Question

a doctor keeps track of the amount of time they spend per patient. the model \\(\hat{y} = 12.248x + 1.7\\) explains the relationship between \\(x\\), the number of visits per year, and \\(y\\), the number of minutes the doctor spends writing in the patients record. interpret the slope in the real-world context.

• for every increase of one visit per year, the doctor is predicted to increase the amount of time writing in the patients record by 1.7 minutes.
• for every increase of one visit per year, the doctor is predicted to increase the amount of time writing in the patients record by 12.248 minutes.
• when the patient does not visit, the doctor spends 1.7 minutes writing in the patients record.
• for every increase of one visit per year, the doctor is predicted to decrease the amount of time writing in the patients record by 12.248 minutes.

Explanation:

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<reasoning>

Identify the variables and model

The linear regression model is given by:
\[\hat{y} = 12.248x + 1.7\]
where:

• \(x\) represents the number of visits per year.
• \(\hat{y}\) represents the predicted number of minutes spent writing in the patient's record.

Identify the slope

In the linear equation of the form \(y = mx + b\), the slope is the coefficient of \(x\):
\[m = 12.248\]

Interpret the slope in context

The slope represents the change in the predicted dependent variable (\(y\)) for each unit increase in the independent variable (\(x\)).
Since the slope is positive (\(+12.248\)), for every increase of one visit per year (\(\Delta x = 1\)), the predicted amount of time spent writing in the record increases by \(12.248\) minutes.
</reasoning>

<answer>
<mcq-option>(A) For every increase of one visit per year, the doctor is predicted to increase the amount of time writing in the patient's record by 1.7 minutes.</mcq-option>
<mcq-correct>(B) For every increase of one visit per year, the doctor is predicted to increase the amount of time writing in the patient's record by 12.248 minutes.</mcq-correct>
<mcq-option>(C) When the patient does not visit, the doctor spends 1.7 minutes writing in the patient's record.</mcq-option>
<mcq-option>(D) For every increase of one visit per year, the doctor is predicted to decrease the amount of time writing in the patient's record by 12.248 minutes.</mcq-option>
</answer>

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Answer:

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<reasoning>

Identify the variables and model

The linear regression model is given by:
\[\hat{y} = 12.248x + 1.7\]
where:

• \(x\) represents the number of visits per year.
• \(\hat{y}\) represents the predicted number of minutes spent writing in the patient's record.

Identify the slope

In the linear equation of the form \(y = mx + b\), the slope is the coefficient of \(x\):
\[m = 12.248\]

Interpret the slope in context

The slope represents the change in the predicted dependent variable (\(y\)) for each unit increase in the independent variable (\(x\)).
Since the slope is positive (\(+12.248\)), for every increase of one visit per year (\(\Delta x = 1\)), the predicted amount of time spent writing in the record increases by \(12.248\) minutes.
</reasoning>

<answer>
<mcq-option>(A) For every increase of one visit per year, the doctor is predicted to increase the amount of time writing in the patient's record by 1.7 minutes.</mcq-option>
<mcq-correct>(B) For every increase of one visit per year, the doctor is predicted to increase the amount of time writing in the patient's record by 12.248 minutes.</mcq-correct>
<mcq-option>(C) When the patient does not visit, the doctor spends 1.7 minutes writing in the patient's record.</mcq-option>
<mcq-option>(D) For every increase of one visit per year, the doctor is predicted to decrease the amount of time writing in the patient's record by 12.248 minutes.</mcq-option>
</answer>

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