A scientist claims that he has developed a model that predicts a person's systolic blood pressure...

A scientist claims that he has developed a model that predicts
a person's systolic blood pressure perfectly. His claim is based on the results
of a multiple linear regression analysis on eight people. He performed the
regression with six predictor variables: height, age, number of children, month
of birthday (January = 1, February = 2, and so on), last digit of social
security number, and right-handedness (= 1 for right-handed, = 0 for
left-handed). The data appear in the following table.

(a) For the scientist's multiple linear
regression analysis, what are the total df? Regression df?

(b) How many df remain for the error? Given
that SSE = 0.79345, test H0: β1= β2= β3= β4= β5=
β6

(c) The parameter estimates from the scientist's model are
given below. Calculate the predicted systolic blood pressure for Subject 6 and
compare it to the actual systolic blood pressure.

(d) The scientist reasons that since the
model predicts the SBP almost perfectly, the statistical significance of the
parameter estimates does not matter. Do you agree with him? Explain.

(e) Perform a simple linear regression
analysis by regressing SBP on height. Test

H0: βι = 0 versus i/ a:
βι > 0. Interpret your results.