Part One: Multiple Regression A nutritionist has a dataset with various cereals and their nutritional breakdown including

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Part One: Multiple Regression

A nutritionist has a dataset with various cereals and their nutritional breakdown including calories, sugars, carbohydrate, protein, total fat, and sodium per portion. Her goal is to estimate the number of calories per portion in a box of cereal based on the sugars, carbohydrate, protein, total fat, and sodium intake. We analyze the data using SAS's REG procedure and observe the results shown in Table 1 (see page 5). 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 sugars, carbohydrate, protein, total fat, and sodium from the SAS output.

4) Using the regression equation, predict the number of calories per portion in a box of cereal with 5 grams sugars, and 15 grams of carbohydrate, 2 grams of protein, 1 gram of total fat amount, and 2 grams of sodium. [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.

Part Two: Logistic Regression

The study was conducted to examine the occurrence of diabetes among females between 31 to 40 years old. To investigate this, we collect information on the number of pregnancies (Pregnant), 2-hours serum insulin (Insulin), body mass index (Mass), and plasma glucose concentration (Glucose). We determine each subject’s diabetic status (Diabetes) as either “positive” (coded as 1) or “negative” (coded as 0).

We analyze the data using SAS's LOGISTIC procedure and observe the results shown in Table 2 (see pages 6-7). 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) Report the odds ratios and 95% confidence intervals for all four independent variables. Based on those confidence intervals, which of the independent variables are significant predictors of the diabetes and which ones are not significant predictors? Be sure to include the reasoning for your decisions.

4) Report p-values of all four independent variables using “Analysis of Maximum Likelihood Estimates” table in the SAS output. Based on the p-values, which of the independent variables are significant predictors of the diabetes and which ones are not significant predictors? Be sure to include the reasoning for your decisions. Compare your answer with part 2, question 3.

In 3-4 sentences (max), discuss what these findings mean from public health perspective.