IM Alg1.3.6 Lesson: Residuals
Mentally calculate how close the estimate is to the actual value using the difference:
actual value - estimated value. Actual value: 24.8 grams. Estimated value: 19.6 grams
Actual value: $112.11. Estimated value: $109.30
Actual value: 41.5 centimeters. Estimated value: 45.90 centimeters
Actual value: -1.34 degrees Celsius. Estimated value: -2.45 degrees Celsius
Use this data from the video about weighing oranges to answer the questions.
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Use technology to make a scatter plot of orange weights and find the line of best fit.
What does the linear model estimate for the weight of the box of oranges for each of the numbers of oranges?
Compare the weights of the box with 3 oranges in it to the estimated weight of the box with 3 oranges in it. Explain or show your reasoning.
How many oranges are in the box when the linear model estimates the weight best? Explain or show your reasoning.
How many oranges are in the box when the linear model estimates the weight least well? Explain or show your reasoning.
The difference 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. For the orange weight data set, what is the residual for the best fit line when there are 3 oranges?
With digital technology, you can graph the residuals all at once. Check out the graph of the residuals. When graphed on the same axes as the scatter plot, what are the coordinates of the point where and has the value of the residual?
Which point on the scatter plot has the residual closest to zero? What does this mean about the weight of the box with that many oranges in it?
How can you use the residuals to decide how well a line fits the data?
Match the scatter plots and given linear models to the graph of the residuals.
Turn the scatter plots over so that only the residuals are visible. Based on the residuals, which line would produce the most accurate estimates? Which line fits its data worst?
Tyler estimates a line of best fit for some linear data about the mass, in grams, of different numbers of apples.
Here is the graph of the residuals.
What does Tyler’s line of best fit look like according to the graph of the residuals?
How well does Tyler’s line of best fit model the data? Explain your reasoning.
Lin estimates a line of best fit for the same data.
The graph shows the residuals.
What does Lin’s line of best fit look like in comparison to the data?
How well does Lin’s line of best fit model the data? Explain your reasoning.
Kiran also estimates a line of best fit for the same data.
The graph shows the residuals.
What does Kiran’s line of best fit look like in comparison to the data?
How well does Kiran’s line of best fit model the data? Explain your reasoning.
Who has the best estimate of the line of best fit—Tyler, Lin, or Kiran? Explain your reasoning.