Question

We have data on the lean body mass and resting metabolic rate for 12 women who are subjects in a study of dieting. Lean body mass, given in kilograms, is a person's weight leaving out all fat. Metabolic rate, in calories burned per 24 hours, is the rate at which the body consumes energy.

Mass (xx)	62.7	48.6	51	55.8	46.4	62.9	45.9	59.7	48.2	55.6	64.4	63.8
Rate (yy)	841.3	904.4	903	892.2	887.6	880.1	914.1	893.3	907.8	868.4	858.6	892.2

Consider the hypothesized linear model y=β0+β1xy

(a) Compute a 99% confidence interval for β1:

(b) Test whether metabolic rate is linearly related to lean body mass. Use α=0.01  
State the test statistic t=

(c) Using α=0.01, which statement best describes the correct conclusion for the test:  
  Enter A or B:
   A. There is not statistically significant evidence of a linear relationship at the α=0.01 level.
   B. There is statistically significant evidence of a linear relationship at the α=0.01 level.

Answer 1

SSE =Syy-(Sxy)2/Sxx=

2,687.5061

	s2 =SSE/(n-2)=	268.7506
std error σ              =	=se =√s2=	16.3936

estimated std error of slope =se(β1) =s/√Sxx=

0.6876

a_)

for 99 % CI value of t=			3.169
margin of error E=t*std error                            =			2.1791
lower bound=estimated slope-margin of error =			-4.2428
Upper bound=estimated slope+margin of error=			0.1154

b)

test stat t =

(bo-β1)/se(β1)=

=

-3.0014

  A. There is not statistically significant evidence of a linear relationship at the α=0.01