The Determinants of the Arterial Blood Pressure (ABP): The determinants of the A
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Question
The Determinants of the Arterial Blood Pressure (ABP): The determinants of the Arterial Blood Pressure cannot be evaluated precisely. Nevertheless, the information gathered from arterial blood pressure provides a useful clue to cardiovascular status. Some main determinants are listed below which are thought to contribute to the arterial blood pressure. Blood Volume: This is the volume of blood available in the system. More volume means that the vessels and the heart have to work harder to pump. (~ 80 ml / kg) Overall Compliance: The elastic characteristics of the vessels contribute to the overall pressure. Expansion of arteries and veins will help lower the blood pressure. Cardiac Output (CO): CO is related to two other factors: heart rate and stroke volume. When heart rate is fast, CO is increased and when stroke volume is high, CO is also increase. When CO increases, it is obvious that the arterial pressure will increase. Peripheral Resistance: The resistance of the arteries is related to the Overall Compliance Characteristic. When peripheral resistance increase, the overall compliance is decrease and thus the increase of arterial blood pressure. Arterial resistance can be measured directly through the Diastolic Blood Pressure (DBP); if high, excessive rigidity may exists in the blood vessels because the vessel does not relax. From a statistical perspective, we wanted to obtain good quantitative measurements of these determinants and then develop a linear model for Arterial Blood Pressure (ABP). From our data, we noted that blood volume was essentially a constant throughout all of our patients; and the elastic character of the vessels was a very difficult measure to obtain. Heart rate (beats per minutes - bpm), Stroke Volume (ml) and Diastolic Blood Pressure were the only three reliable variables that one could measure. If one can assume that these variables follow a normal distribution (or close to it), then a simple multiple linear regression model can be determined. This I have done for you, and the data and results are as follows. Patient ABP (mmHg) DBP (mmHg) Heart Rate (bpm) Stroke Vol (ml) A 123 78 80 70 B 135 90 75 68 C 110 75 64 70 D 85 55 76 66 E 155 95 108 46 F 210 100 115 48 G 105 68 72 68 H 115 70 75 70 I 110 60 68 80 J 110 70 70 72 K 145 98 84 65 L 130 90 80 70 M 93 66 48 95 SUMMARY OUTPUT Regression Statistics R Square __________ Standard Error __________ Observations 13 ANOVA Df SS MS F Regression Residual Total Coefficients Standard Error t Stat P-value Intercept -197.24 DBP (mmHg) 1.00 0.32 3.17 0.01 Heart Rate (bpm) 1.91 0.62 3.10 0.01 Stroke Vol (ml) 1.39 0.80 1.73 0.12 ABP DBP H Rate St Vol ABP (mmHg) 1 DBP (mmHg) 0.859 1 H Rate (bpm) 0.764 0.523 1 St Vol (ml) -0.837 -0.635 -0.829 1 From this information: State the Multiple Regression Equation in a form presentable to the Ministry of Health. (2) Arterial Blood Pressure (ABP) = -197.24+1.00*DBP(mmHg)+1.91*Heart Rate(bpm)+1.39*Stroke Vol(ml) Use this model to predict the arterial blood pressure of a patient who is 51 years old; whose DBP is 82 mmHg; whose heart rate is 110 bpm and whose heart stroke volume is 70 ml. (2) All the values are within model value ranges, substitute into multiple regression equation ABP=-197.24+1.00*82mmHG+1.91*110bpm+1.39*70ml =-197.24+82+210.1+97.3 =192.16192 From the above information,I then ran the prediction model and arrived at the following: ABP (mmHg) SS residual SStotal SSregression Patient y y' y-y' (y-y')2 y-y (y-y )2 y'-y (y'-y )2 A 123 131.0 -8.0 64.3 -2.1 4.3 5.9 35.3 B 135 130.8 4.2 18.0 9.9 98.5 5.7 32.2 C 110 97.5 12.5 157.0 -15.1 227.3 -27.6 762.1 D 85 94.7 -9.7 94.6 -40.1 1606.2 -30.4 921.3 E 155 168.2 -13.2 174.3 29.9 895.4 43.1 1859.7 F 210 189.4 20.6 426.0 84.9 7211.9 64.3 4132.5 G 105 102.9 2.1 4.3 -20.1 403.1 -22.1 490.5 H 115 113.4 1.6 2.4 -10.1 101.5 -11.6 135.4 I 110 103.9 6.1 36.9 -15.1 227.3 -21.2 447.4 J 110 106.7 K 145 151.8 L 130 143.1 M 93 92.6 Mean 125.1 125.1 Complete the above table and then complete the ANOVA Table for the Regression Analysis. (5) Is this a good model; in other words, how much of the variability in predicting the arterial blood pressure is accounted for by the model? (1) Determine the Multiple Standard Error of the Estimate and interpret its meaning (1,1) Perform the “Global” test to determine whether the regression model is valid (has some merit) at 95% confidence. State the Null and Alternative Hypotheses. (1) Construct the appropriate probability density function (PDF) and state the Decision Rule. (2) Determine the test value (2) What is your decision? (1) Evaluate the individual regression coefficients at 95% confidence. State the Null and Alternative Hypotheses. (1) Construct the PDF and state the Decision Rule. (2) Determine the test values (1) What is your decision for each coefficient? (1) What is your interpretation for each coefficient? (1) Is there any evidence of multicollinearity amongst the independent variables? If so, what would be the recommended course of action? (1,1) What is your over-all impression/interpretation of this model? (2) The Determinants of the Arterial Blood Pressure (ABP): The determinants of the Arterial Blood Pressure cannot be evaluated precisely. Nevertheless, the information gathered from arterial blood pressure provides a useful clue to cardiovascular status. Some main determinants are listed below which are thought to contribute to the arterial blood pressure. Blood Volume: This is the volume of blood available in the system. More volume means that the vessels and the heart have to work harder to pump. (~ 80 ml / kg) Overall Compliance: The elastic characteristics of the vessels contribute to the overall pressure. Expansion of arteries and veins will help lower the blood pressure. Cardiac Output (CO): CO is related to two other factors: heart rate and stroke volume. When heart rate is fast, CO is increased and when stroke volume is high, CO is also increase. When CO increases, it is obvious that the arterial pressure will increase. Peripheral Resistance: The resistance of the arteries is related to the Overall Compliance Characteristic. When peripheral resistance increase, the overall compliance is decrease and thus the increase of arterial blood pressure. Arterial resistance can be measured directly through the Diastolic Blood Pressure (DBP); if high, excessive rigidity may exists in the blood vessels because the vessel does not relax. From a statistical perspective, we wanted to obtain good quantitative measurements of these determinants and then develop a linear model for Arterial Blood Pressure (ABP). From our data, we noted that blood volume was essentially a constant throughout all of our patients; and the elastic character of the vessels was a very difficult measure to obtain. Heart rate (beats per minutes - bpm), Stroke Volume (ml) and Diastolic Blood Pressure were the only three reliable variables that one could measure. If one can assume that these variables follow a normal distribution (or close to it), then a simple multiple linear regression model can be determined. This I have done for you, and the data and results are as follows. Patient ABP (mmHg) DBP (mmHg) Heart Rate (bpm) Stroke Vol (ml) A 123 78 80 70 B 135 90 75 68 C 110 75 64 70 D 85 55 76 66 E 155 95 108 46 F 210 100 115 48 G 105 68 72 68 H 115 70 75 70 I 110 60 68 80 J 110 70 70 72 K 145 98 84 65 L 130 90 80 70 M 93 66 48 95 SUMMARY OUTPUT Regression Statistics R Square __________ Standard Error __________ Observations 13 ANOVA Df SS MS F Regression Residual Total Coefficients Standard Error t Stat P-value Intercept -197.24 DBP (mmHg) 1.00 0.32 3.17 0.01 Heart Rate (bpm) 1.91 0.62 3.10 0.01 Stroke Vol (ml) 1.39 0.80 1.73 0.12 ABP DBP H Rate St Vol ABP (mmHg) 1 DBP (mmHg) 0.859 1 H Rate (bpm) 0.764 0.523 1 St Vol (ml) -0.837 -0.635 -0.829 1 From this information: State the Multiple Regression Equation in a form presentable to the Ministry of Health. (2) Arterial Blood Pressure (ABP) = -197.24+1.00*DBP(mmHg)+1.91*Heart Rate(bpm)+1.39*Stroke Vol(ml) Use this model to predict the arterial blood pressure of a patient who is 51 years old; whose DBP is 82 mmHg; whose heart rate is 110 bpm and whose heart stroke volume is 70 ml. (2) All the values are within model value ranges, substitute into multiple regression equation ABP=-197.24+1.00*82mmHG+1.91*110bpm+1.39*70ml =-197.24+82+210.1+97.3 =192.16192 From the above information,I then ran the prediction model and arrived at the following: ABP (mmHg) SS residual SStotal SSregression Patient y y' y-y' (y-y')2 y-y (y-y )2 y'-y (y'-y )2 A 123 131.0 -8.0 64.3 -2.1 4.3 5.9 35.3 B 135 130.8 4.2 18.0 9.9 98.5 5.7 32.2 C 110 97.5 12.5 157.0 -15.1 227.3 -27.6 762.1 D 85 94.7 -9.7 94.6 -40.1 1606.2 -30.4 921.3 E 155 168.2 -13.2 174.3 29.9 895.4 43.1 1859.7 F 210 189.4 20.6 426.0 84.9 7211.9 64.3 4132.5 G 105 102.9 2.1 4.3 -20.1 403.1 -22.1 490.5 H 115 113.4 1.6 2.4 -10.1 101.5 -11.6 135.4 I 110 103.9 6.1 36.9 -15.1 227.3 -21.2 447.4 J 110 106.7 K 145 151.8 L 130 143.1 M 93 92.6 Mean 125.1 125.1 Complete the above table and then complete the ANOVA Table for the Regression Analysis. (5) Is this a good model; in other words, how much of the variability in predicting the arterial blood pressure is accounted for by the model? (1) Determine the Multiple Standard Error of the Estimate and interpret its meaning (1,1) Perform the “Global” test to determine whether the regression model is valid (has some merit) at 95% confidence. State the Null and Alternative Hypotheses. (1) Construct the appropriate probability density function (PDF) and state the Decision Rule. (2) Determine the test value (2) What is your decision? (1) Evaluate the individual regression coefficients at 95% confidence. State the Null and Alternative Hypotheses. (1) Construct the PDF and state the Decision Rule. (2) Determine the test values (1) What is your decision for each coefficient? (1) What is your interpretation for each coefficient? (1) Is there any evidence of multicollinearity amongst the independent variables? If so, what would be the recommended course of action? (1,1) What is your over-all impression/interpretation of this model? (2)
Explanation / Answer
Here dependent variable is ABP and independent variables are DBP, heart rate and stroke volume.
This is the problem of multiple regression.
We have given the output of the regression.
5) Is this a good model; in other words, how much of the variability in predicting the arterial blood pressure is accounted for by the model?
This we can explain by R square.
Rsq = 0.9031 = 90.31%
It expresses the ptoportion of variation in y which is explained by variation in independent variables.
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(1) Evaluate the individual regression coefficients at 95% confidence. State the Null and Alternative Hypotheses
Here we have to test the hypothesis that,
H0 : B = 0 Vs 1 : B not= 0
where B is population slope for independent variable.
Assume alpha = 0.05
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(2) Determine the test value.
Hypothesis follows t-distribution.
There are three t tests since three independent variables.
From the output the test statistics and p-values are :
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(1) What is your decision for each coefficient?
Decision rule is :
If P-value for test statistic is less than 0.05 (alpha) then reject H0 at 5% level of significance and corresponding variable is significcant.
Now we can see that DBP and heart rate are significant variables because P-value for two variables are less than 0.05.
And stroke vol is insignificant variable.
t Stat P-value -2.03833 0.071959 3.169317 0.011378 3.098352 0.012756 1.732245 0.117271Related Questions
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