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)	55.9	58.2	42.4	54.3	59.7	42.9	59.7	55.5	62.1	54.8	42.4	64.2
Rate (yy)	971.1	952.8	984.6	979.7	928.3	966.1	952.3	984.5	933.9	973.2	976.6	939.8

Consider the hypothesized linear model y=β0+β1xy=β0+β1x.

(a) Compute a 9595% confidence interval for β1:β1:  to

(b) Test whether metabolic rate is linearly related to lean body mass. Use α=0.05.α=0.05.
State the test statistic t=t=

(c) Using α=0.05α=0.05, 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=0.05α=0.05 level.
  B. There is statistically significant evidence of a linear relationship at the α=0.05α=0.05 level.

Answer 1

using excel>Data>data analysis >Regression

we have

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.683658
R Square	0.467388
Adjusted R Square	0.414127
Standard Error	15.24797
Observations	12
ANOVA
	df	SS	MS	F	Significance F
Regression	1	2040.284	2040.284	8.775397	0.014231
Residual	10	2325.005	232.5005
Total	11	4365.289
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%
Intercept	1058.201	32.80231	32.25995	1.93E-11	985.1126	1131.289
Mass (x)	-1.77198	0.598171	-2.96233	0.014231	-3.10479	-0.43917

Consider the hypothesized linear model y=β0+β1x

(a) Compute a 95% confidence interval for β1  is -3.10479 to -0.43917

(b)
e the test statistic t=-2.962

(c)

  B. There is statistically significant evidence of a linear relationship at the α=0.05 level.