Biometrics Homework Assignment 5 Page 2 3 Six subjects consu

Biometrics Homework Assignment #5 Page 2 3. Six subjects consumed three beers in a one hour period and their blood alcohol levels were measured, each subject had a different body weight. Plot a graph of blood alcohol as a function of body weight. Fit a linear regression line to these data and plot the regression line on the graph. Conduct an ANOVA for the regression and test the hypothesis that the slope is equal to zero. Use the 5% level of significance. (5 points) [Answer: SSX= 1002, SSY= 0.0064, SSXY=-2.25,b=-0.002246, a=0.2472,SSR= 0.0050524, SSE=0.0013476, F=15.00, F0.05,1,4= 7.71.]

Solution

We plot scatter plot and find regression line first

We get regression line as

0.247-0.002x

The graph of the regression line is:

y = 0.2472 - 0.00246 x

Explanation

We will find an equation of the regression line in 4 steps.

Step 1: Find X?Y and X2 as it was done in the table below.

Step 2: Find the sum of every column:

?X=420 , ?Y=0.54 , ?X?Y=35.55 , ?X2=30402

---------------------------------

Testing for slope:

H0:b=0

Ha: b not equals 0

(two sided test)

---------------------------------------------

F=15, df = 4.

F statistic > F critical. Hence null hypothesis is rejected.

The slope is not equal to 0.

X	Y	X?Y	X?X
51	0.14	7.14	2601
60	0.10	6	3600
66	0.12	7.92	4356
72	0.07	5.04	5184
81	0.05	4.05	6561
90	0.06	5.4	8100