What can be concluded when the correlation between a family's weekly income and restaurant spending is r = 0.30?

When the correlation coefficient, denoted as r, is 0.30, it indicates a positive correlation between the two variables: a family's weekly income and their spending at restaurants. A correlation of 0.30 suggests a moderate positive relationship, which means that as the weekly income of the family increases, their spending at restaurants also tends to increase, albeit not perfectly due to the relatively low strength of the correlation.

This understanding is essential, as it highlights that there is a tendency for families with higher incomes to spend more on dining out, rather than an absolute cause-and-effect relationship. The presence of a correlation does not imply that income is the only factor influencing restaurant spending. Other variables, such as personal habits, family size, or lifestyle choices, can also play a significant role, although they are not reflected in this specific analysis.

In summary, a correlation of 0.30 provides evidence that generally, families with higher incomes are likely to spend more on restaurant dining, thereby confirming the choice that higher income generally correlates with higher spending.