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.
