Question

The data show systolic and diastolic blood pressure of certain people. Find the regression equation, letting the systolic reading be the independent (x) variable. Find the best predicted diastolic pressure for a person with a systolic reading of 148. Is the predicted value close to 90.3, which was the actual diastolic reading? Use a significance level of 0.05. Systolic Diastolic Click the icon to view the critical values of the Pearson correlation coefficient 139 102 112 83 113 57 150 87 129 72 112 80 128 67 139 74 What is the regression equation? ỹ= []+x (Round to two decimal places as needed.) What is the best predicted diastolic pressure for a person with a systolic reading of 148? The best predicted diastolic pressure for a person with a systolic reading of 148 is (Round to one decimal place as needed.) Is the predicted value close to 90.3, which was the actual diastolic reading? O A. The predicted value is exactly the same as the actual diastolic reading. OB. The predicted value is not close to the actual diastolic reading. O C. The predicted value is close to the actual diastolic reading OD. The predicted value is very close to the actual diastolic reading.

Answer 1

From given data X Values 139 112 113 150 129 112 128 139 Y Values 102 83 57 87 72 80 67 74 M: 77.75 M: 127.75 a) Now we have to find the regression equation(r). Mx = Mean of X (and) My Mean of Y. X-My Y- My (X-MX)2 (X - MX/Y - My) 11.25 24.25 126.5625 272.8125 -15.75 5.25 248.0625 -82.6875 -14.75 -20.75 217.5625 306.0625 22.25 9.25 495.0625 205.8125 1.25 -5.75 1.5625 -7.1875 -15.75 2.25 248.0625 -35.4375 0.25 -10.75 0.0625 -2.6875 11.25 -3.75 126.5625 -42.1875 SS: 1463.5 SP: 614.5

We have Sum of X= 1022 Sum of Y = 622 Mean X= 127.75 Mean Y = 77.75 Sum of squares (55x) = 1463.5 Sum of products (SP) = 614.5 Regression Equation = ý= bx + a b= SPISSx= 614.5/1463.5 = 0.41988 a = My-bMx = 77.75 - (0.42*127.75) = 24.10984 = 0.41988X + 24.10984 • y = 24.11+ 0.42x b) Now we have to find û when x = 148. y = 24.11 + 0.42 + 148 = 86.27 ..y = 86.3

c) ŷ = 86.3, which is not close to the actual diastolic reading. :. The predicted value is not close to the actual diastolic reading.

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