Question

A researcher was interested in predicting the birth weight of babies in a particular population. Data was collected from 42 babies and their parents at the time of birth. The following variables were included in the data collection: birth weight (lbs) (Birthweight), gestational age of the baby at birth (weeks) (Gestation), mother's height (mheight) and weight (before pregnancy) (mppwt), mother's age at time of birth (motherage), and mother's smoking status (smokes/does not smoke) (smoker).

The researcher is trying to decide which variables to include in the regression model. To help with this decision, the researcher generated a correlation matrix that includes all of the continuous variables. The matrix is shown below.

rcorr(as.matrix(bwt2), type="pearson")

Birthweight Gestation motherage mheight mppwt

Birthweight 1.00 0.71 0.00 0.37 0.39

Gestation 0.71 1.00 0.01 0.23 0.25

motherage 0.00 0.01 1.00 0.05 0.28

mheight 0.37 0.23 0.05 1.00 0.67

mppwt 0.39 0.25 0.28 0.67 1.00

n= 42

1. Multicollinearity is an issue that can arise in the context of multiple linear regression. Consider the correlation matrix shown above and indicate whether you would expect it to be a problem in this analysis.

a. no, most likely not a problem since the correlations between the predictors are all <.7. b. yes, most likely a problem since the correlation between gestation and birthweight is >.70. c. you cannot tell based on the information provided

2. Again, considering the results (shown above in question 3) from the analysis using smoking status as the predictor of birthweight and using a significance level of .05, is it reasonable to conclude that mean birthweight is statistically different for babies with a non-smoking mother compared to babies with a smoking mother.

a. no, the test of the smoker coefficient would not be considered statistically significant. b. yes, the test of the smoker coefficient would be considered statistically significant. c. there is not enough information to tell

3. Consider the output that is presented in the previous question (5), what percent of the variation in birthweight can be explained by the linear combination of the predictor variables?

a. 86%. b. 62%

Answer 1

1. b. yes, most likely a problem since the correlation between gestation and birthweight is >.70.

2. b. yes, the test of the smoker coefficient would be considered statistically significant.

3. a. 86%

Thankyou for this question. Glad to help you