In: Statistics and Probability
The results of the blood pressure measurements taken of the same patient by fourteen different second-year medical students are listed in the table below.
Systolic Diastolic
138 82
130 91
135 100
140 100
120 80
125 90
120 80
130 80
130 80
144 98
143 105
140 85
130 70
150 100
a. Use your graphing calculator, construct a scatter-plot of the data. Sketch the scatter-plot.
b. Find the value of the linear correlation coefficient and describe the relationship.
c. Find the linear regression equation and sketch on the scatterplot.
d. Find the best diastolic blood pressure for a person with a systolic reading of 122.
e. Find the coefficient of determination. Interpret this value in context of the example.
Systolic (X) | Diastolic (Y) | X * Y | |||
138 | 82 | 11316 | 19044 | 6724 | |
130 | 91 | 11830 | 16900 | 8281 | |
135 | 100 | 13500 | 18225 | 10000 | |
140 | 100 | 14000 | 19600 | 10000 | |
120 | 80 | 9600 | 14400 | 6400 | |
125 | 90 | 11250 | 15625 | 8100 | |
120 | 80 | 9600 | 14400 | 6400 | |
130 | 80 | 10400 | 16900 | 6400 | |
130 | 80 | 10400 | 16900 | 6400 | |
144 | 98 | 14112 | 20736 | 9604 | |
143 | 105 | 15015 | 20449 | 11025 | |
140 | 85 | 11900 | 19600 | 7225 | |
130 | 70 | 9100 | 16900 | 4900 | |
150 | 100 | 15000 | 22500 | 10000 | |
Total | 1875 | 1241 | 167023 | 252179 | 111459 |
Equation of regression line is
b = 0.7692
a =( 1241 - ( 0.7692 * 1875 ) ) / 14
a = -14.3798
Equation of regression line becomes
Coefficient of determination
There is 43.28% of variation in dependent variable is explained by independent variable.