Question

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.

 

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.

Solutions

Expert Solution

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.

orchestra answered 1 year ago
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