INTERPRETING MULTIPLE REGRESSION AND LOGISTIC REGRESSION

Develop hypotheses, to calculate statistics, and to interpret output and summary tables

Focuses on the interpretation of multiple regression and logistic regression

PART ONE: MULTIPLE REGRESSION

Suppose that we are interested in estimating length (in centimeters) among low birth weight infants (defined as weight less than 1500 grams). In particular, we want to investigate whether gestational age (in weeks) and a mother's diagnosis of toxemia during pregnancy (Yes=1/No=0) can help predict an infant's length. To estimate length (LENGTH), we collected data on gestational age (GEST_AGE) and mother's toxemia diagnosis (TOXEMIA) of 100 infants. We analyze the data using SAS's REG procedure and observe the results shown in Table 1 (see page 6). Based on those findings, answer the following questions.

1) Identify the dependent variable and the independent variables in this study. Also, state the Omnibus Null and Alternative hypotheses.

2) Report the test statistic and P-value that should be used to test the Omnibus (or Overall) Null hypothesis. What is your conclusion about the Omnibus Null hypothesis?

3) Report and interpret the parameter estimates for GEST_AGE and TOXEMIA from the SAS output. [Hint: Remember that TOXEMIA is an indicator variable (i.e. 1 vs 0). The parameter estimate will reflect the difference in DV for moms with toxemia (1) compared to moms without toxemia (0).]

According to the output, which of the independent variables are significant predictors of infant length?

4) Using the regression equation (Y = a + b1X1 + B2X2), calculate the predicted length for an infant at a gestational age of 40 weeks and ...

a. Whose mother was diagnosed with toxemia during pregnancy:

b. Whose mother was not diagnosed with toxemia during pregnancy:

[Show your work and wait to round to two decimal places until the end, after the math is done.]

5) Interpret these findings (3-5 sentences max). Your answer should (1) restate the findings, (2) include an interpretation of the R-square value, and (3) state what these findings mean from clinical perspective.

PART TWO: LOGISTIC REGRESSION

Suppose that we are interested in the relationship between age (in years), smoking history (Smoker=1/Non-smoker=0), cholesterol (High=1/Normal=0), and the development of aortic stenosis. To examine this association, we conduct a case-control study, enrolling 110 persons. Among the study subjects, 59 persons have developed aortic stenosis (cases) and 51 persons have not (controls). We collect information regarding age (AGE), smoking history (SMOKE), and cholesterol (CHOLSTRL). We analyze the data using SAS's LOGISTIC procedure and observe the results shown in Table 2 (see pages 7-8). Based on those findings, answer the following questions.

1) Identify the dependent variable and the independent variables in this study. Also, state the Omnibus Null and Alternative hypotheses.

2) Report the test statistic and P-value that should be used to test the Omnibus Null hypothesis (i.e. "Global Null" per SAS). What is your conclusion about the Omnibus Null hypothesis?

3) According to the output, which of the independent variables are significant predictors of aortic stenosis? Which of the independent variables are not significant predictors of aortic stenosis? Be sure to include the reasoning for your decisions.

4) Report the odds ratios for SMOKE, and CHOLSTRL. Interpret each odds ratio with regards to one's odds of developing aortic stenosis.
[Hint: Do not restate the decision that you made in Question 3. This question is about interpreting the point estimate itself. That is, what does an odds ratio greater than one or less than one mean particularly for someone who is a smoker or has high cholesterol? Remember that these two variables are indicator variables (i.e. 1 vs 0). As you interpret them, refer to the question information about the codes for 1 and 0 for each variable.]

5) In 3-4 sentences (max), discuss what these findings mean from public health perspective. In particular, how might these findings inform or guide educational or prevention strategies aimed at minimizing aortic stenosis?

Attachment:- Table.pdf