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Answer :
We are given the least-squares regression line
[tex]$$
\hat{y}=0.1+3.1x,
$$[/tex]
where [tex]$$x$$[/tex] is the tire diameter at the tread and [tex]$$y$$[/tex] is the tire circumference. We need to determine which one of the following statements correctly predicts the circumference:
a.) A tire with a 32-inch diameter at the tread will have a circumference of 86.9 inches.
b.) A tire with a 28-inch diameter at the tread will have a circumference of 99.3 inches.
c.) A tire with a 30-inch diameter at the tread will have a circumference of 93.1 inches.
d.) A tire with a 35-inch diameter at the tread will have a circumference of 124.1 inches.
We can substitute the given diameter into the equation for each option:
1. For a tire with a 32-inch diameter:
[tex]$$
\hat{y} = 0.1 + 3.1 \times 32 = 0.1 + 99.2 = 99.3.
$$[/tex]
The predicted circumference is 99.3 inches, not 86.9 inches as stated in option (a).
2. For a tire with a 28-inch diameter:
[tex]$$
\hat{y} = 0.1 + 3.1 \times 28 = 0.1 + 86.8 = 86.9.
$$[/tex]
The predicted circumference is 86.9 inches, not 99.3 inches as stated in option (b).
3. For a tire with a 30-inch diameter:
[tex]$$
\hat{y} = 0.1 + 3.1 \times 30 = 0.1 + 93.0 = 93.1.
$$[/tex]
The predicted circumference is exactly 93.1 inches, which matches option (c).
4. For a tire with a 35-inch diameter:
[tex]$$
\hat{y} = 0.1 + 3.1 \times 35 = 0.1 + 108.5 = 108.6.
$$[/tex]
The predicted circumference is 108.6 inches, not 124.1 inches as stated in option (d).
Since only option (c) gives a predicted value that matches the statement, we conclude that option (c) is the correct answer.
[tex]$$
\hat{y}=0.1+3.1x,
$$[/tex]
where [tex]$$x$$[/tex] is the tire diameter at the tread and [tex]$$y$$[/tex] is the tire circumference. We need to determine which one of the following statements correctly predicts the circumference:
a.) A tire with a 32-inch diameter at the tread will have a circumference of 86.9 inches.
b.) A tire with a 28-inch diameter at the tread will have a circumference of 99.3 inches.
c.) A tire with a 30-inch diameter at the tread will have a circumference of 93.1 inches.
d.) A tire with a 35-inch diameter at the tread will have a circumference of 124.1 inches.
We can substitute the given diameter into the equation for each option:
1. For a tire with a 32-inch diameter:
[tex]$$
\hat{y} = 0.1 + 3.1 \times 32 = 0.1 + 99.2 = 99.3.
$$[/tex]
The predicted circumference is 99.3 inches, not 86.9 inches as stated in option (a).
2. For a tire with a 28-inch diameter:
[tex]$$
\hat{y} = 0.1 + 3.1 \times 28 = 0.1 + 86.8 = 86.9.
$$[/tex]
The predicted circumference is 86.9 inches, not 99.3 inches as stated in option (b).
3. For a tire with a 30-inch diameter:
[tex]$$
\hat{y} = 0.1 + 3.1 \times 30 = 0.1 + 93.0 = 93.1.
$$[/tex]
The predicted circumference is exactly 93.1 inches, which matches option (c).
4. For a tire with a 35-inch diameter:
[tex]$$
\hat{y} = 0.1 + 3.1 \times 35 = 0.1 + 108.5 = 108.6.
$$[/tex]
The predicted circumference is 108.6 inches, not 124.1 inches as stated in option (d).
Since only option (c) gives a predicted value that matches the statement, we conclude that option (c) is the correct answer.
Thanks for taking the time to read By observing a set of data values Tasha used a calculator for the tire diameter at the tread and circumference data and got an equation. We hope the insights shared have been valuable and enhanced your understanding of the topic. Don�t hesitate to browse our website for more informative and engaging content!
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