise in value of the variable when other increases.
Hence, it must have strong positive correlation.
Therefore, it must have correlation of 0.777.
The scatter plot (c) depicts that overall as the value of one variable increases, the value of other variable also decreases and it can be seen that the data points are very close to each other.
Hence, it must have strong negative correlation.
Therefore, it must have correlation of -0.923.
The scatter plot (d) depicts that overall there is no pattern in which they are moving forward. Hence, the correlation must be very close to zero.
But it can be seen that there are more data points where the value of both the variables have increased.
Therefore, it must have correlation of 0.006.