Question

A study to determine the relationship between the height of a son and the height of his mother and father used a random sample of size n=15 with a multiple regression equation was =22.97+.30x₁+.41x₂where y is the height of the son, x₁is the height of the mother and x₂is the height of the father.  The standard error coefficient for B₁is .06107 and for B₂is .0544.

a.  Predict the height of the son, if the mother’s height is 70 inches and the father’s height is 72 inches.

      b.   Find the 90% confidence interval for the coefficient B₁.

Answer 1

a)predicted height =22.97+.30*70+.41*72 =73.49

b)

sample size n=				15
number of independent variables p=				2
degree of freedom =n-p-1=				12
estimated slope b=				0.3
standard error of slope=sb=sqrt(SSE/(n-p-1))/sqrt(SSx)=					0.061070
for 90 % confidence and 12degree of freedom critical t=					1.7820
90% confidence interval =b1 -/+ t*standard error=					(0.1912,0.4088)