Quiz 3

3. A student who has created a linear model is disappointed to find that her R2value is a very low​ 13%. Complete parts a and b below.

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a) Does this mean that a linear model is not​ appropriate? Explain.

Choose the correct answer below.

1. Yes. If the linear model produces an R2 value of​ 13%, then it is expected that a stronger model will produce an even higher R2 value.​ Therefore, the linear model is not appropriate.
2. No. There is no R2 value that must be met in order for the linear model to be valid. Determining whether the linear model is appropriate involves understanding the context in which the data was collected.
3. No. The linear model is typically preferred because of its simplicity. Using a nonlinear model often introduces unnecessary​ complexity, so the linear model is valid.
4. Yes. If a linear model produces an R2 value under​ 25%, then the linear model is not appropriate.

​b) Does this model allow the student to make accurate​ predictions? Explain.

Choose the correct answer below.

1. Yes. The model allows the student to make accurate predictions because the low R2 value indicates that the data likely came from an observational study or​ survey; given the​ context, the model produces sufficiently accurate predictions.
2. No. A low R2 value indicates that there is a large amount of variation around the regression​ line, which implies that accurate predictions are difficult.
3. Yes. The model allows the student to make accurate predictions because the R2 value exceeds the minimum value required for the linear model to be valid.​ Predictions, then, will be sufficiently accurate for the given data.
4. No. The model does not allow the student to make accurate predictions because the R2 value does not exceed the minimum value required for the linear model to be valid.