A researcher recorded height and weight for 112 male college students. She perfo

Question

A researcher recorded height and weight for 112 male college students. She performed a regression of weight on height and obtained the residuals and standardized residuals for all 112 students. Which of the following is not a possible explanation for a student who obtained a standardized residual of 5.2?

A. This observation represents a regression outlier.

B. The standardized residuals do not have a bell-shaped distribution.

C. This person is much taller than the other students.

D. The relationship between weight and height is not truly linear and the model does not fit well.

Explanation / Answer

a student has a standardized residual of 5.2
now standardized residual means residual divided by its standard error.

so if e is the residual.

then the standardized residual is T=e/standard error(e)

and by assumption mean of e is zero.

so E[T]=0 and V[T]=V[e]/[standard error(e)]2=V[e]/V[e]=1

so a value of 5.2 of standardized residual is very high and very unsual.

a very high standardized residual implies that maybe that point is an outlier

but the standardized residuals always have a bell shaped distribution for linear regression.

hence the correct option is option B.The standardized residuals do not have a bell-shaped distribution. because it can not happen.

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