To determine the appropriate regression model for the given bivariate dataset, we should consider the relationship between the two variables: Hours Worked (x-axis) and Grade (y-axis).
Typically, one would expect a positive correlation between hours worked and test grades, meaning that as the number of hours worked increases, the test grades also increase.
Among the provided options, we need to identify the model that reflects a positive correlation:
- \( f(x) \sim 9x + 100 \) - This indicates a positive slope, suggesting that more hours worked increases the grade.
- \( f(x) \sim -9x + 100 \) - This indicates a negative slope, suggesting that more hours worked decreases the grade.
- \( f(x) \sim 9x + 58 \) - This also indicates a positive slope, suggesting an increase in grades with more hours worked.
- \( f(x) \sim -9x + 58 \) - This indicates a negative slope, suggesting a decrease in grades with more hours worked.
Given that we are looking for a positive correlation, the appropriate regression models would be:
- \( f(x) \sim 9x + 100 \)
- \( f(x) \sim 9x + 58 \)
Without seeing the exact graph, we can't definitively choose between these two positive options. However, if the points cluster around a certain level or trend upwards, either of the two positive options would be valid.
Thus, if you're looking for a model that accurately reflects a positive trend, the response could be either \( f(x) \sim 9x + 100 \) or \( f(x) \sim 9x + 58 \).
If we must select just one based on common practice and given options, we could go with:
\( f(x) \sim 9x + 58 \)
as it suggests a foundational positive relationship.