Final answer:
A correlation coefficient of r = 0.73 implies a positive correlation and linear association between two variables. The slope of the relationship is likely positive, but r itself does not provide the slope's value. Outliers can affect correlation but not necessarily in a weakening manner, and r alone does not imply causation.
Step-by-step explanation:
When you have a correlation coefficient (r) of 0.73 for a given scatterplot, several implications about the relationship between the explanatory and response variables can be made. First, the positive value of r indicates that there is a positive correlation, meaning as one variable increases, so does the other. We can also infer that the relationship has a linear form because correlation coefficients measure linear associations.
The statement that 'The slope must be positive' is a likely inference because a positive correlation often implies a positive slope in the regression equation. However, r does not directly provide the slope value; that requires further calculation. On the other hand, the statement 'The association must be negative' is incorrect, as the value of r would be negative in that case. The claim that 'The association is weakened by outliers' is general and not necessarily implied by r alone. Outliers can affect the correlation by increasing or decreasing the strength of the association, depending on their position relative to the data points in the scatterplot.
Finally, we can note that while the correlation coefficient is a measure of association strength, it does not imply causation and does not alone provide enough information to predict exact values. To obtain prediction equations, you would need to conduct a regression analysis and determine the regression equation.