Question

Research performed at NASA and led by Dr. Emily R. Morey-Holton measured the lengths of the right humerus and right tibia in 11 rats that were sent into space on Spacelab Life Sciences 2. The following data were collected:

Right Humerus (mm), x	Right Tibia (mm), y	Right Humerus (mm), x	Right Tibia (mm), y
24.8	36.05	25.9	37.38
24.59	35.57	26.11	37.96
24.59	35.57	26.63	37.46
24.29	34.58	26.31	37.75
23.81	34.2	26.84	38.5
24.87	34.73

a) Treating the length of the right humerus as the explanatory variable, x, determine the estimates of beta0 and beta1

b) Compute the standard error of the estimate

c) Determine whether the residuals are normally distributed

d) If the residuals are normally distributed, determine sb1

e) If the residuals are normally distributed, test whether a linear relation exists between the length of the right humerus, x, and the length of the right tibia, y, at the alpha=0.01 level of significance

f) If the residuals are normally distributed, construct a 99% confidence interval for the slope of the true least-squares regression line.

g) What is the mean length of the right tibia on a rat whose right humerus is 25.93 mm?

Answer 1

a) beta0= 1.114

beta1= 1.390

b) standard error of estimate= sqrt(sse/n-k)= sqrt(2.20/9)= 0.4944

d) sb1= 0.150

From above residual plot residuals are normally distributed.

e) Null hypothesis H0:

Alternative Hypothesis Ha:

P value from above table is 0.000 which is less than the level of significance therefore we REJECT NULL HYPOTHESIS H0 and conclude that there is linear relationship between x and y.

f) 99% confidence interval of beta1 is (0.902,1.878)

g) x=25.93mm

Y=1.114+1.39*X

Y= 1.114+1.39*25.93

Y= 37.16 mm