To choose the appropriate regression model from the options provided, we need to consider the relationship suggested by the description: a graph titled "Time Spent and Test Grades" plotted in quadrant 1 indicates a positive correlation between hours worked (x-axis) and grades (y-axis). In this context, we would generally expect that as the number of hours worked increases, the test grades would also increase.
In the options provided, the key consideration is the sign of the slope:
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f(x) ∼ −9x + 100: This indicates a negative relationship, meaning that as hours worked increase, grades would decrease, which does not align with the positive correlation we would expect.
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f(x) ∼ 9x + 58: This indicates a positive relationship, suggesting that an increase in hours worked leads to an increase in grades.
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f(x) ∼ −9x + 58: This suggests a negative relationship, similar to the first option.
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f(x) ∼ 9x + 100: This also indicates a positive relationship and suggests higher grades with more hours.
Given that we expect a positive correlation between hours worked and grades, the two viable options are:
- f(x) ∼ 9x + 58
- f(x) ∼ 9x + 100
Without more information about the specific values on the graph, we cannot definitively choose between these two. However, since both exhibit the correct positive trend, we could select either of the positive models.
If forced to choose one among the answers, f(x) ∼ 9x + 58 appears to be an appropriate regression model as it indicates a positive trend with a reasonable y-intercept. However, the latter option with a higher intercept, f(x) ∼ 9x + 100, may also make sense if we were to consider what grades could start from.
Ultimately, if there is no more information provided:
Choose: f(x) ∼ 9x + 58 as an appropriate regression model.