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+100
f left parenthesis x right parenthesis is similar to 9 x plus 10

f(x)∼−9x +58
f left parenthesis x right parenthesis is similar to negative 9 x

f(x)∼−9x+100
f left parenthesis x right parenthesis is similar to negative 9 x plus 10

f(x)∼9x +58

Answer 1

To determine the appropriate regression model based on the description of the graph, we need to consider the typical relationship between time spent working (x-axis) and test grades (y-axis).

1. Positive Relationship: If the graph shows a rising trend, it suggests that as the number of hours worked increases, the test grades also increase. In this case, a positive slope (e.g., \(f(x) \sim 9x + b\)) would be expected.

2. Negative Relationship: Conversely, if the graph indicates that test grades decrease as hours worked increase (which is less common), a negative slope (e.g., \(f(x) \sim -9x + b\)) would be likely.

Since the question doesn't provide a direct visual of the graph, and based on the likely expectation that more study time correlates with better grades, a positive model would generally be more plausible.

Among the options given:

• f(x)∼ 9x + 58 suggests a positive correlation,
• The others indicate negative correlations (which would be less common).

Therefore, if the context implies a positive relationship, the most appropriate regression model among the choices provided would be:

f(x)∼9x + 58.