Use the image to answer the question.

Question

On a graph titled Time Spent and Test Grades, a line and ten points are plotted in quadrant 1 of a coordinate plane. The x-axis is labeled Hours Worked, and the y-axis is labeled Grade.

Which of the following is an appropriate regression model given the bivariate dataset?

(1 point)
Responses

f(x)∼9x
f left parenthesis x right parenthesis is similar to 9 x

f(x)∼−9x+10
f left parenthesis x right parenthesis is similar to negative 9 x plus 10

f(x)∼−9x
f left parenthesis x right parenthesis is similar to negative 9 x

f(x)∼9x+10

Answer 1

To determine the most appropriate regression model from the options provided, we need to analyze the relationship between the two variables: Hours Worked (x) and Grade (y).

Based on the context of the problem, as the time spent working (hours) increases, we would generally expect test grades (y) to also increase, assuming that increased study or work time yields better results. Therefore, a positive correlation is likely.

Given the options:

1. \( f(x) \sim 9x \) indicates a positive linear relationship, which could be appropriate if grades increase consistently with more hours.

2. \( f(x) \sim -9x + 10 \) suggests a negative relationship; as hours increase, grades decrease, which doesn't fit the expected pattern.

3. \( f(x) \sim -9x \) similarly indicates a negative linear relationship, which is also unlikely.

4. \( f(x) \sim 9x + 10 \) indicates a positive relationship with an intercept, suggesting that even without studying, there may still be a base level of grades achieved.

Based on this reasoning, the best options that depict a positive relationship are either \( f(x) \sim 9x \) or \( f(x) \sim 9x + 10 \). Without seeing the actual line plotted, if the line crosses the y-axis above zero, then \( f(x) \sim 9x + 10 \) would be more appropriate, indicating that even without working hours, there is an initial grade.

So, if we must choose, the most appropriate regression model is likely:

f(x) ∼ 9x + 10.