Question

1. Suppose these physicians are interested in further investigating abnormal chromosomal development. They recruit 6 women from a local hospital who meet the following requirements: they have had at least 1 pregnancy loss (miscarriage) in their lifetime, and 2) their doctors properly documented their levels of PAPP-A in the first trimester of each pregnancy. PAPP-A is used as a measure of fetal chromosomal development during the first trimester of development. Low levels of PAPP-A have been associated with many fetal chromosomal abnormalities. The physicians believe that levels of PAPP-A (x variable) may be related to pregnancy loss (y variable): they predict that women with low levels of PAPP-A will experience more pregnancy losses in their lifetime. The data are below. Plot the data in a scatterplot. Draw your best estimate of the regression line. What direction is the correlation?

Subject	1	2	3	4	5	6
# of pregnancy losses in lifetime	2	1	3	6	5	4
Average PAPP-A level during first trimester of pregnancy (in IU/liter)	9.00	9.50	7.00	0.50	2.10	5.50

2. Based on the results of the study described in Question #2, the physicians rerun the same study with 600 women. Results of the correlation analysis are as follows: r = -.464, p = .0091, a = .05. State the direction of the correlation, whether it is significant, and provide an interpretation of the results.

3. What is the r² value and its corresponding interpretation?

Answer 1

Given for a correlation test

r = -.464, p = .0091, a = .05.

the direction of the correlation is opposite to each other because r is negative, which means increase in Average PAPP-A level during first trimester of pregnancy decreases the # of pregnancy losses in lifetime.

here for the correlation test p-value is given as 0.0091 and the level of significance alpha = 0.05,

since p-value is less than alpha we reject null hypothesis and conclude that there is a significant correlation exists between the given variables.

r2 value = r2 = (-0.464)2 = 0.215

Interpretation of r2 : - The model explains 21.5% of the variability between the  # of pregnancy losses in lifetime using the  Average PAPP-A level during first trimester of pregnancy as an independent variable.