Question

The authors of the paper "Statistical Methods for Assessing Agreement Between Two Methods of Clinical Measurement"†...

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.)

Homework Answers

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 (SSX) = 204720.2353
Sum of products (SP) = 198567.1765

Regression Equation = ŷ = bX + a

b = SP/SSX = 198567.18/204720.24 = 0.970

a = MY - bMX = 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

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