Question

The authors of the paper "Statistical Methods for Assessing Agreement Between Two Methods of Clinical Measurement"† compared two different instruments for measuring a person's ability to breathe out air. (This measurement is helpful in diagnosing various lung disorders.) The two instruments considered were a Wright peak flow meter and a mini-Wright peak flow meter. Seventeen people participated in the study, and for each person air flow was measured once using the Wright meter and once using the mini-Wright meter.

Subject	Mini- Wright Meter	Wright Meter	Subject	Mini- Wright Meter	Wright Meter
1	512	494	10	445	433
2	430	395	11	432	417
3	520	516	12	626	656
4	428	434	13	260	267
5	500	476	14	477	478
6	600	557	15	259	178
7	364	413	16	350	423
8	380	442	17	451	427
9	658	650

(a)

Suppose that the Wright meter is considered to provide a better measure of air flow, but the mini-Wright meter is easier to transport and to use. If the two types of meters produce different readings but there is a strong relationship between the readings, it would be possible to use a reading from the mini-Wright meter to predict the reading that the larger Wright meter would have given. Use the given data to find an equation to predict y = Wright meter reading using a reading from the mini-Wright meter. (Round your values to three decimal places.)

ŷ =    +( )x

(b)

What would you predict for the Wright meter reading of a person whose mini-Wright meter reading was 535? (Round your answer to three decimal places.)

(c)

What would you predict for the Wright meter reading of a person whose mini-Wright meter reading was 338? (Round your answer to three decimal places.)

Answer 1

a. Firstly we will find the below table

Sum of X = 7692
Sum of Y = 7656
Mean X = 452.4706
Mean Y = 450.3529
Sum of squares (SS_X) = 204720.2353
Sum of products (SP) = 198567.1765

Regression Equation = ŷ = bX + a

b = SP/SS_X = 198567.18/204720.24 = 0.970

a = M_Y - bM_X = 450.35 - (0.97*452.47) = 11.482

ŷ = 0.970X + 11.482

b. Now for x=535, ŷ = 0.970*535 + 11.482=530.432

c. Now for x=338,  ŷ = 0.970*338 + 11.482=339.342