The correct interpretation is: On average, households with annual incomes that are $1000 higher than other households have monthly debts that are $10.28 higher.
The regression model y = 10.28x + 206.78 represents the relationship between household annual income (x) and monthly debt (y). The coefficient of x (10.28) represents the change in monthly debt for every $1000 increase in annual income. Since the coefficient is positive, it indicates a positive correlation between annual income and monthly debt. This means that as annual income increases, monthly debt also tends to increase.
Interpreting the coefficient as a causal relationship is not appropriate. The regression model only suggests an association between annual income and monthly debt. Other factors, unobserved in the model, could also influence monthly debt.
Therefore, the most accurate interpretation is that, on average, households with annual incomes that are $1000 higher than other households can expect to have monthly debts that are $10.28 higher. This does not necessarily mean that every household with a higher income will have higher debt, but it does suggest a general trend.