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-Weight Meter Weight Meter
1 512 494
2 430 395
3 520 516
4 428 434
5 500 476
6 600 557
7 364 413
8 380 442
9 658 650
10 445 433
11 432 417
12 626 656
13 260 267
14 477 478
15 259 178
16 350 423
17 451 427
(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 Wright meter reading using a reading from the mini-Wright meter. (Round your values to three decimal places.)

Answer 1

Answer:

Step-by-step explanation:

Given data;

n = 17

$\sum x =7692$

$\sum x^2=3685124$

$\sum y =7656\\\\ \sum xy=3662682$

Slope:

$\hat B_1=\frac{n \sum xy - \sum x \sum y}{n \sum x^2 - ( \sum x)^2} \\\\=0.96994$

≅ 0.970

y - intercept :

$\hat B_0 = \frac{\sum y}{n} - \hat B\frac{\sum x}{n} \\\\=11.48178$

≅ 11.482

a)

Equation :

$\hat y = 11.482+0.970x$

b)

Predicted wright meter reading

$\hat y = 11.48178+0.96994(563)\\\\=557.558$

c)Predicted wright meter reading

$\hat y = 11.48178+0.96994(342)\\\\= 343.201$