A Biology student who created a regression model to use a bird's height when perched for predicting its wingspan made these two
statements. Assuming the calculations were done correctly, explain what is wrong with each interpretation. a. An R2 of 93% shows that this linear model is appropriate.
b. A bird 10 inches tall will have a wingspan of 17 inches.
A) Choose the correct choice below.
A. R2 is an indication of the nonlinearity of the model, not the appropriateness of the model. A regression line is the indicator of an appropriate model.
B. R2 is an indication of the nonlinearity of the model, not the appropriateness of the model. A scattered residuals plot is the indicator of an appropriate model.
C. R2 is an indication of the strength of the model, not the appropriateness of the model. A scattered residuals plot is the indicator of an appropriate model.
D. R2 is an indication of the strength of the model, not the appropriateness of the model. A regression line is the indicator of an appropriate model.
B) Choose the correct choice below.
A. Regression models give predictions, not actual values. The student should have said, "The model predicts that a bird 10 inches tall is expected to have a wingspan of 17 inches."
B. Regression models give averages, not actual values. The student should have said, "A bird 10 inches tall will, on average, have a wingspan of 17 inches."
C. Regression models give probabilities, not actual values. The student should have said, "A bird 10 inches tall will probably have a wingspan of 17 inches."
D. Regression models give actual values, but the student should have said, "The model states that a bird 10 inches tall will have a wingspan of 17 inches."
The wingspan is the dependent variable while the bird height is the independent variable.
a) Since R2 is the dependent variable, it can be expressed by the independent variable. An R2 of 93% represents 93% of the variation in the wingspan which can be explained by using the birds height. This means that the appropriateness of the model should not be determined by R2 but by using a scatter plot.
b) The model predicts the value of wingspan using the value of bird height. We cannot say that the bird 10 inches tall has a wingspan if 17 inches instead, we say that the wingspan of the bird which is 10 inches tall is 17 inches.
It is therefore possible that the wing span is not exactly 17 inches
