Here are several scatterplots. The calculated correlations are $-0.021,0.736$, 0.951 , and -0.923 . Which is which? Match each scatterplot with its calculated correlation. (a) (b) (c) (d) Points: 0 of 1 Save (a) (b) (c) (d)
Solution
Step 1 ：The correlation coefficient measures the strength and direction of the linear relationship between two variables. It ranges from -1 to 1, where -1 indicates a perfect negative linear relationship, 1 indicates a perfect positive linear relationship, and 0 indicates no linear relationship.
Step 2 ：We are given four correlation coefficients and four scatterplots. We need to match each scatterplot with its calculated correlation.
Step 3 ：A scatterplot with a correlation of -0.021 would show points scattered all over the plot with no clear pattern, indicating no linear relationship.
Step 4 ：A scatterplot with a correlation of 0.736 would show points that are somewhat close to a straight line sloping upwards, indicating a moderate to strong positive linear relationship.
Step 5 ：A scatterplot with a correlation of 0.951 would show points very close to a straight line sloping upwards, indicating a very strong positive linear relationship.
Step 6 ：A scatterplot with a correlation of -0.923 would show points very close to a straight line sloping downwards, indicating a very strong negative linear relationship.
Step 7 ：Without the actual scatterplots, we can't definitively match each one with its calculated correlation. However, based on the characteristics described above, we can make educated guesses.
