Question

A Biology student who created a regression model to use a​ bird's Height when perched for predicting its Wingspan made the following two statements. Assuming the calculations were done​ correctly, explain what is wrong with each interpretation. ​a) My Upper R squared of​ 93% shows that this linear model is appropriate. ​b) A bird 10 inches tall will have a wingspan of 17 inches. ​a) What is wrong with the statement​ "My Upper R squared of​ 93% shows that this linear model is​ appropriate"?

Answer 1

Answer:

(A) A scatter plot is used to determine if the linear model is appropriate.

(B) A linear model estimates the value of the dependent variables.

Step-by-step explanation:

The regression model is formed to estimate the Wingspan using the bird's Height when perched.

The model is of the form:

$Wingspan=\beta Bird's\ height\ + \alpha +\epsilon$

(A)

The R squared value is a statistic that is used to determine the proportion of variation in the dependent variable that can be explained by the independent variables.

R squared value of 93% indicates that 93% variation in the Wingspan is explained y the bird's height when perched.

To determine whether the linear model is appropriate one could use a scatter plot. A scatter plot is used to determine whether the provided data is representing the linear relation between two variables.

(B)

The regression model is:

$Wingspan=\beta Bird's\ height\ + \alpha +\epsilon$

This model is used to estimate the wingspan for any provided bird's height.

It does provided an accurate value of the dependent variable.

Thus, a bird with height 10 inches can have an estimated wingspan of 17 inches.