Westonci.ca offers fast, accurate answers to your questions. Join our community and get the insights you need now. Get immediate and reliable answers to your questions from a community of experienced professionals on our platform. Connect with a community of professionals ready to provide precise solutions to your questions quickly and accurately.
Sagot :
To determine the residual for the point [tex]\((3,6)\)[/tex] given the line of best fit equation [tex]\( y = 5x - 2.5 \)[/tex], follow these steps:
1. Identify the given point and equation:
- Point [tex]\((x, y_{\text{actual}}) = (3, 6)\)[/tex]
- Line of best fit equation: [tex]\( y = 5x - 2.5 \)[/tex]
2. Calculate the predicted value [tex]\( y_{\text{predicted}} \)[/tex]:
Substitute [tex]\( x = 3 \)[/tex] into the equation [tex]\( y = 5x - 2.5 \)[/tex]:
[tex]\[ y_{\text{predicted}} = 5(3) - 2.5 \][/tex]
[tex]\[ y_{\text{predicted}} = 15 - 2.5 \][/tex]
[tex]\[ y_{\text{predicted}} = 12.5 \][/tex]
3. Determine the actual value [tex]\( y_{\text{actual}} \)[/tex]:
From the given point, [tex]\( y_{\text{actual}} = 6 \)[/tex].
4. Calculate the residual:
The residual is the difference between the actual [tex]\( y \)[/tex] value and the predicted [tex]\( y \)[/tex] value:
[tex]\[ \text{Residual} = y_{\text{actual}} - y_{\text{predicted}} \][/tex]
Substitute the values:
[tex]\[ \text{Residual} = 6 - 12.5 \][/tex]
[tex]\[ \text{Residual} = -6.5 \][/tex]
Thus, the residual for the point [tex]\((3,6)\)[/tex] is [tex]\(-6.5\)[/tex]. Therefore, the correct answer is:
A. -6.5
1. Identify the given point and equation:
- Point [tex]\((x, y_{\text{actual}}) = (3, 6)\)[/tex]
- Line of best fit equation: [tex]\( y = 5x - 2.5 \)[/tex]
2. Calculate the predicted value [tex]\( y_{\text{predicted}} \)[/tex]:
Substitute [tex]\( x = 3 \)[/tex] into the equation [tex]\( y = 5x - 2.5 \)[/tex]:
[tex]\[ y_{\text{predicted}} = 5(3) - 2.5 \][/tex]
[tex]\[ y_{\text{predicted}} = 15 - 2.5 \][/tex]
[tex]\[ y_{\text{predicted}} = 12.5 \][/tex]
3. Determine the actual value [tex]\( y_{\text{actual}} \)[/tex]:
From the given point, [tex]\( y_{\text{actual}} = 6 \)[/tex].
4. Calculate the residual:
The residual is the difference between the actual [tex]\( y \)[/tex] value and the predicted [tex]\( y \)[/tex] value:
[tex]\[ \text{Residual} = y_{\text{actual}} - y_{\text{predicted}} \][/tex]
Substitute the values:
[tex]\[ \text{Residual} = 6 - 12.5 \][/tex]
[tex]\[ \text{Residual} = -6.5 \][/tex]
Thus, the residual for the point [tex]\((3,6)\)[/tex] is [tex]\(-6.5\)[/tex]. Therefore, the correct answer is:
A. -6.5
We hope our answers were useful. Return anytime for more information and answers to any other questions you have. Thanks for using our service. We're always here to provide accurate and up-to-date answers to all your queries. Thank you for visiting Westonci.ca, your go-to source for reliable answers. Come back soon for more expert insights.