Question
Use the image to answer the 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 9 x
f(x)∼−9x +58
f left parenthesis x right parenthesis is similar to negative 9 x
f(x)∼−9x+100
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 9 x
f(x)∼−9x +58
f left parenthesis x right parenthesis is similar to negative 9 x
f(x)∼−9x+100
Answers
Answered by
GPT-4o mini
To determine the appropriate regression model for the relationship between time spent (Hours Worked) and test grades, we should consider the general trend observed in the dataset. Since it is common for grades to increase with more hours worked, we typically expect a positive correlation.
1. The options with "−9x" suggest a negative correlation, which is not expected in this context.
2. The options with "9x" indicate a positive correlation.
Now, evaluating the constant terms:
- If we assume that as hours worked increases, grades also increase, we can focus on the models f(x) ∼ 9x + 10 and f(x) ∼ 9x + 58, as they both show positive slopes.
- The specific numerical value of the intercept would depend on the points plotted in the dataset.
Without seeing the data, we can't definitively choose an intercept. However, if the dataset shows that grades start from a reasonable point (not too high), then a model like f(x) ∼ 9x + 10 might be more appropriate compared to those with larger intercepts (like +58).
Based on typical scenarios and considering the plausible range for grades based on hours worked, if we had to pick one from the options given:
**f(x) ∼ 9x + 10** looks like a reasonable guess for an appropriate regression model, as it suggests a positive linear relationship consistent with many educational contexts.
However, please choose the option that fits best with the data points if you are able to observe the graph more closely!
1. The options with "−9x" suggest a negative correlation, which is not expected in this context.
2. The options with "9x" indicate a positive correlation.
Now, evaluating the constant terms:
- If we assume that as hours worked increases, grades also increase, we can focus on the models f(x) ∼ 9x + 10 and f(x) ∼ 9x + 58, as they both show positive slopes.
- The specific numerical value of the intercept would depend on the points plotted in the dataset.
Without seeing the data, we can't definitively choose an intercept. However, if the dataset shows that grades start from a reasonable point (not too high), then a model like f(x) ∼ 9x + 10 might be more appropriate compared to those with larger intercepts (like +58).
Based on typical scenarios and considering the plausible range for grades based on hours worked, if we had to pick one from the options given:
**f(x) ∼ 9x + 10** looks like a reasonable guess for an appropriate regression model, as it suggests a positive linear relationship consistent with many educational contexts.
However, please choose the option that fits best with the data points if you are able to observe the graph more closely!
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