Suppose we are interested in identifying predictive factors of sleep apnoea. We recruit 40 subjects and collect data on their Apnoea-hypopnoea Index (AI-II). We also collect data on predictive variables of body mass index (BMI), systolic blood pressure (SBP), age (AGE) and gender (coded as GEN=1 if female, GEN=0 if male). AHI is represented by the number of am and hypom events per hour of sleep. We analyze the data using SAS's REG procedure and observe the results shown in Table 1 (see page 5). Based on those ndings, 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) From the SAS output, report and interpret the parameter estimates for the three continuous independent variables: (1) body mass index (BMI) in kg/mz, (2) systolic blood pressure (SBP) in mmHg, and (3) age (AGE) in year. According to the SAS output, which of the four independent variables (including gender) are signicant predictors for linear change in the sleep apnoea severity? Which ones are not signicant predictors? 4) Using the regression equation, predict the sleep apnoea severity for a female (GEN=1) with a BMI of 28 kg/mz, a SBP of 140 mm Hg and an age of 42 years. 5) Interpret these ndings (3-5 sentences max). Your answer should (1) restate the ndings, and (2) include an interpretation of the Rsquare value. Table 1: Output for Part One Multiple Linear Regression The REG Procedure Model: MODEL1 Dependent Variable: AHI Number of Observations Read 40 Number of Observations Used 40 Analysis of Variance Sum of Mean Source DF Squares Square F Value Pr > F Model 627.49819 156.87455 2.74 0.0441 Error 35 2005.53325 57.30095 Corrected Total 39 2633.03144 Root MSE 7.56974 R-Square 0.2383 Dependent Mean 23.53875 Adj R-Sq 0.1513 Coeff Var 32.15863 Parameter Estimates Parameter Standard Variable DF Estimate Error t Value Pr > It) Intercept 1 -11.64674 11.49000 -1.01 0.3177 BMI 0.36856 0. 16016 2.30 0.0275 SBP 0.12866 0.04931 2.61 0.0133 AGE 0. 14623 0. 11909 1.23 0.2277 GEN 1 -2.26937 2.48261 -0.91 0.3669