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5. How many oranges are in the basket when the linear model estimates the weight least well? Explain or show your reasoning. The di erence between the actual value and the value estimated by a linear model is called the residual. If the actual value is greater than the estimated value, the residual is positive. If the actual value is less than the estimated value, the residual is negative.
6. For the orange weight data set, what is the residual for the best t line when there are 3 oranges? On the same axes as the scatter plot, plot this residual at the point where
7. and has the value of the residual.
Find the residuals for each of the other points in the scatter plot and graph them.
8. Which point on the scatter plot has the residual closest to zero? What does this mean about the weight of the basket with that many oranges in it?
9. How can you use the residuals to decide how well a line ts the data?
Student Response
1. 2. 3.
4. 5. 6.
The equation of the best t line is
2.06 kilograms ( )
The actual weight is 1.798 kg and the estimated weight is 2.06 kg. Therefore the actual weight is 0.262 kg less than the estimate.
4 oranges are in the basket when the estimate is best. The di erence between the estimated weight and the actual weight is only 0.026 kg while the other points are farther from the line.
3 oranges are in the basket when the estimate is worst. The di erence between the estimated weight and the actual weight is 0.262 which is the most of any of the values.
The residual is -0.262 ( ).
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Teacher Guide Algebra