Based on an observational study, a clinical psychologist finds that the relation

Question

Based on an observational study, a clinical psychologist finds that the relationship between the number of weeks spent in a therapy hospital and number of seizures per week can be described by the following equation:

seizures per weekˆ=14.090.91×(weeks in hospital)

The R2 for this model is 0.90, and you can assume that all of the conditions for linear regression to be valid have been met. Suppose that you use this model to predict the number of seizures per week for a patient who has been at the hospital for 20 weeks. What is the predicted number of seizures per week for that patient?

Answer:

What is the most likely explanation for the prediction you obtained for the previous problem?

Select one:

a. The linear regression model was likely developed using data on patients who did not stay at the hospital for longer than ~15 weeks.

b. The relationship between weeks spent in the hospital and number of seizures per week is nonlinear.

c. The variance of the residuals was not constant.

d. There were a number of influential points of high leverage in the data that skewed the linear regression model.

Explanation / Answer

a. The linear regression model was likely developed using data on patients who did not stay at the hospital for longer than ~15 weeks.

If the model would be valid for 15 weeks then it would not be useful to predict the value of y for 20 weeks.

Option A is correct.

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