Section 7.1, revised Exercise 9: A blood pressure measurement consists of two numbers: the systolic pressure, which is the maximum pressure taken when the heart

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Section 7.1, revised Exercise 9: "A blood pressure measurement consists of two numbers: the systolic pressure, which is the maximum pressure taken when the heart is contracting, and the diastolic pressure, which is the minimum pressure taken at the beginning of the heartbeat. Blood pressures were measured, in millimeters of mercury (mmHg), for a sample of 14 adults. Assume that blood pressures follow a bivariate normal distribution.\" Scatterplot of Diastolic Pressure on Systolic Pressure 90 a E g 53 g 3 Coefficients: g Estimate Std. Error t value Pr(>lt|) % ",3 (Intercept) 9.8440 20.3102 0.485 0.63663 '79 systolic 8.5692 0.1725 3.299 0.m35 " a: s1 .2 "- D Simif. codes: 0 "\"' 8.001 \"" 0.31 \"' 0.05 '.' 0.1 ' ' 1 8 105 110 115 120 125 130 '35 Residual standard error: 5.91 on 12 degrees of freedom Hultiple R-squared: 0.4756. Adjusted R-squored: 0.4319 SystolicPressure(mmHg) F-stotistic: 15.35 on 1 and 12 DF. p-volue: 0.006353 Residuals vs. X Normal Q-G Plot 2 2 U In g In 3 E a 5 o w :2 6 m we "r 105 110 115 120 125 130 135 '1 0 1 Systolic Pressure (mmHg) Theoretical Quantiles a. Use the scatterplot to describe the relationship between diastolic and systolic pressures. b. Use the diagnostic plots to determine whether linear regression is appropriate for these data. Make sure to address all four assumptions of the linear model. For the following parts, assume that the assumptions/conditions hold, regardless of what you found in part (b). c. For what range of values of systolic pressure should we use the linear model to predict diastolic pressure? Why should we not use values outside of this range? d. Predict the diastolic pressure when systolic pressure is 125. e. One observation had a systolic pressure of 115 mmHG and a diastolic pressure of 83 mmHg. Predict the diastolic pressure and calculate the residual for this observation