Question

An article of the American Journal of Clinical Pathology, by Metz et al. (A-4) published the comparison of three methods to determine the percentage of dysmorphic erythrocytes in the urine. They obtained the following results when using the A (X) and B (Y) methods in 75 urine samples.

Draw a scatter diagram and obtain the regression equation and graph it on the diagram.

X            Y            X            Y            X            Y            X            Y

0            0            20          16          65          55          89          81

0            1            16          18          66          71          90          80

0            11          17          30          67          70          91          90

2            0            19          30          69          71          90          97

5            0            20          29          74          60          92          89

6            3            18          35          75          59          93          98

7            3            25          32          73          70          93          97

9            5            30          40          75          69          94          98

8            6            32          45          76          70          95          89

9            7            39          49          78          80          95          95

10          15          40          50          78          82          95          97

10          17          48          41          77          90          95          98

13          13          47          43          82          73          97          85

15          8            57          42          85          74          98          95

18          7            50          60          85          80          99          95

19          9            60          65          86          75          100        96

20          9            60          70          88          74          100        100

16          13          59          69          88          83          100        99

19          16          62          70          88          91                       

Answer 1

The regression equation of Y on X is given by

Y= 2.199 + 0.9503 X

Scatterplot ofy vs x 100 80 60 40 20 00 o 20 40 60 80 100

The blue line on the scatter plot represents the regression line .

n = 75; beta(0) = 2.199 beta(1)= 0.9503 ...least square estimates.