Use the following to answer the question(s) below.
A newly developed drug is tested to determine absorption levels in a patient's bloodstream. A patient is injected with the drug and the concentration (units/cc) in the patient's blood is measured every hour for seven hours. Below is the output from fitting a linear regression model.
-Re-expressing these data results in the following model The residuals plotted against the fitted values for this model is shown below. What is true about the predicted concentration level after 10 hours has elapsed?
A) The predicted value is 0.1000 units/cc.
B) This value is considered as a regular one.
C) This value is accurate because R2 = 100%.
D) The predicted value is 1.2589 units/cc, and this value is considered an extrapolation.
E) All of the given statements are true.

Question

Use the following to answer the question(s) below.
A newly developed drug is tested to determine absorption levels in a patient's bloodstream. A patient is injected with the drug and the concentration (units/cc) in the patient's blood is measured every hour for seven hours. Below is the output from fitting a linear regression model.  
-Re-expressing these data results in the following model  The residuals plotted against the fitted values for this model is shown below.  What is true about the predicted concentration level after 10 hours has elapsed?
A) The predicted value is 0.1000 units/cc. 
B) This value is considered as a regular one. 
C) This value is accurate because R2 = 100%. 
D) The predicted value is 1.2589 units/cc, and this value is considered an extrapolation. 
E) All of the given statements are true.

Quizplus · Accepted Answer

Based on the linear regression model and re-expressed data, the predicted concentration level after 10 hours has elapsed can be calculated by plugging in the value of 10 for the predictor variable ("time") in the equation:
concentration = -0.1021 + 0.1466*time

Thus, concentration at 10 hours = -0.1021 + 0.1466*10 = 1.2589 units/cc.

Since this value is outside of the range of the original data (which was measured for only 7 hours), it is considered an extrapolation rather than an interpolation, and may be less reliable. Therefore, option D is the only correct choice.

Option A is incorrect because it refers to a different value (0.1000 units/cc) which is not mentioned in the question or provided data.

Option B is subjective and not supported by any evidence.

Option C is incorrect because while a high R-squared value (not 100% in this case) does indicate a good fit between the model and the data, it does not guarantee accuracy when making predictions outside of the observed range.

Therefore, the correct answer is D.

Use the Following to Answer the Question(s) Below