Answered

(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 [tex]y[/tex] (Wright meter reading) using a reading from the mini-Wright meter. (Round your values to four decimal places.)

[tex]
\hat{y} = 11.4818 + 0.9699x
[/tex]

(b) What would you predict for the Wright meter reading of a subject whose mini-Wright meter reading was 569? (Round your answer to three decimal places.)

[tex]\square[/tex]

(c) What would you predict for the Wright meter reading of a subject whose mini-Wright meter reading was 339? (Round your answer to three decimal places.)

[tex]\square[/tex]



Answer :

GinnyAnswer
Let's solve each part of the problem step-by-step using the provided equation.

### Part (a):
The given linear equation to predict Wright meter readings ([tex]$\hat{y}$[/tex]) using the mini-Wright meter readings (x) is:

[tex]\[ \hat{y} = 11.4818 + 0.9699x \][/tex]

### Part (b):
We need to predict the Wright meter reading for a subject whose mini-Wright meter reading is 569.

Given:
[tex]\[ x = 569 \][/tex]

Substitute [tex]\(x\)[/tex] into the equation:

[tex]\[ \hat{y} = 11.4818 + 0.9699 \cdot 569 \][/tex]

[tex]\[ \hat{y} \approx 563.355 \][/tex]

Therefore, the predicted Wright meter reading for a mini-Wright meter reading of 569 is approximately [tex]\(563.355\)[/tex].

### Part (c):
We need to predict the Wright meter reading for a subject whose mini-Wright meter reading is 339.

Given:
[tex]\[ x = 339 \][/tex]

Substitute [tex]\(x\)[/tex] into the equation:

[tex]\[ \hat{y} = 11.4818 + 0.9699 \cdot 339 \][/tex]

[tex]\[ \hat{y} \approx 340.278 \][/tex]

Therefore, the predicted Wright meter reading for a mini-Wright meter reading of 339 is approximately [tex]\(340.278\)[/tex].

### Summary of Answers:
- Part (b): Predicted Wright meter reading for a mini-Wright meter reading of 569 is [tex]\(563.355\)[/tex].
- Part (c): Predicted Wright meter reading for a mini-Wright meter reading of 339 is [tex]\(340.278\)[/tex].

Other Questions