INTERPRETING MULTIPLE REGRESSION
AND LOGISTIC REGRESSION
Biostat Assignments provide opportunities for you to develop hypotheses, to calculate statistics, and to interpret output and summary tables. Each assignment focuses on one or two of the statistical concepts discussed in the weekly readings. Biostat Assignment 5 focuses on the interpretation of multiple regression and logistic regression. There are 10 questions below; each question is worth 1 point. Submit your completed assignment through the linkprovided on Blackboard.
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:
5) Write a one-paragraph summary of your interpretation of these findings. In your summary, include an interpretation of the R-square value. At the end of your summary, discuss the generalizability of these results. What do the 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 110persons. 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 you made in Question 3. This is question is about interpreting the point estimate - that is, what does the odds ratio mean 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 1and 0 for each variable.]
5) Write a one-paragraph summary of your interpretation of these findings. Towards the end of your summary, include a discussion about the generalizability of these results. What do the findings mean from clinical perspective?