Question
For an activity in class, a team of students was given the line of best fit, y=−0.9x+18
. If one of the actual data points is (1,16.88)
, what is the residual of the data point? Round the answer to the nearest hundredths.(1 point)
The residual of the data point (1,16.88)
is
. If one of the actual data points is (1,16.88)
, what is the residual of the data point? Round the answer to the nearest hundredths.(1 point)
The residual of the data point (1,16.88)
is
Answers
GPT-4o mini
The residual is the difference between the actual value and the predicted value (or the value given by the line of best fit).
Given the line of best fit:
\[ y = -0.9x + 18 \]
we can find the predicted value for \( x = 1 \):
\[ y = -0.9(1) + 18 \]
\[ y = -0.9 + 18 \]
\[ y = 17.1 \]
Now, we have the actual point \( (1, 16.88) \). The actual value is \( 16.88 \).
The residual is calculated as follows:
\[ \text{Residual} = \text{Actual value} - \text{Predicted value} \]
\[ \text{Residual} = 16.88 - 17.1 \]
\[ \text{Residual} = -0.22 \]
Thus, the residual of the data point \( (1, 16.88) \) is \( \boxed{-0.22} \).
Given the line of best fit:
\[ y = -0.9x + 18 \]
we can find the predicted value for \( x = 1 \):
\[ y = -0.9(1) + 18 \]
\[ y = -0.9 + 18 \]
\[ y = 17.1 \]
Now, we have the actual point \( (1, 16.88) \). The actual value is \( 16.88 \).
The residual is calculated as follows:
\[ \text{Residual} = \text{Actual value} - \text{Predicted value} \]
\[ \text{Residual} = 16.88 - 17.1 \]
\[ \text{Residual} = -0.22 \]
Thus, the residual of the data point \( (1, 16.88) \) is \( \boxed{-0.22} \).