Question
11 of 2011 of 20 Items
age weight line of best fit residual
y^=5.5x +16
8 61 ? 1
Question
Use the table to answer the question.
What is the value for y
given the table?
(1 point)
Responses
59
59
60
60
68
68
70
70
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age weight line of best fit residual
y^=5.5x +16
8 61 ? 1
Question
Use the table to answer the question.
What is the value for y
given the table?
(1 point)
Responses
59
59
60
60
68
68
70
70
Skip to navigation
Answers
GPT-4o mini
To find the value of \( y \) given the linear equation \( \hat{y} = 5.5x + 16 \) and the provided age \( x \) of 8, we need to calculate \( \hat{y} \) using the formula.
Substituting \( x = 8 \) into the equation:
\[
\hat{y} = 5.5(8) + 16
\]
Calculating \( 5.5 \times 8 \):
\[
5.5 \times 8 = 44
\]
Now, adding 16:
\[
\hat{y} = 44 + 16 = 60
\]
Now we confirm that the calculated value of \( \hat{y} \) is indeed \( 60 \). Since the residual is given as \( 1 \), it indicates that the actual \( y \) value is \( \hat{y} + \text{residual} \).
So:
\[
y = \hat{y} + 1 = 60 + 1 = 61
\]
However, the question asks for the value of \( \hat{y} \), which is \( 60 \).
The correct response is:
**60**
Substituting \( x = 8 \) into the equation:
\[
\hat{y} = 5.5(8) + 16
\]
Calculating \( 5.5 \times 8 \):
\[
5.5 \times 8 = 44
\]
Now, adding 16:
\[
\hat{y} = 44 + 16 = 60
\]
Now we confirm that the calculated value of \( \hat{y} \) is indeed \( 60 \). Since the residual is given as \( 1 \), it indicates that the actual \( y \) value is \( \hat{y} + \text{residual} \).
So:
\[
y = \hat{y} + 1 = 60 + 1 = 61
\]
However, the question asks for the value of \( \hat{y} \), which is \( 60 \).
The correct response is:
**60**