Systolic 125 107 126 110 110 107 113 126 Diastolic 78 54 81 68 66 83 71 72
Plot the data using a scatter plot.
What is the association (positive or negative)?
Find the linear correlation coefficient r.
Test if there is a significant linear correlation between the two blood pressures.
Find the regression equation.
Find the best predicted diastolic blood pressure for a person with a systolic reading of 122.
The correct answer and explanation is :
Scatter Plot Analysis:
The scatter plot above illustrates the relationship between systolic and diastolic blood pressures. From the plot, you can see that there seems to be a moderate positive correlation between the two variables, meaning as the systolic blood pressure increases, the diastolic blood pressure tends to increase as well.
Association:
The association between systolic and diastolic blood pressure is positive. This means that generally, higher systolic pressures are associated with higher diastolic pressures, although the relationship is not perfectly linear.
Linear Correlation Coefficient (r):
The linear correlation coefficient, denoted as r, is approximately 0.474. This value suggests a moderate positive correlation. A correlation of 0.474 indicates that there is some degree of linear relationship between systolic and diastolic blood pressure, but it is not a very strong correlation.
Significance of the Linear Correlation:
To test if there is a significant linear correlation, you would typically perform a hypothesis test using a significance level (e.g., 0.05). With a correlation of 0.474, we can say that there is some linear relationship, but to conclude significance, we would need to compare this value to the critical value for correlation based on the sample size. However, in this case, since the correlation is not very high, further statistical analysis (such as a p-value test) is needed to confirm significance.
Regression Equation:
The regression equation is:
[ \text{Diastolic BP} = 0.5144 \times \text{Systolic BP} + 12.22 ]
This equation allows you to predict diastolic blood pressure based on a given systolic blood pressure.
Predicted Diastolic for Systolic 122:
Using the regression equation, the predicted diastolic blood pressure for a person with a systolic reading of 122 mmHg is approximately 74.97 mmHg.
This means that for a systolic blood pressure of 122, we would expect the diastolic pressure to be around 75 mmHg, according to the linear regression model.