PART ONE: PEARSON CORRELATION Suppose that we are interested in the strength of association between HbAlc levels (the dependent variable Y) and anxiety/depression measurement using HADS score (the independent variable X) among 10 outpatients receiving treatment for type 2 diabetes. Blood HbAlc levels are reflective of how well diabetes is controlled. Blood HbAlc level and anxiety/depression using HADS scale were collected and provided in the table below: Subjects HADS Level HbAlc levels X-Xbar (X-Xbar)' Y-Ybar (Y-Ybar) (X-Xbar)(Y-Ybar) (x) (Y) 40 -2.4 5.76 -1.4 1.96 3.36 00 - 41 -1.4 1.96 -0.4 0.16 0.56 11 47 1.6 2.56 5.6 31.36 8.96 30 4.4 19.36 -11.4 129.96 50.16 35 -3.4 11.56 -6.4 40.96 21.76 37 -1.4 1.96 -4.4 19.36 6.16 13 47 3.6 12.96 5.6 31.36 20.16 14 49 4.6 21.16 7.6 57.76 34.96 16 48 6.6 43.56 6.6 43.56 43.56 40 -3.4 11.56 -14 1.96 4.76 Total 132.4 358.4 194.4 From White (2020), we know that the formula for the Pearson product moment correlation coefficient is: E(X -X ) ( Y- Y) r = VE ( X -X ) [ ( X- Y) 1) Using the information in the table provided, calculate correlation coefficient (r) and show your work.2) Interpret the size of r in two ways. First, give your interpretation the index value both in terms of direction (positive or negative) and strength (weak, moderate, or strong). Second, give your interpretation if the squared value of r. Suppose that ve additional adults were enrolled in the study (total adult outpatients = 15). The blood HbAlc level and HADS scale were collected. We analyze the data using SAS's CORR procedure and observe the result shown in table 1 (see page 6). Based on those ndings, answer the following questions. 3) Identify the dependent variable and the independent or explanatory variable in this study. Also, state the Null and Alternative hypotheses. 4) Report the correlation coefcient and P-value that should be used to test the Null hypothesis. Based on that information, what conclusion can you make about the Null hypothesis? (i.e. Reject or Fail to Reject the Null). Table 1: Output for Part One Simple Linear Regression The CORR Procedure 2 Variables: HADS HbA1c Simple Statistics Variable N Mean Std Dev Sum Minimum Maximum HADS 15 10.06667 3.93640 151.00000 5.00000 16.00000 HbA1c 15 42.33333 5.97216 635.00000 30.00000 49.00000 Pearson Correlation Coefficients, N = 15 Prob > |r| under HO: Rho=0 HADS HbA1c HADS 1.00000 0.89531 <.0001 hba1c>